Circle Calculator

Circle

Enter the measurement you have and select which one it is.

I know the

ValueIn whatever unit you are working in

Sector angleFor the sector, arc and chord figures

AREA

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Radius—

Diameter—

Circumference—

Area—

Area in terms of π—

Circumference in terms of π—

Sector, arc and chord at that angle

Sector area—

Arc length—

Chord length—

Segment area—

Angle in radians—

Share of the whole circle

Sector is the pie slice including the two straight edges; segment is only the part cut off by the chord. Confusing the two is the single most common error in this calculation.

Going backwards from area or circumference

Most circle problems in the wild run in reverse: you know the area of a plot and need the radius, or you measured around a pipe and need its diameter. Rearranged, r = √(A/π) and r = C/2π. Selecting a different known value above just applies the matching rearrangement — there is no separate formula to look up.

Why area scales with the square

Double the radius and the circumference doubles, but the area quadruples. This is why a 16-inch pizza is not twice the food of an 8-inch one but four times it, and why doubling the diameter of a pipe roughly quadruples its flow capacity. It is the most practically useful consequence of πr² and the one people most consistently get wrong when comparing sizes.

Sector, arc, chord and segment

A sector is the wedge, like a slice of pie: area = (θ/360) × πr². An arc is the curved edge of that wedge: length = (θ/360) × 2πr. A chord is the straight line joining the two ends of the arc: 2r·sin(θ/2). A segment is what is left when you cut the sector along the chord — the sector minus the triangle.

These are the numbers behind pie chart labels, curved skirting, culvert flow depth and the set-out for any curved road or rail alignment.

Exact values versus decimals

The "in terms of π" fields give the exact answer — 100π rather than 314.159. Keep the exact form through a multi-step calculation and round only at the end; rounding π early is the usual source of answers that drift in the third decimal place and fail a marking scheme.

Frequently Asked Questions

How do I find the radius if I only know the area?

Divide the area by π and take the square root: r = √(A/π). Select "Area" as your known value above and the radius is returned directly, along with the diameter and circumference.

What is the difference between a sector and a segment?

A sector is the pie-slice shape bounded by two radii and the arc. A segment is the smaller region cut off by a straight chord, which is the sector with the central triangle removed. Both are calculated above.

Is circumference the same as perimeter?

Yes — circumference is simply the specific name for the perimeter of a circle. C = 2πr, or equivalently πd.

How many decimal places of π does this use?

It uses the full double-precision value built into your browser, about 15 significant digits. That is far beyond any physical measurement, so rounding in the display is always the limiting factor, not π itself.

Where these numbers come from

Sources

Official publications only. Links open the original document in a new tab.

National Institute of Standards and Technology Special Publication 811 — Guide for the use of the SI Significant figures and rounding conventions
National Institute of Standards and Technology CODATA fundamental physical constants Values of the fundamental physical constants