Circle Radius from Circumference Calculator

Formula

r = C/(2π)

Worked example

With Circumference: 31.42 units, radius is 5.000648 units.

Calculation method

The rule is r = C/(2π).

For this circle radius from circumference example, changing circumference from 31.42 units to 32.42 units while keeping the other inputs fixed changes radius from 5.000648 units to 5.159803 units.

Reading radius

Circumference has linear units, whereas area has square units. Doubling a radius doubles circumference but quadruples area. In the worked values on this page, circumference 31.42 units produce radius 5.000648 units.

Practical use

Use circle measurements for wheels, round plots, containers, and construction layouts. The specific task here is to find radius from circumference.

Limits and common mistakes

Do not enter diameter where a formula expects radius. Check whether the result should describe a boundary or an enclosed surface. Verify circumference in units before interpreting radius; a value measured on another basis would answer a different question.

Why the relationship works

A circle is determined by its radius, the center-to-edge distance. Diameter is twice that length; circumference follows the boundary; area covers the interior. Radius enters area squared but circumference only once. If the input is a measured diameter, divide it by two before using a radius-based rule. The circle radius from circumference rule uses circumference (units) in r = C/(2π); read each symbol as the field named on this page.

Interpreting another set of values

For circle radius from circumference, the fields labeled circumference (units) are the known quantities. The calculator solves for radius in units using r = C/(2π). A radius, diameter, and circumference are lengths; area covers the inside. Check that the output unit changes appropriately if a length is squared, and distinguish the radius entered from the full width. When comparing two calculations, keep their units and input definitions identical.

For a second circle radius from circumference check, keep the other default inputs fixed and change circumference from 31.42 units to 33.42 units. Radius changes from 5.000648 units to 5.318958 units. This is a comparison of two particular cases. Repeat it near the values relevant to your task; do not assume that every formula changes at a constant rate.

Checks and limits

Keep linear and square units distinct. A result for circumference, diameter, or radius is a length, while area is in square units. Squaring a unit as well as a number is necessary: a circle with radius in centimeters has area in square centimeters. Round only after the calculation if a measurement is approximate. The reported radius is 5.000648 units in the worked example. Keep its stated unit or counting convention when checking it against another calculation.