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Toolbox · Circle calculator

Circle calculator

Radius, diameter, circumference or area as input; the figure marks the radius, diameter and circumference

Formula

C=2\pi r,\quad S=\pi r^2

C = 2 pi r, S = pi r^2

Enter radius r; everything else follows.

Presets

Tap an edge, angle or region to see how it is computed

Radius, diameter, circumference

Area and more

Relationr5

d=2r=10,\ C=2\pi r=31.416

Area S78.54

Circumference C31.416

Radius r5

Diameter d10

r5d10C31.416S78.54

Steps

5 / 5

1Given
$r=5$
Collect the given quantities first.
2Find diameter
$d=2r=2\times5=10$
The diameter is twice the radius.
3Circumference
$C=2\pi r=2\times3.14159\times5=31.416$
Circumference C = 2 pi r.
4Area
$S=\pi r^2=3.14159\times5^2=78.54$
Apply the area formula; the unit is squared.
5Result
$r=5,\ d=10,\ C=31.416,\ S=78.54$
Collect all computed quantities.

Concept

A circle is the set of points at a fixed distance from a fixed point: the centre and the radius.

C = 2 pi r and S = pi r^2. Scaling the radius by k scales the circumference by k and the area by k^2.

Going further

What pi is: pi is the ratio of circumference to diameter, the same for every circle, about 3.14159265 and irrational.
Squaring the circle: Inscribed regular polygons approximate the circle better as the side count grows - the classical method for computing pi.
Circles in daily life: Manhole covers are round because the diameter is constant, so they cannot fall through; round wheels keep the axle height constant.

Common mistakes

Do not mix radius and diameter: d = 2r.
Area is in square units, circumference is not.
Whether to use pi = 3.14 or keep pi depends on the question; this tool keeps pi exact.

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