Circle Calculator
Pick which property of the circle you know — radius, diameter, circumference or area — type the value, and the calculator returns the other three using exact π.
Area (A = π·r²)
314.159265 square units
- Radius (r)
- 10
- Diameter (d = 2r)
- 20
- Circumference (C = 2πr)
- 62.83
A circle is defined by one number — the radius. From r, d = 2r, C = 2πr and A = πr². The calculator inverts these to back out r from whichever input you supply.
How to use this calculator
Choose what you already know about your circle: the radius (r), the diameter (d), the circumference (C) or the area (A). Type the value in any linear unit you like — centimetres, metres, inches or feet — and the calculator returns the remaining three measurements. Linear outputs (radius, diameter, circumference) come back in the same unit; the area comes back in the squared unit.
How the calculation works
Every property of a circle reduces to one number — the radius r. From r the calculator computes diameter d = 2r, circumference C = 2πr and area A = πr². If you provide one of the other three, it inverts the formula first: from a diameter, r = d/2; from a circumference, r = C/(2π); from an area, r = √(A/π). Once r is known the other three follow directly. π is used at full machine precision (about 16 significant figures), so the only rounding happens at display time.
Worked example
Take a circle with radius r = 5. Diameter d = 2·5 = 10. Circumference C = 2π·5 = 10π ≈ 31.415927. Area A = π·5² = 25π ≈ 78.539816 square units. Reversing it: if instead you knew the area A = 25π, then r = √(25π/π) = √25 = 5, and the same diameter and circumference fall out. Whether the unit is centimetres, metres or inches, the ratios are identical — only the numbers scale.
Frequently asked questions
What is the formula for the area of a circle?
A = π·r², where r is the radius. The constant π (≈ 3.14159265…) is the ratio of any circle's circumference to its diameter and shows up in both the area and circumference formulas. If you only know the diameter d, then r = d/2 and A = π·(d/2)² = π·d²/4.
How do I find the radius from the circumference?
Rearrange C = 2πr to get r = C / (2π). For example, a circumference of 31.4159… gives r = 31.4159… / (2π) ≈ 5. The calculator does this inversion automatically when you pick "circumference" as the known input.
How do I find the radius from the area?
Rearrange A = π·r² to get r = √(A/π). For example, an area of 78.5398… square units gives r = √(78.5398…/π) ≈ 5. Once r is known, diameter and circumference follow as 2r and 2πr.
What is the difference between radius and diameter?
The radius is the distance from the centre of the circle to any point on its edge. The diameter is the distance straight across the circle through the centre — so d = 2r. Many real-world measurements (pipe sizes, wheels, plates) are given as diameters, while geometry formulas are usually written in terms of the radius.
Can I use any unit?
Yes. The circle formulas are scale-invariant, so the unit you put in is the unit you get out. Enter the radius in centimetres and the diameter and circumference come back in cm, with the area in cm². Enter inches and everything is in inches and square inches. Just stay consistent within one calculation and remember that area is in squared units.
Why use π at full precision instead of 3.14?
π is irrational, so any short decimal version (3.14, 3.1416, 22/7) is an approximation. JavaScript's Math.PI is accurate to about 16 significant figures, which is far more than any physical measurement could need. Using the full constant means rounding only happens at display time, never during the calculation — so chained computations (going from circumference back to area, for example) stay exact.