3: Measuring Circles

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3: Measuring Circles

How to Measure a Landscape Circle

Circles in your landscape design help direct attention to the center of the shape, creating an instant focal point on any plant or design element placed there. Measuring the area of the circle is essential when you're buying mulch, rocks or grass seed to fill the circle. Calculating the number of square feet inside the circle isn't as easy as measuring around the perimeter of the circle. Instead, use a basic math formula to determine the square footage.

Measure the diameter of the circle, which is the distance across the middle of the circle. This should be the widest part of the shape. If you're unsure where the center line is, measure in three places using your best guess and write down the longest measurement. For landscape purposes, you don't need the precise number, just the closest you can easily find.

Divide the diameter by 2 to determine the radius. For example, if your circle is 20 feet wide, the radius is 10.

Multiply the radius by itself. If your radius is 10, multiply it by 10 to get 100.

Multiply that number by pi, which is 3.14. If your radius squared is 100, multiply that by pi to get 314 square feet.

• If you're planting circles within circles, such as a circle of hedges inside a circle of blooming annuals surrounded by grass, find the area of the large circle first. Define the smaller circles by laying a garden hose inside the larger circle, then measure the diameter of the smaller circles. Find the area of all three circles. Subtract the smallest circle's area from the middle circle's area to determine the planting area in the middle circle for the annuals. Subtract the middle circle's area from the largest circle's area to determine the planting area for the grass. For example, if the large circle has an area of 314, the middle circle has an area of 190 and the smallest circle has an area of 75, subtract 75 from 190 and 190 from 314. When buying mulch or seed, you'll need enough for 124 square feet for the outer layer and 115 square feet for the middle section. Use the full area of the smallest circle, meaning you'll need 75 square feet of hedge.

Based outside Atlanta, Ga., Shala Munroe has been writing and copy editing since 1995. Beginning her career at newspapers such as the "Marietta Daily Journal" and the "Atlanta Business Chronicle," she most recently worked in communications and management for several nonprofit organizations before purchasing a flower shop in 2006. She earned a BA in communications from Jacksonville State University.

Now, take your flexible measuring tape and measure the circumference each circle, then write down the measurements by the circles. Next, measure across the center with a ruler and record each size.

take the diameter(distance across the center ) and multiply by 3.14159265.

OK you don't have to multiply by all the digits of pi, pi is an irrational number, it never ends and never repeats, so people usually just round to 3.14 and call that close enough. so, multiply each diameter by 3.14 and write down the results.

Understanding the Square footage:

To understand how to calculate square footage we must first begin with the definition of area. An area is the size of a two-dimensional surface. The area of a circle is the space contained within its circumference (outer perimeter). To find out the area of a circle, we need to know its diameter which is the length of its widest part. The diameter should be measured in feet (ft) for square footage calculations and if needed, converted to inches (in), yards (yd), centimetres (cm), millimetres (mm) and metres (m).

The formula:
Area of a Circle = π x (Diameter/2)^2
π = 3.142
Answer = (π x (Diameter/2)^2) square area
Abbreviations of unit area: ft 2 , in 2 , yd 2 , cm 2 , mm 2 , m 2

Where do you need it in daily life?

Our Square Footage Calculator helps you calculate the area required for making circular landscaping designs, carpeting, wall decals, centre moulding on a ceiling and floor tiling.

Easily Find The Area Of A Circle (And Related Use Cases)

Technology has advanced and with that, there have been many calculators which help users precisely measure things even from the comfort of their laptop or mobile phone. Our area of circl calculator lets you easily find the area, circumference, radius or specific diameter of any circle.

All you need to do is fully understand the variables of this formula including the:

• r (radius)
• d (diameter)
• C (circumference)
• A (area)
• π = pi = 3.1415926535898
• √ = square root

With any of these variables (A, C, r or d) of a circle, you can precisely measure the other three unknowns. You can use this formula in many real world examples such as when building a house, drilling, filling holes with concrete etc. Essentially, the formula gives you accurate details on how much material you need or how big the surface (you will drill into) needs to be.

However, you should also be aware that the area of a circle calculator demands other things which you need to know before measuring.

Things You Need To Take Care About Measuring An Area Of A Circle.

Circles are complex shapes. Perhaps, their main variable is the radius – which is measured from the center of the circle to any of its sides. Essentially, the diameter is twice the radius – or any line that goes from one side of the circle to the other while crossing its center.

The circumference of a circle, however, is not that commonly understood by many. Essentially, this variable can be defined as the distance around the circle or the entire length of the circuit along the circle.

The π (pi) variable is basically a constant which cannot be expressed as a fraction but applies to all calculations – including the area of a circle calculator – whereas the √ (square foot) is basically the total surface within a circle.

Used since ancient geometrics, all of these variables let you precisely calculate anything related to a circle. However, instead of doing things manually, now you can use our area of a circle calculator and make use of the ready circle formula.

Solve the Common Geometry Problem Today With Our Area Of A Circle Calculator.

Whether you are in class solving a math test or need an accurate calculation about the area of a circle for a project that you are building, the formula for area of a circle is simple – but not that simple when you are left with a pen and paper.

This is why and how our Area Of A Circle Calculator can help you and instantly solve your questions. All you need is another variable to get the other three and solve the problem immediately.

Now, you can finally use and apply the Area Of A Circle calculator everywhere – and quickly get to the information you need – without going in circles!

What measurements do you need?

You need to know the diameter of the circle in either feet (ft), inches (in), yards (yd), centimetres (cm), millimetres (mm) or metres (m).

What can you calculate with this tool?

You can calculate the area of the circle border in square feet, in square inches, square yards, square centimetres, square millimetres and square meters. Yes, our tool is that awesome.

Our calculator gives you the option of calculating the exact cost of materials. All you have to do is enter the price per unit area and voila, you have the total cost of materials in a single click!

To convert among square feet, square inches, square yards, square centimetres, square millimetres and square meters you can utilize the following conversion table.

 Square feet to square yards multiply ft 2 by 0.11111 to get yd 2 Square feet to square meters multiply ft 2 by 0.092903 to get m 2 Square yards to square feet multiply yd 2 by 9 to get ft 2 Square yards to square meters multiply yd 2 by 0.836127 to get m 2 Square meters to square feet multiply m 2 by 10.7639 to get ft 2 Square meters to square yards multiply m 2 by 1.19599 to get yd 2 Square meters to square millimetres multiply the m 2 value by 1000000 to get mm 2 Square meters to square centimetres multiply the m 2 value by 10 000 to get cm 2 Square centimetres to square metres multiply the cm 2 value by 0.0001 to get mm 2 Square centimetres to square millimetres multiply the cm 2 value by 100 to get mm 2 Square millimetres to square centimetres multiply the mm 2 value by 0.000001 to get cm 2 Square millimetres to square metres multiply the mm 2 value by 1000000 to get m 2

Detect and Measure Circular Objects in an Image

This example shows how to automatically detect circles or circular objects in an image and visualize the detected circles.

Step 1: Load Image

Read and display an image of round plastic chips of various colors. Besides having plenty of circles to detect, there are a few interesting things going on in this image from a circle detection point-of-view:

There are chips of different colors, which have different contrasts with respect to the background. On one end, the blue and red ones have strong contrast on this background. On the other end, some of the yellow chips do not contrast well with the background.

Notice how some chips are on top of each other and some others that are close together and almost touching each other. Overlapping object boundaries and object occlusion are usually challenging scenarios for object detection.

Step 2: Determine Radius Range for Searching Circles

Find the appropriate radius range of the circles using the drawline function. Draw a line over the approximate diameter of a chip.

The length of the line ROI is the diameter of the chip. Typical chips have diameters in the range 40 to 50 pixels.

Step 3: Initial Attempt to Find Circles

The imfindcircles function searches for circles with a range of radii. Search for circles with radii in the range of 20 to 25 pixels. Before that, it is a good practice to ask whether the objects are brighter or darker than the background. To answer that question, look at the grayscale version of this image.

The background is quite bright and most of the chips are darker than the background. But, by default, imfindcircles finds circular objects that are brighter than the background. So, set the parameter 'ObjectPolarity' to 'dark' in imfindcircles to search for dark circles.

Note that the outputs centers and radii are empty, which means that no circles were found. This happens frequently because imfindcircles is a circle detector , and similar to most detectors, imfindcircles has an internal detection threshold that determines its sensitivity. In simple terms it means that the detector's confidence in a certain (circle) detection has to be greater than a certain level before it is considered a valid detection. imfindcircles has a parameter 'Sensitivity' which can be used to control this internal threshold, and consequently, the sensitivity of the algorithm. A higher 'Sensitivity' value sets the detection threshold lower and leads to detecting more circles. This is similar to the sensitivity control on the motion detectors used in home security systems.

Step 4: Increase Detection Sensitivity

Coming back to the chip image, it is possible that at the default sensitivity level all the circles are lower than the internal threshold, which is why no circles were detected. By default, 'Sensitivity', which is a number between 0 and 1, is set to 0.85. Increase 'Sensitivity' to 0.9.

This time imfindcircles found some circles - eight to be precise. centers contains the locations of circle centers and radii contains the estimated radii of those circles.

Step 5: Draw the Circles on the Image

The function viscircles can be used to draw circles on the image. Output variables centers and radii from imfindcircles can be passed directly to viscircles .

The circle centers seem correctly positioned and their corresponding radii seem to match well to the actual chips. But still quite a few chips were missed. Try increasing the 'Sensitivity' even more, to 0.92.

So increasing 'Sensitivity' gets us even more circles. Plot these circles on the image again.

Step 6: Use the Second Method (Two-stage) for Finding Circles

This result looks better. imfindcircles has two different methods for finding circles. So far the default method, called the phase coding method, was used for detecting circles. There's another method, popularly called the two-stage method, that is available in imfindcircles . Use the two-stage method and show the results.

The two-stage method is detecting more circles, at the Sensitivity of 0.92. In general, these two method are complementary in that have they have different strengths. The Phase coding method is typically faster and slightly more robust to noise than the two-stage method. But it may also need higher 'Sensitivity' levels to get the same number of detections as the two-stage method. For example, the phase coding method also finds the same chips if the 'Sensitivity' level is raised higher, say to 0.95.

Note that both the methods in imfindcircles find the centers and radii of the partially visible (occluded) chips accurately.

Step 7: Why are Some Circles Still Getting Missed?

Looking at the last result, it is curious that imfindcircles does not find the yellow chips in the image. The yellow chips do not have strong contrast with the background. In fact they seem to have very similar intensities as the background. Is it possible that the yellow chips are not really 'darker' than the background as was assumed? To confirm, show the grayscale version of this image again.

Step 8: Find 'Bright' Circles in the Image

The yellow chips are almost the same intensity, maybe even brighter, as compared to the background. Therefore, to detect the yellow chips, change 'ObjectPolarity' to 'bright'.

Step 9: Draw 'Bright' Circles with Different Color

Draw the bright circles in a different color, by changing the 'Color' parameter in viscircles .

Note that three of the missing yellow chips were found, but one yellow chip is still missing. These yellow chips are hard to find because they don't stand out as well as others on this background.

Step 10: Lower the Value of 'EdgeThreshold'

There is another parameter in imfindcircles which may be useful here, namely 'EdgeThreshold'. To find circles, imfindcircles uses only the edge pixels in the image. These edge pixels are essentially pixels with high gradient value. The 'EdgeThreshold' parameter controls how high the gradient value at a pixel has to be before it is considered an edge pixel and included in computation. A high value (closer to 1) for this parameter will allow only the strong edges (higher gradient values) to be included, whereas a low value (closer to 0) is more permissive and includes even the weaker edges (lower gradient values) in computation. In case of the missing yellow chip, since the contrast is low, some of the boundary pixels (on the circumference of the chip) are expected to have low gradient values. Therefore, lower the 'EdgeThreshold' parameter to ensure that the most of the edge pixels for the yellow chip are included in computation.

Step 11: Draw 'Dark' and 'Bright' Circles Together

Now imfindcircles finds all of the yellow ones, and a green one too. Draw these chips in blue, together with the other chips that were found earlier (with 'ObjectPolarity' set to 'dark'), in red.

All the circles are detected. A final word - it should be noted that changing the parameters to be more aggressive in detection may find more circles, but it also increases the likelihood of detecting false circles. There is a trade-off between the number of true circles that can be found (detection rate) and the number of false circles that are found with them (false alarm rate).

Proposition one Edit

Proposition one states: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle. Any circle with a circumference c and a radius r is equal in area with a right triangle with the two legs being c and r. This proposition is proved by the method of exhaustion. [6]

Proposition two Edit

The area of a circle is to the square on its diameter as 11 to 14.

This proposition could not have been placed by Archimedes, for it relies on the outcome of the third proposition. [6]

Proposition three Edit

This approximates what we now call the mathematical constant π. He found these bounds on the value of π by inscribing and circumscribing a circle with two similar 96-sided regular polygons. [7]

Circle Calculator

Please provide any value below to calculate the remaining values of a circle.

While a circle, symbolically, represents many different things to many different groups of people including concepts such as eternity, timelessness, and totality, a circle by definition is a simple closed shape. It is a set of all points in a plane that are equidistant from a given point, called the center. It can also be defined as a curve traced by a point where the distance from a given point remains constant as the point moves. The distance between any point of a circle and the center of a circle is called its radius, while the diameter of a circle is defined as the largest distance between any two points on a circle. Essentially, the diameter is twice the radius, as the largest distance between two points on a circle has to be a line segment through the center of a circle. The circumference of a circle can be defined as the distance around the circle, or the length of a circuit along the circle. All of these values are related through the mathematical constant &pi, or pi, which is the ratio of a circle's circumference to its diameter, and is approximately 3.14159. &pi is an irrational number meaning that it cannot be expressed exactly as a fraction (though it is often approximated as 22/7) and its decimal representation never ends or has a permanent repeating pattern. It is also a transcendental number, meaning that it is not the root of any non-zero, polynomial that has rational coefficients. Interestingly, the proof by Ferdinand von Lindemann in 1880 that &pi is transcendental finally put an end to the millennia-old quest that began with ancient geometers of "squaring the circle." This involved attempting to construct a square with the same area as a given circle within a finite number of steps, only using a compass and straightedge. While it is now known that this is impossible, and imagining the ardent efforts of flustered ancient geometers attempting the impossible by candlelight might evoke a ludicrous image, it is important to remember that it is thanks to people like these that so many mathematical concepts are well defined today.

One needs to know just the radius or the diameter of a circle in order to calculate its circumference. If the radius is given, applying the formula is straightforward. For example, the circumference of a circle with a radius of 4 inches is simply 2 x 3.14159 x 4 = 25.13 inches.

If the diameter is given instead, first divide it by two, then repeat the above process. For example, if the diameter is 16 feet, then the radius is 16 / 2 = 8 feet. The circumference is therefore 2 x 3.14159 x 8 = 50.26 feet.

Share this knowledge with your friends!

Post by Jia Liu on August 4, 2018

Last reply by: Kevin Zhang
Sun Aug 21, 2016 3:14 PM

Post by Kevin Zhang on August 21, 2016

do you make your own slides?

Post by Nancy Reyes on September 22, 2014

How do I know where to put the segments in addition postulate? Does the order matter?

Post by Henriana Tommy on March 1, 2014

How do you know when to write it as 58 squared and not just 58? Does it matter?

Post by Alexis Rodriguez-Gilbert on October 22, 2013

section segment addition postulate

Post by Alexis Rodriguez-Gilbert on October 22, 2013

im not understanding how you are working the problem out and getting the ultimate answer. are we adding multiplying.

Post by julius mogyorossy on September 15, 2013

I spoke too soon, she corrected that mistake, could not E be to the left of D and F.

Last reply by: Professor Pyo
Thu Jan 2, 2014 3:40 PM

Post by julius mogyorossy on September 15, 2013

QP + PR does not = PR, that is a mistake.

Post by Shahram Ahmadi N. Emran on July 12, 2013

Just a quick heads up, your distance formula in your quick notes is incorrect and you might want to include the correlation between the PyT formula and the distance formula, so that it is clear why you are supposed to add the two components instead of the subtraction that you highlight. It super confused at me at first until I looked it up.

Post by Shahram Ahmadi N. Emran on July 12, 2013

For the question: "Write a mathematical sentence given segments ED and EF." E does not have to be in the middle:

in the case:
E-------D------F
the mathematical sentence would be EF - ED = DF

E----F-------------D
the mathematical sentence would be ED - EF = DF

Also, in the question, ED and EF should have a bar over them because you are talking about segments and not measures

Last reply by: Professor Pyo
Fri Aug 2, 2013 2:40 AM

Post by julius mogyorossy on June 3, 2013

Ms. Pyo, I am probably making a fool out of myself again, ask Dr. Carleen, but what would the absolute value of 2 + -5, be, it seems to me it would be 3, but it seems that mathematicians think it should be 7. I was very interested to learn that quadratic equations lie when they are factored, they lie and tell the truth at the same time. Luckily I don't have to factor or use a test point to see where the solution set is, I can see it when I see the equation(s). I found Algebra 2 very interesting, I can't wait to see what Calculus is all about, I have no clue what Trigonometry is about. I have been blessed with incredible instincts, super human, life over death, they are the reason I am still alive. I think I am going to make an incredible discovery having to do with Geometry, I have always sensed incredible potential in Geometry, I have read that incredible things have been allegedly proven having to do with Geometry, I wonder if it is true. Some day I shall do these experiments myself. The knowledge Dr. Carleen gave to me forced scientists to surrender to me, unofficially, some day, officially. I never thought I would see that day, I thought they would do me like Pasteur. Some day you shall know what I am referring to.

Last reply by: Professor Pyo
Fri Aug 2, 2013 2:33 AM

Post by Manfred Berger on May 27, 2013

So what the Segment Addition Postulate is saying is basically that colinearity is transitve, isn't it?

Last reply by: Manfred Berger
Mon May 27, 2013 11:47 AM

Post by bo young lee on February 19, 2013

at the educator.com where can i find more about the
pythagorean theorem.

Post by Kenneth Montfort on February 18, 2013

Just a quick heads up, your distance formula in your quick notes is incorrect and you might want to include the correlation between the PyT formula and the distance formula, so that it is clear why you are supposed to add the two components instead of the subtraction that you highlight. It super confused at me at first until I looked it up.

Post by Edward Hook on February 18, 2013

Everybody loves your teaching style Mary and I have to say that I do too!

Last reply by: Habibo Ali
Wed Feb 5, 2014 10:19 AM

Post by Mohammed Abdullah on December 13, 2012

In the video it shows d=square root x1-x2)squared+(x1+x2) squared, in the quick notes they subtract the square roots.

Last reply by: Professor Pyo
Sat Mar 2, 2013 1:53 AM

Post by chun yung on November 27, 2012

I have a question on the distance formula, why do they have to make it (x2-x1)+(y2-y1) if u put (x1-x2)+(y1-y2)u could get the same answer.

Post by Catherine Henderson on July 31, 2012

Post by Joseph Reich on June 20, 2012

For the question: "Write a mathematical sentence given segments ED and EF." E does not have to be in the middle:

in the case:
E-------D------F
the mathematical sentence would be EF - ED = DF

E----F-------------D
the mathematical sentence would be ED - EF = DF

Also, in the question, ED and EF should have a bar over them because you are talking about segments and not measures

Post by Giri Iyer on November 10, 2011

Very well done and explained.. I am teaching my son geometry and these lessons are so clear conceptually that even I can recall these concepts now :)

Six Circle-Cutting Techniques

A round up of some obvious (and not so obvious) techniques for cutting a circle in a woodworking shop.

As a woodworker and mechanical sculpture maker, I often make circles and discs. Whether they are for a shop clock, lazy Susan finishing turntable, cams, round tabletops or used as toy wheels, my goal is the same: I want them made true, and precisely the size I want them to be — in a safe and efficient manner.

I don't know how many ways there are to skin a cat (my apologies to all cat lovers), but I do know, and use, more than half a dozen different ways to cut circles. In this article, I have selected six methods from my bag of tricks. I'll show you both how they work and how to get the best results from each technique. I'll also share tricks for cutting circles without leaving any pivot holes on the finished piece. So if you've ever been challenged by circle cutting, here are some tool options to try.

When creating circles with a hole saw, make sure to drill with light pressure and retract it often to clear trapped sawdust.

What has to be the world's simplest way to make small circles (from 3/4" up to 7" diameter) is to use a hole saw and a backer board (to prevent blowout). Apart from the backer board, I have two other drilling tips to share.

First, did you know that you can double the cutting depth of a hole saw? Here's how: Start drilling with the hole saw on one side of the workpiece and, once the pilot bit has poked through, flip the wood over and continue cutting using the same pilot hole. Second, the key to cutting a burn-free disc is to start with a sharp hole saw and don't force the saw into the wood. Let the teeth cut slowly. Retract the hole saw often to reduce friction and help clear the sawdust.

Belt/Disc Sander

The jig for a disc sander has an adjustable runner on top.

With the aid of a jig, your disc sander can be turned into a circle-making tool. The sanding circle jig I have is relatively simple. Start with a piece of 1/2" or 3/4" plywood that's a little bigger than the table of the disc sander. Position and glue a cleat to the bottom face of the plywood base such that when the cleat is in the miter slot, it positions the base about 1/16" from the sanding disc. Cut a dado on the top surface perpendicular to the underside cleat, and fit a runner into the dado. To complete the jig, insert a finish nail near one end of the runner. You can see my completed jig in the photo.

To cut a circle, clamp the jig to the table of the disc sander with the cleat in the miter slot. Drill a small hole in the center of the bottom face of the workpiece and fit the workpiece over the finish nail. Push the runner forward until the workpiece contacts the spinning sanding disk, then clamp the runner in place. Sand the workpiece by slowly rotating it clockwise until a circle is formed. Reset the runner forward and sand the edges of the circle in the same manner until you reach the desired circle diameter.

Use the jig to cut circles on your sander by rotating the workpiece clockwise. The clamped runner and a finish nail establish the circle's radius.

To avoid excessive burns on the edges, rotate the workpiece steadily and use a clean sanding disc. I clean mine periodically with a crepe block. I have also found that positioning the workpiece and jig closer to the center of the sanding disc, where it spins more slowly, helps reduce endgrain burning.

On the band saw jig, draw a line perpendicular to the blade. Mark circle radii on this line.

Cutting out circles on a band saw with a jig works on the same principle as the disc sander method. The workpiece turns on a pivot pin, and rotating it into the saw blade cuts a circle. If you need a quick, simple circle jig, start with a 3/4" plywood base roughly the size of the band saw table with a miter slot cleat glued to the bottom. Place the cleat in the miter slot and push the jig into the spinning blade until the base's back edge is flush with the table edge. Then attach a block underneath to stop the jig here. Draw a line across the jig that's perpendicular to the blade and even with the tips of the teeth — here's where you'll insert a finish nail pivot.

To use the jig, drill a small hole on the bottom of the workpiece at its center and place it over the finish nail installed in the jig. Push the jig forward on the saw table until it stops, and clamp it in place. Now rotate the workpiece clockwise into cross grain first (so the blade doesn't pull into long grain) to cut out a circle. Use a side table if needed to help support large workpieces.

To use the band saw jig, orient your cut so that it starts across the grain of your workpiece, then rotate the piece clockwise.

Having cut many circles on my band saw, I have some proven pointers to share. First, use a sharp and properly tensioned blade. I'll suggest a 1/8"- or 1/4"-wide blade to help you steer through smaller circles with tighter curves. Second, position the blade guides and thrust bearings close to the blade, to keep the blade from twisting during cutting. Then, make sure the cutting edge of the teeth aligns perfectly with the centerline of the pivot point on the jig, or the circle will not be true. Finally, orient the workpiece so knots in softwood are clear of the blade's cutting path.

Router and Trammel

The jig's large hole fits a 1/2" guide bushing.

I'm sure you already know how to draw a circle with a string and a pencil. The principle behind the use of a router and a trammel to make circles is the same. Just look at the trammel as the string and the router bit as the pencil. You can buy an aftermarket trammel, but if you have 11 minutes to spare — and who doesn't — why not make your own for free? Cut a 4" x 24" arm from 1/4" plywood scrap (5 minutes), drill a 1/2" center hole 4" from one end for the guide bushing (5 minutes), and draw a center line from the hole to the other end (1 minute). You're done!

Measure the desired radius from the edge of the bit.

Next, install a 1/2" O.D. guide bushing and a straight bit or up-cut spiral bit in a router and place the router in the jig. Measure the desired radius from the cutting edge of the bit and insert a finish nail through the jig's arm.

When using a router and trammel method to cut circles, feed the router counterclockwise in a series of progressively deeper passes.

To use the trammel, insert a finish nail through the arm to mark the circle radius you need, and drill a small hole into the center of the workpiece. Install the trammel pivot in the workpiece. I also usually place a sacrificial board underneath the workpiece. Rout down into the workpiece in a counterclockwise direction. If the workpiece is thicker than 1/4", make multiple passes to cut out the circle.

Use machine screws to attach a plywood arm to the base of your jigsaw for a circle-cutting method especially appropriate for shop projects.

In place of a router, you can also accomplish the trammel technique with a jigsaw mounted to a long plywood or MDF arm. I favor this setup for shop projects when the quality of the circle's edge is not that critical.

Cut away the overhang of your shop-made jig after placing it in your table saw's miter slot.

Believe it or not, a table saw can produce very smooth and clean circles safely, and it handles thick stock very well, too. In this technique, you use a sliding jig and, rather than creating a circle in one step, you progressively change the shape of a workpiece into a circle.

To use the table saw jig, rotate and expose one workpiece corner at a time.

The sliding jig is just a panel-cutting jig, but without the fence. Cut a piece of 1/2" or 3/4" plywood or MDF to about 20" by 20" and attach a hardwood runner to the bottom face that fits into your table saw's miter slot. Place the jig in the right-side miter slot and cut away the overhang. Now draw a line across the jig, perpendicular to the blade, for setting radii with a pivot pin.

Trim the corners of the square to form an octagon.

To use the jig, start with a roughly square workpiece and drill a small hole at its center, underneath. Next, measure and mark the desired radius from the blade on the line and insert a finish nail at the mark. Place and rotate the workpiece on the jig so one corner overhangs the jig's edge. Hold down the workpiece with your hand or a toggle clamp and slide the jig forward to trim the corner. Then slide the jig back, rotate the workpiece to expose a new corner, and cut the second corner.

Continue cutting corners until your workpiece is roughly round, then slide the jig forward, beyond the blade’s front teeth, and rotate your piece clockwise to form a perfect circle.

Keep sawing off more corners of the piece to form an octagon, then a 16-sided piece, and so on until it is roughly round. In the final step, set the sliding jig with the perpendicular line beyond the front teeth of the blade. Now rotate the piece clockwise to true the piece into a perfect circle. How slick is that?!

Router Table

Build this sliding jig (mine is made of MDF and shown upside-down) to suit the size of your router table. You can use it for small or large circles.

The last method, one that I have developed and published as a shop tip, can handle small and large circles alike on the router table. It involves using a sliding jig on the router table and a 1/2"-dia. spiral or straight bit. My method offers two unique features compared to the trammel method: 1) You can make the cut in increments without the need to adjust the bit height and 2) You can cut circles of different diameters without moving the pivot pin mounted in the jig.

To make the sliding jig, cut a 1/4" or 1/2" plywood or MDF board several inches longer than your router table's top and about half as wide. Attach a pair of side cleats and a stop cleat underneath the board. Position the stop cleat such that the bit's cutting edge just touches the jig's front edge. Insert a pivot finish nail into the jig's top face 1" from the front edge.

Measure and set the jig to the desired radius, then install a clamp on the router table as a stop block.

To make the circle, place the jig on the router table so the center of the finish nail and the router bit's closest edge to it are separated by the desired radius. Install a clamp on the router table as a stop block for the jig. Drill a small center hole in the bottom face of the workpiece and place it on the finish nail. Then, hold down the workpiece and gradually slide the jig forward until it hits the stop block. Just rotate the workpiece counterclockwise against the bit to rout the circle in one pass.

Hold the workpiece down on its pivot, and rotate it counterclockwise against the bit to form a circle.

If you need to make a different circle, whether larger or smaller, simply reposition the stop block to change the desired radius between the pivot nail and the bit. Then rout as previously described.

No Centerpoint Circles

Want circles without center holes when using a hole saw? Just retract the pilot bit and use a drill press with the workpiece clamped securely. The bit won't touch the wood, but it will still cut a perfect circle, as shown above.

Sometimes, your projects may require circles without centerpoint holes in them. If you use a hole saw, you can eliminate that middle hole by retracting the pilot bit in the arbor so the bit doesn't contact the wood when drilling. However, this will require that you use a drill press for cutting the circle instead of attempting it freehand with a handheld drill — there won't be any guide for the hole saw with the pilot bit retracted. Be sure to clamp the workpiece down securely to your drill press table and against a sturdy fence. Otherwise, the spinning saw will probably grab and spin the workpiece out of your hand and then throw it from the table or even straight into you — definitely not good!

For the other techniques I've shared here, you can avoid centerpoint holes in the final circle by double-face taping a scrap board to the workpiece and drilling the pivot hole into the scrap board only. Remove the scrap board after the circle is made and voila! No centerpoint.

Need a Circle? Pick the Best Cutting Option for Your Project.

So, there you are: a full arsenal of proven circle-cutting techniques and tips at your disposal! As a general guideline, I have also compiled a summary table to help you select the circle-cutting methods that might best suit your projects. Build the jigs, practice the cuts, and soon you'll find yourself making a lot of circles (and you can always find good uses for them).