Circumference Calculator

Quick Answer

Last updated: 2 November 2026 ·How we calculate this: C = 2πr and A = πr²

How This Circumference Calculator Works

Choose what you know, the radius, diameter, circumference or area, and enter the value and unit. The calculator finds the radius first, then works out the circumference, diameter and area, and shows each step. When you start from the radius or diameter, it also gives the exact answer in terms of π.

How to Use the Circumference Calculator

1. Choose whether you know the radius, diameter, circumference or area.
2. Enter the value.
3. Choose the unit.
4. Press Calculate.
5. Read the circumference, radius, diameter, area and steps.

Core Formulas

• From radius: C = 2πr
• From diameter: C = πd
• From area: C = 2√(πA)
• Radius from circumference: r = C ÷ 2π
• Area: A = πr² = C² ÷ 4π

Key Terms

• Circumference: the distance around a circle.
• Radius: the distance from the center to the edge.
• Diameter: the distance across a circle through its center.
• Pi (π): about 3.14159, the ratio of a circle’s circumference to its diameter.
• Area: the space inside the circle.

Worked Example

A round table has a diameter of 48 inches. How much edge trim do you need?

• C = πd = π × 48 = 48π
• C ≈ 150.80 inches, or about 12.57 feet
• Area = π × 24² ≈ 1809.56 square inches

Real-Life Examples

• Bike wheels: a 26-inch wheel travels about 81.7 inches per turn.
• Garden edging: a round bed 10 ft across needs about 31.4 ft of edging.
• Running track: a circle with a 50 m radius is about 314.2 m around.
• Pizza size: a 14-inch pizza has about 153.9 sq in of area, versus 113.1 for a 12-inch.

Circumference vs Area

• Circumference: the length around the circle, in units like inches.
• Area: the space inside, in square units like square inches.
• Doubling the radius: doubles the circumference but makes the area four times larger.

Circumference for Common Diameters

In the same unit as the diameter. Area is in square units.

Tips for Measuring a Circle

• Measure the diameter across the widest part, through the center.
• Wrap a string or tape around round objects to measure circumference directly.
• Use the same unit for every measurement.
• Area units are squared: square inches, square feet and so on.

Parts of a Circle and Related Lengths

Many real tasks use a piece of a circle rather than the whole thing. Once you know the radius, you can find these too.

• Semicircle perimeter: half the circumference plus the diameter, πr + 2r. For r = 5, that is about 25.7080.
• Arc length: the part of the circumference for an angle θ in degrees is (θ ÷ 360) × 2πr. A 90° arc with r = 5 is about 7.8540. Our Arc Length Calculator does this for any angle.
• Distance per turn: a wheel moves one circumference each full turn, so distance = turns × πd.
• Ring or washer: the area between two circles is π(R² − r²), where R is the outer radius.

If you only have a curved edge, such as part of a round patio, measure the straight width across the curve and its height at the middle. The radius is (width² ÷ 8h) + h ÷ 2, where h is the height. Then use the radius here to find the full circle.

Common Mistakes to Avoid

• Using the diameter in C = 2πr. Use πd for the diameter, or halve it first.
• Mixing up circumference and area. Area uses r², circumference does not.
• Rounding π too early. Using 3.14 can cause small errors on large circles.
• Forgetting square units for area.
• Measuring off-center. A diameter must pass through the center.

Frequently Asked Questions

References & Sources