Circumference To Radius

Convert any circle circumference value to its radius instantly using r = C / (2pi). Free online geometry calculator with chart for students, teachers, and professionals.

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About This Calculator

The Circumference to Radius Calculator is a simple yet powerful geometry tool that converts the circumference of any circle into its radius. This is one of the most fundamental calculations in geometry, used across education, engineering, construction, and design worldwide.

This calculator uses the formula r = C / (2pi), derived from the standard circumference formula C = 2pir. Simply enter any circumference value and the radius is computed instantly with up to four decimal places of precision. A visual chart shows the linear relationship between circumference and radius values.

How to use

  1. Enter the circumference of the circle in any unit (inches, feet, centimeters, meters, etc.)
  2. Click Calculate to instantly get the radius
  3. View the result and explore the chart showing the radius versus circumference relationship

Regional Notes

Global: The circumference-to-radius formula r = C / 2pi is universal and works identically in all unit systems. The calculator accepts any unit of length -- inches (US customary), feet, centimeters, meters (metric system used in India and Europe), or kilometers.

India (IN): Students studying under CBSE, ICSE, and state boards encounter circle geometry, including circumference and radius, from Class 7 onwards. This tool helps verify homework and understand the linear relationship between circumference and radius.

United States (US): Used in K-12 geometry curricula and common in construction projects (pipes, circular patios, arches). Input values in inches or feet as needed.

United Kingdom (UK): Part of the GCSE mathematics curriculum. Useful for students and professionals in engineering and design fields.

Frequently Asked Questions

How do I convert circumference to radius?

To convert circumference (C) to radius (r), use the formula r = C / (2pi). For example, if the circumference is 31.42 units, the radius is 31.42 / (2 x 3.14159) = 5 units. This calculator does the math instantly for any circumference value.

What is the formula to find radius from circumference?

The formula to find the radius from the circumference is r = C / (2pi), where C is the circumference, r is the radius, and pi (pi) is approximately 3.14159. This is derived from the circumference formula C = 2pir, rearranged to solve for r.

What units does this calculator support?

This calculator supports any unit of length (inches, feet, centimeters, meters, kilometers, miles, etc.). The radius will be in the same unit as the circumference you enter. Simply enter the circumference value with your desired unit and the result will match.

Can I calculate radius from a circle's area instead of circumference?

Yes, you can also find the radius from the area using the formula r = sqrt(A/pi), where A is the area. If you only have the diameter, the radius is simply half the diameter. For circumference, our calculator uses the formula r = C / (2pi) for direct conversion.

Is the circumference to radius calculation the same in inches, feet, and meters?

Yes, the mathematical formula r = C / (2pi) works identically for any unit system. Whether you measure in inches (US customary), centimeters (metric), or any other unit, the formula stays the same. The radius result will always be in the same unit as the circumference you provide.

How accurate is this circumference to radius calculator?

This calculator uses the mathematical constant pi (pi) to high precision and displays results with up to four decimal places. The accuracy depends only on the precision of your input value. For most practical applications in geometry, construction, and education, the result is exact within the displayed decimal places.

What is the relationship between circumference and radius?

The relationship between circumference and radius is linear: circumference equals 2pi times the radius (C = 2pir). This means if you double the radius, the circumference doubles as well. Conversely, the radius equals the circumference divided by 2pi, which is the formula this calculator uses. A chart on the results page visualizes this direct linear relationship.

When would I need to convert circumference to radius in real life?

Converting circumference to radius is useful in many real-world situations: finding the radius of a round table or circular garden from its measurement around the edge, determining the radius of a pipe or wheel from its circumference for engineering projects, solving geometry problems in education (US, UK, and India curricula), and in construction for laying out circular foundations or arches.