Radius From Circumference Calculator
Calculate radius from a positive circle circumference using r = C ÷ (2π). See a 31.42 cm example, three-decimal rounding and browser number limits.
Formula: r = C ÷ (2π)
Enter a positive circumference in centimeters. Decimal values are supported; the radius is returned in centimeters and rounded to three decimal places.
The Radius From Circumference Calculator applies one fixed circle relationship. Enter a positive, finite circumference in centimetres, select Calculate, and the widget returns the radius in centimetres. It does not infer units or convert measurements.
Circumference is the distance around a circle, while radius is the distance from its centre to its edge. The OpenStax physics reference table gives the relationship C = 2πr. Rearranging that equation for radius gives r = C ÷ (2π).
How to Use the Radius From Circumference Calculator
- Measure or identify the circle’s circumference in centimetres.
- Enter a finite value greater than 0 in the Circumference field.
- Select Calculate.
- Read the radius in centimetres, displayed to three decimal places.
The default circumference is 31.42 cm. Selecting Calculate divides 31.42 by 2π. The unrounded result is about 5.000648 cm, so the interface displays 5.001 cm. Changing the input clears the previous result; select Calculate again after an edit.
Radius Formula and Worked Example
r = C ÷ (2π)Here, r is radius, C is circumference and π is the mathematical constant pi. For the default value, r = 31.42 ÷ (2π) ≈ 5.000648, which rounds to 5.001 cm. Multiplying that unrounded radius by 2π returns the original circumference apart from normal floating-point effects.
Use one consistent length unit. Division by the dimensionless number 2π means the radius has the same length unit as the circumference. This widget labels both values in centimetres and does not perform conversion. The NIST SI length reference identifies the centimetre as a metric length unit derived from the metre.
Input Limits, Browser Numbers and Rounding
Zero and negative circumferences are rejected because a geometric circumference must be greater than 0. The entry must also parse as a finite JavaScript number. Values outside the browser’s finite-number range are invalid. Very large finite inputs retain limited significant-digit precision, while extremely small positive values can underflow during division.
The calculation uses JavaScript’s numeric value of π and standard floating-point arithmetic. The visible radius is rounded to three decimal places. A small positive result below 0.0005 cm can therefore display as 0.000 cm even though the accepted circumference is positive. Display rounding does not increase the precision of the original measurement.
If circumference is not the measurement you have, choose a related calculator whose inputs match your task: the Circle Circumference Calculator, Circle Area Calculator or Circle Radius Calculator.
Frequently asked questions
How do I calculate radius from circumference?
Divide the positive circumference C by 2π. The formula is r = C/(2π).
What inputs does this calculator accept?
Enter a finite circumference greater than 0. Zero, negative values and values outside the browser’s finite-number range are rejected.
What does a circumference of 31.42 cm return?
31.42 divided by 2π is about 5.000648, so the calculator displays a radius of 5.001 cm.
Which units does the calculator use?
The field and result are labelled in centimetres. This calculator does not convert units, so use a consistent length unit.
How is the radius rounded?
The calculation uses JavaScript floating-point arithmetic and the visible result is rounded to three decimal places.
What happens with extremely small or large values?
Very large finite values have limited significant-digit precision. Extremely small positive results may underflow or display as 0.000 cm after rounding.
Does the result update automatically?
No. Select Calculate after entering a circumference. Changing the input clears the previous result until you calculate again.