About the circle calculator
The circle calculator finds the radius, diameter, circumference and area from any one of them. You can also enter a sector angle to get the arc length and the area of the sector.
Everything is shown in your chosen length unit, with area in the unit squared.
Who should use the circle calculator
- Students learning about π.
- Makers, bakers and gardeners sizing circular items.
- Anyone converting between a circle's measurements.
How to use the circle calculator: what each input means
- Known measurement
- Radius, diameter, circumference or area.
- Value and unit
- A positive number and a length unit.
- Sector angle
- Optional, from 0 to 360 degrees.
How the circle calculator works: method and formula
Whatever you enter is first converted to the radius: r = d ÷ 2, r = C ÷ 2π or r = √(A ÷ π). The other measurements follow from the radius. For a sector with angle θ, arc length = θ ÷ 360 × 2πr and area = θ ÷ 360 × πr².
- Circumference
- C = 2πr = πd
- Area
- A = πr²
- Sector area
- A = (θ ÷ 360) × πr²
How to read your circle calculator result
Circumference grows in proportion to the radius, while area grows with the square of it, so doubling the radius quadruples the area. π is approximately 3.14159265.
Circle Calculator worked example
A circle with a radius of 5 cm and a 60° sector.
- Diameter = 2 × 5 = 10 cm.
- Circumference = 2 × π × 5 = 31.4159 cm.
- Area = π × 5² = 78.5398 cm².
- Sector (60°): arc length 5.2360 cm, area 13.0900 cm².
Circumference 31.42 cm, area 78.54 cm².
Practical uses of the circle calculator
- Sizing a round table cover or pizza.
- Finding the length of fencing around a circular bed.
- Maths homework on π.
Assumptions and limitations of this calculator
- Perfect circles only.
- Results use a double-precision value of π.