Circumference to Radius Calculator

The formula is r = C / (2π), where C is the circumference and π ≈ 3.14159. This is derived by rearranging the circumference formula C = 2πr.

Divide the circumference by π: d = C / π. Since the diameter is twice the radius, this is equivalent to d = 2 × (C / 2π) = C / π.

The circumference is exactly 2π times the radius: C = 2πr. This means the circumference is approximately 6.2832 times the radius. For every unit increase in radius, the circumference increases by about 6.28 units.

Yes. The formula r = C / (2π) works for any circle regardless of size — from a coin to a planet. The calculator is unit-agnostic; just ensure your circumference is in consistent units.

The calculator uses π to full floating-point precision (approximately 15 decimal places), so results are accurate to machine precision. For most practical purposes, the results are exact.

Circumference must be positive since it represents a physical distance. The calculator will reject negative or zero values and display an error message prompting you to enter a valid positive number.

First find the radius: r = C / (2π). Then use A = πr² = π × (C / 2π)² = C² / (4π). For example, if C = 20, then A = 400 / (4π) ≈ 31.83.

Any consistent linear unit works — inches, feet, meters, centimeters, etc. The radius will be in the same units as the circumference. The area will be in square units of whatever you used.

That calculator uses C = 2πr (multiplying by 2π). This calculator uses the inverse: r = C / (2π) (dividing by 2π). They are mathematical inverses of each other.

No. Ellipses do not have a single radius. The circumference of an ellipse requires elliptic integrals and cannot be converted to a single radius value. This calculator is strictly for circles.

The calculator uses JavaScript's Math.PI constant, which is accurate to approximately 15 decimal places: 3.141592653589793. This is more than sufficient for any practical calculation.

Multiply the computed radius by 2π and check that it equals your original circumference. For example, if r = 5, then C = 2 × π × 5 ≈ 31.4159. This verifies the calculation.

The ratio is always 2π ≈ 6.2832. The circumference is always about 6.28 times the radius, regardless of the circle's size. This is a fundamental constant of circles.

First find the radius: r = √(A/π). Then find the circumference: C = 2πr = 2π√(A/π) = 2√(πA). For example, if A = 50, then C = 2√(50π) ≈ 25.07.

Yes, for any circle with positive radius, the circumference is always greater. Since C = 2πr and 2π ≈ 6.28, the circumference is always about 6.28 times larger than the radius.

The ratio is exactly π ≈ 3.14159. This is, in fact, the definition of π — the ratio of a circle's circumference to its diameter. It is the same for every circle in Euclidean geometry.

Engineers use this conversion when measuring pipe circumferences to determine pipe diameters, when calculating wheel sizes from tire circumferences, and when designing circular components from perimeter specifications.

The relationship C = 2πr has been known since ancient times. Archimedes approximated π by inscribing and circumscribing polygons around circles. The formula connects linear measurement (circumference) to radial geometry.

The calculator processes one circumference at a time. For multiple circles, enter each circumference separately. You can quickly compute several by repeating the process.

The calculator handles any positive value within JavaScript's floating-point range (up to approximately 10³⁰⁸). For extremely small values, results may lose precision due to floating-point limitations.

On the unit circle (radius = 1), the circumference is exactly 2π. This is why radians are defined as arc length divided by radius — one radian subtends an arc of length equal to the radius.

The Circumference to Radius Calculator uses standard mathematical formulas validated against authoritative references. The specific formula is displayed in the calculator interface with a detailed explanation of each variable.

Each calculator includes a step-by-step worked example showing exactly how the formula is applied. You can follow these steps with pen and paper to verify any result.

The Circumference to Radius Calculator accepts numeric inputs including integers and decimals. Invalid inputs (letters, special characters) are rejected with clear error messages.