Circumference Calculator
A free math practice tool for middle school students
How to use the calculator
1To find the circumference, enter the radius and select Calculate.
2You can change the numerical value used for π.
3Select Use π to calculate with the full value of π.
4To find the radius, leave the radius blank, enter the circumference, and select Calculate.
5The calculator converts values even when you select different units for radius and circumference.
6Select Clear to remove the values before starting another calculation.
Understanding circumference
Circumference is calculated as 2 × π × radius. If the radius is r and the circumference is C, the formula is C = 2πr.
Circumference formula
C = 2 × π × r
What is the circumference of a circle with a 6 cm radius?
Using π = 3.14: 2 × 3.14 × 6 = 37.68 cm
Using π: 2 × π × 6 = 12π cm
Calculating with different units
When the radius and circumference use different units, convert them to a common unit before applying the formula.
What is the circumference in meters when the radius is 30 cm?
Because 30 cm = 0.3 m, 2 × 3.14 × 0.3 = 1.884 m
Using π: 2 × π × 0.3 = 0.6π m
Finding the radius from the circumference
Use r = C/(2π) to find the radius. Divide the circumference by 2 and π.
What is the radius when the circumference is 31.4 cm?
Using π = 3.14: r = 31.4/(2 × 3.14)
r = 5 cm
Circumference examples
Q.
What is the circumference of a circle with a 6 cm radius? (π = 3.14)
A.
2 × 3.14 × 6 = 37.68 cm
Q.
What is the circumference of a circle with a 4 cm radius? (Use π)
A.
2 × π × 4 = 8π cm
Q.
What is the radius of a circle with a circumference of 31.4 cm? (π = 3.14)
A.
31.4 ÷ (2 × 3.14) = 5 cm
Q.
What is the radius of a circle with a circumference of 24π cm?
A.
24π ÷ (2π) = 12 cm
Common uses
- 1Calculating circumference in geometry problems
- 2Working backward from circumference to radius
- 3Practicing calculations that include unit conversion
- 4Checking formulas and answers before a test
- 5Checking circular dimensions for crafts and design
Important notes
- Enter values greater than zero for the radius, circumference, and π
- When a radius is present, the calculator uses it to calculate the circumference
- Leave the radius field blank when calculating a radius from a circumference
- Turn on Use π when you want to calculate with the full value of π
- When units differ, confirm the unit selected for the result
Frequently asked questions
Q1: Can I calculate with either 3.14 or π?
A: Yes. Enter a numerical value such as 3.14, or select Use π to calculate with π.
Q2: Can I find the radius from the circumference?
A: Yes. Leave the radius field blank and enter the circumference to calculate the radius.
Q3: Does the calculator support unit conversion?
A: Yes. It supports millimeters, centimeters, meters, and kilometers.
Q4: What happens if I enter both values?
A: When the radius field contains a value, the calculator recalculates the circumference from that radius.
Q5: Can I use negative values?
A: No. Enter values greater than zero for the radius and circumference.