Circle Calculator

Mathematics

Calculate circle radius, diameter, circumference, area, arc length, and sector area from any single known dimension. Interactive geometry solver with high-precision π evaluations.

°
Calculated Result
31.415927

Circumference · area 78.539816

Radius
5
Diameter
10
Sector area
19.634954
Arc length
7.853982
Formula: C = 2πr · A = πr²

About this calculator

Circles are ubiquitous in structural engineering, pipe design, automotive wheels, and architectural layouts. Knowing any one property—whether it is the radius, diameter, circumference, or total area—allows you to derive all other geometric metrics.

This tool lets you input any single circle metric alongside an optional central arc angle to compute complete perimeter, boundary area, arc sector area, and segment chord properties.

How It Works & Formula

FormulaC = 2πr · A = πr² · sector = (θ/360)πr²

The formulas relate diameter d = 2r, circumference C = 2πr, area A = πr², and circular sector area A_sector = (θ / 360°) × πr². Reversing these equations allows solving for radius r from area or circumference.