Area of a Circle Calculator
The area of a circle is π times the radius squared. Enter a radius, diameter, or circumference and get the area instantly, with the substitution written out.
Example: with I know the Radius (r) · Value 5 → Area (A): 78.54.
Computed by the calculator below using its default values. Change any input to see your own numbers.
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Check it outArea of a circle formula: A = πr²
The area of a circle formula is A = πr² — multiply π ≈ 3.14159 by the radius squared. A radius of 5 gives π × 25 ≈ 78.54 square units. Starting from the diameter, halve it first (or use A = πd² ÷ 4): a 12 in plate has π × 6² ≈ 113.10 sq in. From a circumference, recover the radius with r = C ÷ (2π), then square it.
One wording trip-up: a circle is a flat, two-dimensional shape, so its “surface area” is simply its area — there is no separate formula. (If you’re picturing a ball, that’s a sphere, whose surface area is 4πr², four times the circle’s.) And the answer is always in squared units: measure in feet, get square feet.
How it’s calculated
A = πr², with π ≈ 3.14159 (JavaScript’s full-precision Math.PI). From a diameter the radius is d ÷ 2; from a circumference it is C ÷ (2π) — equivalent to A = πd²/4 and A = C²/(4π). Rounding only at display (2 decimals).
Results update as you type and are estimates, not professional advice — verify important decisions with a qualified professional.
Common mistakes
- Squaring the diameter in A = πr² — halve it first, or the area comes out 4× too big.
- Doubling instead of squaring — πr² means r × r, so r = 5 gives π × 25, not π × 10.
- Dropping the squared units — an area in ft² can't be compared with a length in ft.
Frequently asked questions
How do you find the area of a circle?
Square the radius and multiply by π: A = πr². For r = 5, that’s π × 25 ≈ 78.54.
What is the area of a circle with a 10 inch diameter?
Halve the diameter to get r = 5 in, then A = π × 5² ≈ 78.54 sq in.
What is the surface area of a circle?
For a flat circle it’s the same thing as its area, πr². The formula 4πr² applies to a sphere’s surface, not a circle.
How do I find the area from the circumference?
r = C ÷ (2π), then A = πr² — equivalently A = C² ÷ (4π). A circumference of 31.42 gives an area of about 78.56.
Why is the answer in square units?
Area counts how many unit squares fit inside the shape, so lengths in cm give areas in cm².