# Circle Calculator

Calculate circle area, circumference, diameter, and radius from any known value. Free online circle calculator with instant results and formulas.

## What this calculates

Calculate any circle property from a single known value. Enter the radius, diameter, circumference, or area, and this calculator instantly computes all other measurements.

## Inputs

- **Known Value** — options: Radius, Diameter, Circumference, Area — Select which value you know.
- **Value** — The measurement of the selected property.

## Outputs

- **Radius** — Distance from center to edge.
- **Diameter** — Distance across the circle through the center (2r).
- **Circumference** — The perimeter of the circle (2 x pi x r).
- **Area** — The area enclosed by the circle (pi x r^2).

## Details

The circle is one of the most fundamental shapes in geometry. All points on a circle are equidistant from the center, and this distance is called the radius.

Circle Formulas

- Diameter: d = 2r

- Circumference: C = 2 x pi x r = pi x d

- Area: A = pi x r^2

Where r is the radius and pi is approximately 3.14159265358979.

Working Backwards

From circumference: r = C / (2pi). From area: r = sqrt(A / pi). From diameter: r = d / 2. Once you know the radius, all other properties follow directly.

Circles appear everywhere in engineering (wheels, gears, pipes), architecture (domes, arches), nature (planets, bubbles), and mathematics (trigonometry, polar coordinates, complex numbers).

## Frequently Asked Questions

**Q: How do I calculate the area of a circle?**

A: The area of a circle is A = pi x r^2, where r is the radius. If you know the diameter d, use r = d/2 first. For example, a circle with radius 5 has area = pi x 25 = 78.54 square units. You can also calculate area from the circumference by first finding the radius.

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

A: Circumference is the specific term for the perimeter of a circle. While perimeter refers to the total boundary length of any shape, circumference applies exclusively to circles. The circumference equals pi times the diameter, or 2 x pi x radius.

**Q: What is pi and why is it important?**

A: Pi (approximately 3.14159) is the ratio of a circle's circumference to its diameter. It is the same for every circle, regardless of size. Pi is an irrational number, meaning its decimal digits never end or repeat. It appears throughout mathematics, physics, engineering, and statistics.

**Q: How do I find the radius from the area?**

A: To find the radius from the area, use r = sqrt(A / pi). For example, if the area is 50 square centimeters, then r = sqrt(50 / 3.14159) = sqrt(15.915) = 3.989 cm. This formula is derived by solving A = pi x r^2 for r.

**Q: What is a sector of a circle?**

A: A sector is a pie-shaped region bounded by two radii and an arc. Its area equals (theta / 360) x pi x r^2, where theta is the central angle in degrees. If theta is in radians, the area is (theta / 2) x r^2. A semicircle is a sector with theta = 180 degrees.

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Source: https://vastcalc.com/calculators/math/circle
Category: Math
Last updated: 2026-04-21