Circle Calculator
Calculate radius, diameter, circumference, and area. Enter any one value.
Enter any one value (radius, diameter, circumference, or area) and the calculator will automatically compute the remaining three properties.
Enter any one measurement of a circle (radius, diameter, circumference, or area) and this calculator instantly computes all the others. It also calculates arc length, sector area, and chord length for any central angle, making it a complete circular geometry tool for students and professionals alike.
Circle Formulas
All measurements of a circle are related through the radius (r) and the constant π (pi ≈ 3.14159). Given any one measurement, you can derive the rest using these relationships.
Diameter: d = 2r Circumference: C = 2πr = πd Area: A = πr² Arc length: L = r × θ (θ in radians) = (θ/360) × 2πr (θ in degrees) Sector area: A = ½r²θ (radians) = (θ/360) × πr² (degrees)
To convert degrees to radians: multiply by π/180. Example: 90° = π/2 radians.
Circle vs Sphere
A circle is 2D (area, circumference). A sphere is the 3D counterpart. Do not confuse 2D circle formulas (A = πr²) with 3D sphere formulas (V = 4/3 πr³, surface area = 4πr²). This calculator handles the 2D circle; use the volume calculator for spheres.
Frequently Asked Questions
What is pi (π) and why does it appear in circle calculations?⌄
Pi is the ratio of any circle's circumference to its diameter, always equal to approximately 3.14159 regardless of the circle's size. It is irrational (never ending, never repeating). Pi appears wherever circles and spheres are involved in mathematics.
What is the difference between circumference and perimeter?⌄
Circumference is the specific term for the perimeter (boundary length) of a circle. Perimeter is the general term used for polygons. Circumference = 2πr, which is the total distance around the circular boundary.
What is a sector of a circle?⌄
A sector is a "pie slice" portion of a circle defined by two radii and the arc between them. The central angle determines what fraction of the full circle the sector represents. A 90° sector is one quarter of the circle, with area = (90/360) × πr² = πr²/4.
What is the area of a circle with circumference 20?⌄
From C = 2πr, solve for r: r = C/(2π) = 20/(2π) = 10/π ≈ 3.183. Then A = πr² = π × (10/π)² = 100/π ≈ 31.83 square units.