Circle Calculator

Give any one of radius, diameter or circumference and the page reconstructs the other two lengths plus the disk’s area, keeping the rim (a length) distinct from the filled disk (a length squared).

How to use

Choose which measurement you already have: radius from the centre, diameter across the middle, or circumference around the rim.
Enter that single positive length in the unit you selected. The other two lengths appear as details beside the area.
Treat C = 2πr as a length and A = πr² as unit². A number that looks similar (radius 2, area about 12.57) is not interchangeable with a 12.57 length.
Stop here if the object is a ball, a pipe’s interior or a can. Those are sphere, cylinder or cone problems on the volume and surface-area pages.

How it works

One length fixes a circle. Diameter is twice the radius. Distance around the rim is 2πr. The filled disk is πr². Start from a tape around a wheel and the page inverts C = 2πr to get r = C / (2π), then fills d and A. Start from a diameter stamped on a pipe and it halves that stamp before the same formulas run. π here is the JavaScript constant Math.PI, not a hand-rounded 3.14 unless you later round the displayed result.

A bicycle wheel, a pizza, a round tablecloth and a circular irrigation head all use this family of relations. If you know the radius of a 5-unit circle you already know d = 10, C = 10π and A = 25π. If a coach only quotes “the track is 400 m around a circular loop,” this page recovers the radius before you size a radius-dependent fixture.

People swap circumference and area because both involve π. They are different dimensions. Painting the disk is area. Buying trim to edge the disk is circumference. A radius of 5 cm gives a 10 cm diameter, a 10π cm rim and a 25π cm² disk — three different units of meaning even though they share the same r.

This is not a sphere. The skin of a ball is 4πr² and the interior is ⁴⁄₃πr³; those live on the surface-area and volume pages. It is also not an ellipse: a stretched oval needs two semi-axes on the area calculator. Sector, segment and annular-ring formulas are not implemented here — you would split those into a full circle minus another circle, or use a fraction of πr² by hand.

Zero and negative inputs are rejected. A circumference of zero is a point, not a circle. Do not mix a millimetre radius with a metre circumference; convert to one length unit first so the derived diameter and area stay honest.

Formula

d = 2r
C = 2πr
A = πr²
r = C / (2π)

Worked examples

From radius 5
r = 5 → d = 10, C = 10π, A = 25π
From circumference
C = 10π → r = 5

Useful notes

This is a planar circle, not a sphere. Sphere volume and surface area have their own pages.
Any one of r, d or C is enough; the other two lengths are derived, not typed twice.
Area is the primary result; radius, diameter and circumference are listed as details.
π is Math.PI. Rounding to 3.14 by hand will not match the page’s extra digits.

FAQ

How do I find circumference from radius?: Multiply the radius by 2π. C = 2πr.
How do I find area from diameter?: Radius is half the diameter, then A = πr². A diameter of 10 gives r = 5 and area 25π.
Why are there two different units?: Radius, diameter and circumference are lengths. Area is length squared. They are not interchangeable.
If I only have a wheel’s circumference, can I still get the area?: Yes. Choose circumference, enter C, and the page sets r = C / (2π) before A = πr². A rim of 10π gives r = 5 and area 25π.
Does this size a circular tank’s capacity?: No. Capacity of a can or silo is a cylinder or sphere volume (unit³). This page stops at the flat disk and its rim.

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