Convert circumference to diameter or radius, reverse-solve circumference, and view area, arc lengths, inches, and centimeters with accurate unit conversion.
Circumference to Diameter Formula
To find the diameter from the circumference, divide the circumference by pi:
d = C / pi
The same circle’s radius and area follow directly from the diameter:
r = d / 2
A = pi * d^2 / 4
Where:
- d is the diameter, the distance straight across the circle through its center.
- C is the circumference, the distance around the circle.
- r is the radius, half of the diameter.
- A is the area enclosed by the circle.
- pi is the constant ratio of any circle’s circumference to its diameter, about 3.14159.
The diameter formula is the circumference formula C = pi * d rearranged to solve for d. For an ideal circle, dividing circumference by pi gives diameter. Choose diameter or radius from a known circumference, or circumference from a known diameter. The calculator also reports area and quarter- and half-circle arc lengths. For an irregular tree trunk, the result is a circular approximation.
Circle Values for Common Circumferences
The values below are rounded to two decimal places and assume the circumference and diameter share the same unit.
| Circumference (C) | Diameter (d) | Radius (r) | Area (A) |
|---|---|---|---|
| 10 | 3.18 | 1.59 | 7.96 |
| 25 | 7.96 | 3.98 | 49.74 |
| 50 | 15.92 | 7.96 | 198.94 |
| 100 | 31.83 | 15.92 | 795.77 |
To convert any circumference to a diameter quickly without the calculator, multiply by about 0.3183, which is the value of 1 / pi.
Example Problems
Example 1. A circle has a circumference of 31.4 inches. Find its diameter.
Divide the circumference by pi: d = 31.4 / 3.14159 = 9.995 inches, or about 10 inches. The radius is half of that, 5 inches.
Example 2. A tree trunk measures 88 cm around. Find the diameter.
d = 88 / 3.14159 = 28.01 cm. So the trunk is roughly 28 cm across.
Frequently Asked Questions
How do you convert circumference to diameter?
Divide the circumference by pi. Since C = pi * d, rearranging gives d = C / pi. For example, a circumference of 20 units gives a diameter of 20 / 3.14159 = 6.37 units.
Why do you divide by pi instead of multiplying?
The circumference is always pi times larger than the diameter, so the diameter is the smaller value. To reverse a multiplication by pi you divide by pi, which shrinks the circumference back down to the distance across the circle.
Can you get the radius and area from the circumference too?
Yes. Once you have the diameter, the radius is half of it (r = d / 2) and the area is A = pi * d^2 / 4. The calculator returns all of these at once, so entering only the circumference gives you the diameter, radius, and area together.
