# Circumference Calculator

Calculate the circumference of a circle from its radius, diameter, or reverse-solve from circumference. Also shows area. Uses C = 2πr and A = πr².

## What this calculates

Find the circumference of any circle instantly. Enter the radius, diameter, or an existing circumference measurement to get all the key properties. For example, a circle with radius 5 has a circumference of about 31.416 and an area of about 78.54.

## Inputs

- **I know the...** — options: Radius, Diameter, Circumference — Select which measurement you already know.
- **Value** — The measurement you selected above.

## Outputs

- **Circumference** — The distance around the circle (C = 2πr).
- **Radius** — Distance from center to edge.
- **Diameter** — Distance across the circle through center (2r).
- **Area** — Area enclosed by the circle (πr²).

## Details

**Circumference Formulas**

The circumference (perimeter) of a circle can be calculated two ways:

- **From radius:** C = 2πr
- **From diameter:** C = πd

Since the diameter is just twice the radius (d = 2r), these formulas are equivalent.

**Finding Radius from Circumference**

If you know the circumference and need the radius, rearrange the formula: r = C / (2π). A circle with circumference 31.416 has a radius of about 5.

**Area of a Circle**

This calculator also computes the area using A = πr². Knowing both circumference and area is useful for anything from sizing circular gardens to calculating pipe flow capacity.

**Real-world example:**

A running track's inner lane has a radius of 36.5 meters. Its circumference is 2 x π x 36.5 = 229.34 meters, which matches the standard 200m straight + two curves layout.

## Frequently Asked Questions

**Q: What is the formula for circumference?**

A: The circumference of a circle is C = 2πr, where r is the radius. Equivalently, C = πd, where d is the diameter. Pi (π) is approximately 3.14159.

**Q: How do you find the radius from the circumference?**

A: Divide the circumference by 2π. The formula is r = C / (2π). For example, if the circumference is 50, the radius is 50 / (2 x 3.14159) = 7.958.

**Q: What is the difference between circumference and area?**

A: Circumference is the distance around the circle (a length, measured in units like cm or ft). Area is the space enclosed inside the circle (measured in square units like cm² or ft²). A circle with radius 10 has circumference 62.83 and area 314.16.

**Q: Why is pi used in circumference calculations?**

A: Pi (π) is the ratio of a circle's circumference to its diameter. Every circle, regardless of size, has the same C/d ratio of approximately 3.14159. This constant relationship is what makes the formula C = πd universal.

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Source: https://vastcalc.com/calculators/math/circumference
Category: Math
Last updated: 2026-04-08