Utilnaro

Geometry formulas

Circle area and circumference

Calculate radius, diameter, circumference, or area of a circle from one known measurement.

Formula

A=πr2;C=2πr A = πr²; C = 2πr

The circle area is π times the radius squared, while its circumference is 2π times the radius.

Circle area and circumference calculator

What do you want to calculate?

Known quantity

Choose one known quantity. The others are derived through the radius.

Circle diagram
rdA ?
  • r · Radius: known value
  • d · Diameter: related value
  • A · Area: value being calculated (?)
  • C · Circumference: related value

Result

78.539816 m²

Calculation path

A = π × r²

r = 5 m

Symbols and units

SymbolQuantitySISupported units
rradiusDistance from the centre to the circle.mm, cm, mm, km
ddiameterLength through the centre between two points on the circle; d = 2r.mm, cm, mm, km
CcircumferenceLength of the circle boundary.mm, cm, mm, km
AareaArea enclosed by the circle.m²m², cm², mm², km²

Formula rearrangements

Calculate radius

r = d / 2 = C / 2π = √(A / π)

Calculate diameter

d = 2r

Calculate circumference

C = 2πr = πd

Calculate area

A = πr²

Worked examples

Area from a five-centimetre radius

A circle has a radius of 5 cm. Calculate its area.

  1. 1Step 1: Use A = πr².
  2. 2Step 2: Square the radius: 5² = 25.
  3. 3Step 3: Multiply by π to obtain 25π cm², approximately 78.54 cm².

Result: 25π cm² ≈ 78.54 cm²

Circumference from diameter

A circle has a diameter of 12 m. Calculate its circumference.

  1. 1Step 1: Use C = πd.
  2. 2Step 2: Substitute d = 12 m.
  3. 3Step 3: Multiply by π to obtain 12π m, approximately 37.70 m.

Result: 12π m ≈ 37.70 m

Sources and review