Circle Calculator

How to use this circle calculator

Choose the common dimension unit and the known measurement. Enter a dot-decimal or scientific-notation value, not an expression such as 10π. Area input uses the square of the selected length unit; the other inputs use length. Changing the known measurement loads an example, while changing the unit keeps the number and reinterprets its label rather than converting it. Results update only when the input and recovered radius fall within the supported positive ranges. Use the diagram to confirm which quantity you measured.

How the calculation works

A circle consists of points at a fixed distance from its center in a plane. That distance is radius r. Diameter d passes through the center between opposite edges and equals twice the radius. Circumference C is the full boundary length, while area A is the region enclosed by that boundary. A single positive value of any one of these quantities fixes an ideal circle's size, which is why the calculator can recover all four without requesting several redundant measurements.

If radius is known, compute diameter as 2r, circumference as 2πr and area as πr². For a hypothetical radius of 5 cm, diameter is 10 cm, circumference is about 31.4159 cm and area is about 78.5398 cm². The area label is squared because two length dimensions are involved. A circumference measured in centimeters must not be reported as square centimeters merely because it describes a curved boundary.

If diameter is known, divide it by two before using the radius formulas. A stated diameter of 18 ft gives radius 9 ft, circumference 18π ft and area 81π ft². Substituting the full diameter into πr² would multiply the correct area by four. The dimension illustration marks both quantities to make this error easier to spot. It is a schematic with fixed proportions, not a drawing from which a real measurement should be taken.

If circumference is supplied, divide it by 2π to recover radius. A circumference of 12π in an educational worksheet gives radius 6, diameter 12 and area 36π in compatible units. The field accepts the numerical value of that circumference, not the symbolic expression itself. Preserve sufficient digits when copying a rounded circumference; the calculated radius can only reflect the precision of the value actually entered, not an unavailable original measurement.

If area is supplied, recover radius with √(A/π). For an entered area of 100 m², radius is approximately 5.6419 m and diameter approximately 11.2838 m. This operation does not convert square meters into meters by changing a label: it uses the circle equation to infer a linear dimension. The result assumes that the region really is a complete circle. An irregular outline with the same area does not necessarily have that radius or circumference.

The model uses JavaScript's Math.PI throughout rather than rounding π to 3.14 before multiplication. Display rounding happens after calculation, so a manually reproduced answer using fewer digits can differ slightly. A doubling of radius doubles circumference but quadruples area; this scaling relationship is a useful independent check. It also explains why treating a ten-percent increase in radius as a ten-percent increase in area would give the wrong geometric comparison.

Only positive, nondegenerate circles are accepted. The radius, whether supplied or recovered, must lie between 1e-9 and 1e12 in the chosen unit. Area and boundary input modes use corresponding broader ranges but still validate that recovered radius. Blank input, zero, negative values, nonfinite results and unsupported symbolic text do not produce a valid answer. The numeric range is an interface limit, not an assertion of measurement accuracy over that enormous physical scale.

All dimensions must describe one circle using one consistent unit. The selector changes labels without changing input numbers, so switching a value of 5 from cm to m deliberately describes a larger circle. Use a length or area converter if you need to express an existing measurement in another unit. This page is not an arc-length, sector-area, ellipse, annulus or spherical-volume calculator. Use the relevant shape tool rather than adapting a full-circle result without a stated model.

Formulas

Worked examples

Common uses

Accuracy and limitations

Uses double-precision arithmetic and Math.PI with display rounding only. Positive recovered radius must stay within 1e-9–1e12 selected length units; input modes have quantity-appropriate limits.

The diagram is schematic. Measurements describe a complete ideal circle only, not an arc, sector, ellipse, annulus or sphere. Unit selection relabels numbers and does not convert them.

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