Circumference to Radius Calculator

Work backwards from a circle's circumference to its radius, diameter and area.

How the Math Works

The Circumference to Radius Calculator uses the fundamental relationship between a circle's perimeter and its radius. Since the circumference (C) of a circle is given by C = 2πr, we can rearrange this formula to solve for radius: r = C ÷ (2π). This means we simply divide the known circumference by 2π (approximately 6.2832) to find the radius. The calculator performs this division instantly, eliminating manual calculation errors and saving time when working with circular measurements.

Practical Applications

To use this calculator practically, enter the measured circumference of any circular object into the input field. The calculator will immediately display both the radius and diameter, which are essential for construction projects, engineering designs, and manufacturing processes. For example, if you measure a circular pipe's outer edge as 31.416 inches, the calculator determines the radius is 5 inches, helping you select appropriate fittings or calculate cross-sectional areas for flow rate analysis.

Day-to-Day Use

This calculation proves useful in everyday scenarios like determining the right size cushion covers for round tables, selecting appropriately sized pots for plants, or calculating material needs for circular garden beds. When replacing a roundabout's protective barrier or ordering custom circular signs, knowing the radius from a measured circumference ensures precise ordering without waste. Even DIY projects benefit — whether you're creating a circular tapestry or planning a round dining table, this tool helps translate measurements between circumference and radius effortlessly.

Worked example

Circumference 31.42 → radius 5, diameter 10.

FAQ