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Circumference Calculator
Use this circumference calculator to find the distance around any circle in seconds. Enter the radius, the diameter, or the area — whichever one you know — and the calculator works out the circumference, along with all four circle measurements, so you can check your work at a glance.
Enter a positive number. Use the same unit for everything — inches, feet, centimeters, or any other length unit. Area is in square units.
How it works
A circle is defined by its center and its radius. Every other measurement of the circle follows from that one length, because the number pi (about 3.14159) links the straight-line measurements across a circle to the curved distance around it. That is why you only need to know one of the radius, diameter, or area to find the rest.
Radius is the distance from the center of the circle to any point on its edge. It is the most common starting point in geometry problems, and it is half the diameter. If you know the radius, multiply it by 2 and then by pi to get the circumference.
Diameter is the distance straight across the circle, passing through the center. It is exactly twice the radius, so a circle with a radius of 5 inches has a diameter of 10 inches. If you know the diameter, multiply it by pi — one step, and you have the circumference.
Area is the amount of flat space inside the circle, measured in square units. It is the least direct starting point, because you have to undo a square to get back to a length. First divide the area by pi, take the square root to find the radius, and then use the radius formula. The calculator does all of that in one step with the formula above.
The calculator always shows all four values — radius, diameter, area, and circumference — no matter which one you entered. That makes it easy to spot a mistake: if the diameter is not exactly twice the radius, or the area does not match, something was typed wrong. Pi is never exactly 3.14; the calculator uses the full precision of pi built into your browser, and results are rounded to four decimal places for display.
Worked example
A round pizza pan has a radius of 5 inches, and you want to know how long a strip of trim you need to go around its edge. That length is the circumference.
Step 1: Write down what you know. The radius r is 5 inches.
Step 2: Use the radius formula, C = 2 × π × r. That is 2 × 3.14159 × 5.
Step 3: Multiply 2 × 5 to get 10, then multiply 10 × 3.14159 to get 31.4159 inches.
Step 4: Check the other measurements. The diameter is 2 × 5 = 10 inches. The area is π × 5² = 3.14159 × 25 = 78.5398 square inches.
Try it yourself: choose "Radius", enter 5, and press Calculate. The tool gives exactly the same answer — circumference 31.4159, with a diameter of 10 and an area of 78.5398. You would need a trim strip just over 31.42 inches long, so buy a little extra for the join.
FAQ
How do you find the circumference of a circle from its radius?
Multiply the radius by 2 and then by pi (about 3.14159). The formula is C = 2 x pi x r. For example, a circle with a radius of 5 inches has a circumference of 2 x 3.14159 x 5 = 31.42 inches.
How do you find the circumference from the diameter?
Multiply the diameter by pi. The formula is C = pi x d. A circle with a diameter of 10 inches has a circumference of 3.14159 x 10 = 31.42 inches, the same circle as one with a radius of 5 inches.
Can you find the circumference if you only know the area?
Yes. First work out the radius from the area with r = the square root of (area divided by pi), then use C = 2 x pi x r. In one step, C = 2 x the square root of (pi x area). For an area of 78.54 square inches, the circumference is 31.42 inches.
What is the difference between circumference, diameter, and radius?
The radius is the distance from the center of a circle to its edge. The diameter is the distance straight across the circle through the center, exactly twice the radius. The circumference is the distance all the way around the edge of the circle, about 3.14159 times the diameter.
What units should I use for circumference?
Use the same unit for every measurement. If the radius is in inches, the circumference comes out in inches; if the radius is in feet, the circumference is in feet. Area is in square units, so an area of 78.54 square inches belongs with a radius in inches, not feet.