Math

Radius Calculator

How to Find the Radius of a Circle

Find the radius of any circle by entering a known measurement. If you know the area, circumference, or diameter, this calculator derives the radius using the appropriate reverse formula.

Circle Calculation Tips

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Try an Example

Pick a scenario to see how the calculator works, then adjust the values

Unit Circle

The fundamental circle with radius 1, used throughout mathematics.

Key values: Radius = 1 · Area = 3.14 · Circumference = 6.28

Pizza (12-inch)

A standard 12-inch diameter pizza for area and slice calculations.

Key values: Diameter = 12 in · Area = 113.1 sq in · 45-degree slice

Circular Garden

A garden bed with a 5-meter radius for landscaping calculations.

Key values: Radius = 5 m · Area = 78.54 sq m · Circumference = 31.42 m

Documentation

This calculator is also known as Radius Calculator.

Read the complete guide

Reverse Formulas

Formulas to find radius from other measurements:

Category	Value
From diameter	r = d / 2
From area	r = sqrt(A / pi)
From circumference	r = C / (2 pi)

Examples

Running Track Radius

A running track has curved sections with a total circumference of 231.22 m. What is the radius?

r = 231.22 / (2 pi) = 36.80 m.

Key takeaway: The IAAF standard inner radius is 36.50 m. The small difference is because the measurement line is 30 cm from the inner edge.

Finding Radius in Practice

Common situations where you need to find the radius:

Measuring around a circular object (circumference) and needing the radius for area calculations
Working backwards from a known area to find the dimensions
Converting between diameter (what you measure with calipers) and radius (what formulas use)

Frequently Asked Questions about Radius Calculator

How do I find the radius from the area?

Use r = sqrt(A / pi). For example, if the area is 100, then r = sqrt(100 / pi) = sqrt(31.83) = 5.64.

How do I find the radius from the circumference?

Use r = C / (2 pi). For example, if the circumference is 44, then r = 44 / (2 pi) = 7.00.

What is the difference between radius and diameter?

The radius is the distance from the center to the edge; the diameter is the distance across the circle through the center. The diameter is always twice the radius: d = 2r.