Circle Calculator

Circle at a glance#

A circle calculator finds the area, circumference and diameter of a circle from its radius r, the distance from the center to the edge. The area is pi times the radius squared (A = pi r squared), the circumference is two times pi times the radius (C = 2 pi r), and the diameter is twice the radius (d = 2r). These formulas use pi, about 3.14159.

Worked example: for a radius of 5, the area is 3.14159 times 25, which is about 78.54 square units. The circumference is 2 times 3.14159 times 5, which is about 31.42 units, and the diameter is 2 times 5, which is 10.

The circumference and area values in the table are rounded to two decimal places using pi as 3.14159. If you know the circumference or area instead of the radius, you can work backwards: the radius is the circumference divided by 2 pi, or the square root of the area divided by pi.

Enter your radius, diameter, circumference or area in the calculator above for the exact values. Results are rounded, so the final decimal place can shift slightly depending on how many digits of pi you use.

How to use the circle calculator#

Pick which value you know (radius, diameter, circumference or area), type it into the calculator above, and it returns the other three. Units like inches or meters do not change the math; they only label the result, so use one consistent unit. Pi defaults to about 3.14159, which is accurate enough for almost any practical job.

Working backwards from circumference or area#

The radius is the starting point for every circle formula, so if you know a different value, find the radius first. From the circumference, radius = C / (2 pi). From the area, radius = square root of (A / pi). From the diameter, radius = d / 2.

Two shortcuts skip the radius step. If you know the circumference and want the area directly, area = C² / (4 pi). If you know the area and want the diameter, diameter = 2 times the square root of (A / pi).

Example: solving from a known circumference#

Say a circle has a circumference of 44. The radius is 44 / (2 pi), which is about 7.0. The diameter is twice that, about 14.0. The area is 44² / (4 pi), which is 1936 / 12.566, or about 154.1 square units.

Circle terms#

• Radius: the distance from the center to any point on the edge.
• Diameter: the distance straight across through the center, equal to two radii.
• Circumference: the distance around the circle.
• Area: the space enclosed inside the circle.

Frequently asked questions#

How do I find the area of a circle from the radius?#

Use A = pi r². Square the radius, then multiply by pi. For a radius of 5, that is pi times 25, or about 78.54 square units.

What is the formula for the circumference of a circle?#

Circumference is C = 2 pi r, or C = pi d if you have the diameter. For a radius of 5, the circumference is 2 times pi times 5, about 31.42.

Can I find the diameter from the area?#

Yes. Diameter = 2 times the square root of (A / pi). Divide the area by pi, take the square root to get the radius, then double it.

How do I find the area if I only know the circumference?#

Use A = C² / (4 pi). Square the circumference, then divide by 4 pi. This avoids finding the radius first.

How do I get the radius from the diameter?#

Divide the diameter by 2. The radius is always half the diameter, so r = d / 2.

Do the units change the result?#

No. Inches, centimeters, feet and meters all use the same formulas. The unit only labels the answer, so keep every input in the same unit.