Circle Calculator

For a circle with radius r, diameter is d = 2r, circumference is C = 2πr, and area is A = πr².

When diameter is known, use r = d ÷ 2. When circumference is known, use r = C ÷ (2π). When area is known, use r = √(A ÷ π).

The calculator applies the correct inverse formula to recover one unrounded radius, then derives every other measurement from that same radius.

Choose the circle measurement you already know: radius, diameter, circumference, or area. Enter a positive value and select the unit that describes it.

The calculator first converts the entered measurement to radius. It then calculates diameter, circumference, and area from that one unrounded radius, keeping every displayed result consistent with the same circle.

Open Display precision to choose from zero through eight decimal places. This changes formatting only; it does not round the values used by later formulas.

Radius is the distance from the centre to the boundary. Diameter passes through the centre and is exactly twice the radius. Circumference is the distance around the boundary, while area measures the enclosed two-dimensional region.

Radius, diameter, and circumference are lengths, so they use units such as centimetres or feet. Area uses square units such as cm² or ft² because it measures two dimensions.

A radius can be used directly. A diameter is divided by two, a circumference is divided by 2π, and an area is divided by π before taking the positive square root.

Once radius is known, every other value follows from the standard formulas. Using one common intermediate value avoids inconsistencies caused by chaining separately rounded answers.

Circumference is the perimeter of a circle. It equals 2πr when radius is known and πd when diameter is known.

The constant π is the ratio of a circle's circumference to its diameter. Because that ratio is the same for every ideal circle, the same formula works at every scale.

The area enclosed by a circle is π multiplied by the square of its radius. A radius of 5 cm therefore gives an area of 25π cm², approximately 78.54 cm².

Area grows with the square of radius. Doubling the radius doubles the diameter and circumference but multiplies area by four.

When circumference is known, divide it by 2π. When area is known, divide it by π and take the positive square root.

Inverse results are only as accurate as the entered measurement. A circumference rounded to the nearest centimetre cannot recover an exact original radius, even though the calculator carries more decimal places internally.

Select the unit that already describes the entered number. The interface carries that label through the results and automatically adds a squared symbol to area.

Changing the unit selector does not convert the number. For example, changing 10 cm to inches without first converting the numeric value would describe a different circle.

When converting area between units, square the length conversion factor. Since 1 m equals 100 cm, 1 m² equals 10,000 cm² rather than 100 cm².

The calculation engine uses JavaScript's Math.PI value instead of replacing π with 3.14 or 22/7. Those shorter values can be useful estimates, but they introduce additional rounding error.

The precision control affects only what appears on screen. For multi-step work, keep the calculator's full result or enough decimal places for the purpose and round once at the end.

Very small and very large finite values may be displayed in scientific notation so significant digits remain readable.

Circumference can estimate edging around a circular garden, the length around a pipe, a wheel's travel per revolution, or the border of a round tabletop. Area can estimate floor covering, paint coverage, cross-sectional area, fabric, or material inside a circular boundary.

These calculations assume the entered dimension represents the intended circle. For pipes, rings, and containers, confirm whether the measurement is an inside diameter, outside diameter, centreline diameter, or nominal size.

Real objects can be slightly oval, deformed, rough, tapered, or manufactured within a tolerance. Measuring at one position may not represent the complete object.

For higher-stakes fabrication or engineering, measure more than one diameter, use suitable calibrated equipment, preserve significant figures, and account for tolerance and uncertainty separately.

Use an annulus calculation for a ring with inner and outer radii, an ellipse calculation for an oval, and sector or arc formulas when only part of a circle is involved.

The calculator runs locally in the browser. The measurement, unit label, precision choice, and calculated results are not sent to an external calculation service.

Clipboard access is requested only when a result is copied.