What are my circle's measurements?
Type any one of the radius, diameter, circumference, or area, and the other three appear as you type.
- Diameter
- 10 in
A circle of radius 5 in has a diameter of 10 in, a circumference of 31.42 in, and an area of 78.54 in².
- Circumference
- 31.42 in
- Area
- 78.54 in²
Diameter: 10 in. A circle of radius 5 in has a diameter of 10 in, a circumference of 31.42 in, and an area of 78.54 in².
How to calculate
Finds the radius, diameter, circumference, and area of a circle from any one of them, with C = 2πr and A = πr².
Example with the default inputs (Radius 5 in): A circle of radius 5 in has a diameter of 10 in, a circumference of 31.42 in, and an area of 78.54 in².
Formula: d = 2r, C = 2πr = πd, and A = πr², where r is the radius.
- π is the full-precision value 3.141592653589793…, not 3.14 or 22/7.
- Every length is in the unit shown next to it, and the area is in the square unit shown next to it.
- Each value must be greater than 0.
Worked examples
Each example is checked against the calculator on every build.
- Radius 196.9 in gives Diameter 393.7 in, Circumference 1,237 in, Area 121,737 in².Source: hand calculation in content.mdx: d = 2 × 5 = 10, C = 2π × 5 = 31.4159, A = π × 5² = 78.5398
- Diameter 472.4 in gives Radius 236.2 in, Circumference 1,484 in, Area 175,301 in².Source: hand calculation in content.mdx: r = 12 ÷ 2 = 6, C = π × 12 = 37.6991, A = π × 6² = 113.0973
- Circumference 3,937 in gives Radius 626.6 in, Diameter 1,253 in, Area 1,233,453 in².Source: hand calculation in content.mdx: r = 100 ÷ 2π = 15.9155, A = C² ÷ 4π = 795.7747
- Area 77,500 in² gives Radius 157.1 in, Diameter 314.1 in, Circumference 986.9 in.Source: hand calculation in content.mdx: r = √(50 ÷ π) = 3.9894, C = 2√(πA) = 25.0663
How it works
A circle is set by one number: its radius r, the distance from the centre to the edge. Every other measure follows from r:
- Diameter: d = 2r
- Circumference (the distance around): C = 2πr, which is the same as C = πd
- Area (the space inside): A = πr²
Type any one of the four values. The calculator finds the radius first, then the other two:
- from the diameter: r = d ÷ 2
- from the circumference: r = C ÷ 2π
- from the area: r = √(A ÷ π)
Assumptions
- π is the full-precision value 3.141592653589793…, not 3.14 or 22/7.
- Each value is greater than 0.
- Each box has its own unit. Lengths are converted through metres and areas through square metres, with 1 in = 0.0254 m exactly. The formulas give the same numbers in any one unit: a radius of 5 in gives an area of 78.54 in², and a radius of 5 m gives 78.54 m².
Worked examples by hand
Radius 5. d = 2 × 5 = 10. C = 2 × π × 5 = 10π = 31.4159. A = π × 5² = 25π = 78.5398.
Diameter 12. r = 12 ÷ 2 = 6. C = π × 12 = 37.6991. A = π × 6² = 36π = 113.0973.
Circumference 100. r = 100 ÷ (2 × π) = 15.9155, so d = 31.8310. A = π × 15.9155² = 100² ÷ (4π) = 795.7747.
Area 50. r = √(50 ÷ π) = √15.9155 = 3.9894, so d = 7.9788 and C = 2π × 3.9894 = 25.0663.
Other questions people ask
How do I find the area of a circle from its circumference?
First find the radius, r = C ÷ 2π, then the area, A = πr². In one step, A = C² ÷ 4π. A circumference of 100 cm gives a radius of 15.92 cm and an area of 795.77 cm².
How do I find the radius from the area?
Divide the area by π and take the square root: r = √(A ÷ π). An area of 50 in² gives a radius of √(50 ÷ 3.14159…) = 3.99 in.
What is the difference between circumference and area?
The circumference is a length: the distance around the circle, in inches, centimetres, or feet. The area is the space inside, in square units such as in² or cm². Doubling the radius doubles the circumference but makes the area four times as large.
Why is the diameter twice the radius?
The radius runs from the centre to the edge. The diameter runs from edge to edge through the centre, so it is one radius out and one radius back: d = 2r.
What value of π does the calculator use?
It uses π to about 16 significant figures, 3.141592653589793. Using 3.14 instead gives answers that are about 0.05% too small, which is enough to change the second decimal place of a larger circle.
Can I mix units, such as a radius in feet and an area in square inches?
Yes. Each box has its own unit switch, and the calculator converts between them. The answer changes unit, not size.