Area of a Circle Calculator
Enter the radius, diameter or circumference of a circle and get its area instantly — computed with A = πr² at full π precision, in whatever unit you measured.
Area (A = π·r²)
78.539816 square units
- Area in terms of π
- 25·π
- Radius (r)
- 5
- Diameter (d = 2r)
- 10
- Circumference (C = 2πr)
- 31.42
A = πr². From a diameter, r = d/2 so A = πd²/4; from a circumference, r = C/(2π) so A = C²/(4π). π is used at full machine precision — rounding only happens at display time.
How to use this calculator
Pick which measurement of your circle you already have — the radius (centre to edge), the diameter (all the way across through the centre) or the circumference (the distance around) — and type its value. Any linear unit works: centimetres, metres, inches, feet. The calculator returns the area in the matching squared unit, along with the area expressed as a multiple of π and the other two linear measurements for reference.
How the calculation works
The area of a circle is A = πr², where r is the radius. If you supply a diameter, the calculator first halves it (r = d/2), which is the same as A = πd²/4. If you supply a circumference, it recovers the radius with r = C/(2π), equivalent to A = C²/(4π). π is used at JavaScript's full machine precision (about 16 significant figures), so nothing is rounded until the result is displayed. Because the formula is scale-invariant, the unit you enter is the unit you get back — squared.
Worked example
A circular patio has a radius of 5 metres. Its area is A = π·5² = 25π ≈ 78.54 m². Measured across instead? A 10 m diameter gives the same circle: r = 10/2 = 5, so again 78.54 m². And if you only walked the edge and measured a circumference of 31.42 m, then r = 31.42/(2π) ≈ 5 m — same answer. Doubling the radius to 10 m does not double the area: A = π·10² = 100π ≈ 314.16 m², four times as much, because area scales with the square of the radius.
Frequently asked questions
What is the formula for the area of a circle?
A = π·r², where r is the radius and π ≈ 3.14159265. It is one of the oldest results in geometry — Archimedes proved that a circle has the same area as a right triangle with the circle's radius and circumference as its two legs, which is exactly ½·r·(2πr) = πr².
How do I find the area of a circle from the diameter?
Halve the diameter to get the radius, then square it and multiply by π: A = π·(d/2)² = π·d²/4. For example, a 10 cm diameter gives A = π·100/4 = 25π ≈ 78.54 cm². Most real-world measurements (pipes, plates, wheels) are diameters, so this is the version you will use most often.
How do I find the area of a circle from the circumference?
Recover the radius first with r = C/(2π), then apply A = πr² — or use the combined form A = C²/(4π). A circumference of 31.4159 gives A = 31.4159²/(4π) ≈ 78.54 square units. This is handy when you can only measure around an object, like a tree trunk or a column.
What units does the area come back in?
The squared version of whatever unit you entered. A radius in centimetres gives an area in cm²; metres give m²; inches give in². The formula itself is unit-agnostic — just stay consistent within one calculation, and remember that converting an area between units means squaring the conversion factor (1 m² = 10,000 cm², not 100).
Why does doubling the radius quadruple the area?
Because the radius is squared in A = πr². Scaling r by any factor k scales the area by k². Double the radius (k = 2) and the area is 4× bigger; triple it and the area is 9× bigger. This is why a 12-inch pizza is more than twice the pizza of an 8-inch one — (12/8)² = 2.25 times the area.
What is the area of a semicircle or quarter circle?
Take the full circle's area and divide by 2 or 4. A semicircle of radius r has area πr²/2, and a quarter circle has πr²/4. For a semicircle of radius 5, that is 25π/2 ≈ 39.27 square units — half of the 78.54 the full circle gives.