TAHA Engineering Toolsby TAHA Knowledge Lab

Units & Geometry

Circle Calculator

Area, circumference, radius and diameter — enter any one of them.

Inputs

Calculate from
Circle showing diameter d through the centre, radius r from the centre to the edge, circumference C around the edge and area A inside.drA — areaC — circumference
Diameter d passes through the centre (d = 2r). Circumference C is the distance round the edge (C = πd). Area A is the space inside (A = πr²). Diagram not to scale.

Result

Area
7,853.98
Circumference
314.159
Radius
50

A circle with this size has an area of 7,853.98 mm² and a circumference (perimeter) of 314.159 mm.

Educational estimate — check the assumptions below.

About this calculator

Every measurement of a circle follows from its radius. Enter whichever value you know — the diameter of a shaft, the circumference measured with a tape around a pipe or tank, or a required flow area — and get all the others.

Formula

d = 2r    C = 2πr = πd    A = πr² = πd² ÷ 4

From circumference: r = C ÷ 2π.  From area: r = √(A ÷ π). π is used to full computer precision.

Worked example

A circle of diameter 100 mm:

  • Radius = 100 ÷ 2 = 50 mm
  • Circumference = π × 100 = 314.159 mm
  • Area = π × 50² = 7853.98 mm²

Tip: to find a pipe’s outside diameter without callipers, wrap a tape around it and divide the circumference by π.

Assumptions and limitations

  • A perfect circle. Real parts have roundness tolerances.

References

  • Euclidean geometry of the circle.