Circle Calculator

How to use the circle calculator

1. Choose the measurement you already know: radius, diameter, circumference or area.
2. Type its value. Any unit works; pick it from the list if you want the results labeled (area comes out in square units).
3. Optionally enter a central angle in degrees for the arc, chord, sector and segment of that slice.

Circle formulas

The radius r runs from the center to the edge and the diameter d is twice that, straight across. The circumference C is the distance around the circle, and the area A is the space inside it. Pi (π ≈ 3.14159265) is the ratio of any circle's circumference to its diameter; the calculator uses its full double-precision value. Each formula can be turned around, so knowing any one measurement fixes the other three.

For a slice of the circle with central angle θ, the arc length is the curved edge, the chord is the straight line joining its ends, the sector is the pizza-slice area and the segment is the sliver between the chord and the arc. Convert degrees to radians with θ × π ÷ 180 before using the formulas by hand.

Worked examples

• From the radius. A circle of radius 5 has diameter 10, circumference 2π × 5 = 10π ≈ 31.4159 and area π × 5² = 25π ≈ 78.5398.
• From the circumference. A circumference of 10 gives r = 10 ÷ 2π ≈ 1.5915, so the diameter is about 3.1831 and the area about 7.9577.
• From the area. An area of 100 gives r = √(100 ÷ π) ≈ 5.6419 and a circumference of about 35.4491.
• A quarter circle. With r = 5 and θ = 90°, the arc is 7.854, the chord 7.0711, the sector area 19.635 and the segment area 7.135.

Area grows with the square of the size

Because the area depends on r², doubling the diameter makes a circle four times larger. That is why one 12-inch pizza (113.1 square inches) has more to eat than two 8-inch pizzas (50.3 square inches each, 100.5 in total). The same rule applies to pipes: a pipe with twice the diameter has four times the cross-section.

Circle table for radius 1 to 10

Tips and common mistakes

• Radius or diameter? Most measuring is done across the circle, which gives the diameter. Halve it before using πr².
• Square the radius, not the product. πr² means π × (r × r). Calculating (π × r)² gives an answer about 3.14 times too big.
• Area units are squared. A radius in centimeters gives an area in square centimeters. To change units, convert the radius first.
• Measuring a round object. Wrap a tape around it to get the circumference, then use the calculator to find the diameter: it is often more accurate than measuring straight across.

For other shapes, including sectors and ellipses, see the area calculator. For cylinders, cones and spheres, use the volume calculator or the surface area calculator.