Geometry
Area of a Circle Calculator
Enter a radius, diameter, circumference, or a known area — get the area from A = πr², in any unit, with every other circle measure and a full step-by-step solution.
Solve for the area
Enter the measure you know — the area and every other figure update as you type.
Area
78.5398
Radius r
5 cm
Diameter d
10 cm
Circumf. C
31.4159 cm
Uses full-precision π
Try an example
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The basics
What is the area of a circle?
The area of a circle is the amount of flat space it covers. It depends only on the distance from the centre to the edge — the radius. There is one formula that does all the work, and a couple of identities for when you are handed a different measure instead.
A = π r²
The one formula
Square the radius r, then multiply by π (about 3.14159). That is the whole calculation — every other version of the problem reduces to this.
r = 5 → π × 5² = π × 25 ≈ 78.54
π = C ÷ d
What π is
π is the fixed ratio of any circle's circumference to its diameter. It is irrational, so its decimals run on forever — which is why we keep it as a symbol rather than writing it out.
3.14159265…
Method
How to calculate it by hand
Three steps when you start from the radius. If you start from the diameter or circumference, add one short step at the front to find r.
- 1
Find the radius
If you already have r, skip ahead. From a diameter, halve it; from a circumference, divide by 2π.
r = d ÷ 2 or r = C ÷ 2π - 2
Square the radius
Multiply the radius by itself. Squaring is why area grows so fast — double r and this number quadruples.
r² = r × r - 3
Multiply by π
Multiply that square by π. The result is the area, in the square of whatever unit you measured in.
A = π × r²
Worked examples
See it from each starting point
The same circle (radius 5), reached three ways. Whatever you are given, you end at the same area.
Given r = 5
A = π × r² → π × 5² → π × 25
Square the radius: π × 25
Multiply by π: 78.5398
A = 78.5398 square units
Shortcuts
Area from any starting measure
You don't always have to find the radius first. Each known quantity has a direct formula that folds the conversion in.
A = π r²
From the radius
The base case. Square the radius and multiply by π.
r = 5 → 78.54
A = π d² ÷ 4
From the diameter
Because the radius is half the diameter, r² becomes d² ÷ 4. Handy for anything measured edge-to-edge.
d = 10 → 78.54
A = C² ÷ 4π
From the circumference
Substitute r = C ÷ 2π into the formula and simplify. Useful for anything you can wrap a tape around.
C ≈ 31.42 → 78.54
r = √(A ÷ π)
Back to the radius
Run the formula in reverse to recover the radius from a known area — a sanity check, and the tool's “Area” mode.
A = 78.54 → r = 5
Where it shows up
Why it matters in the real world
Circle area is everywhere a round thing meets a quantity — material, coverage, flow, or price per square inch.
Pizza value
Food & value
A pizza's “size” is its diameter, but the food you get is the area. A 16-inch pie has four times the pizza of an 8-inch one — the squaring at work.
π r²
Building & trades
Pouring a circular patio, sizing a round rug, or tiling a fountain all come down to the area in square feet so you can buy the right amount of material.
Cross-section
Pipes & flow
The cross-sectional area of a pipe or cable sets how much water, air, or current it can carry — found straight from its inside diameter.
Quick chart
Area of a circle by radius or diameter
The fast lookup for “area of a circle with radius X” and “with diameter X”. Each cell shows the area in square units, plus the exact multiple of π.
Look up byArea in square units, exact (π) and rounded.
r = 1
3.14
= 1π
r = 2
12.57
= 4π
r = 3
28.27
= 9π
r = 4
50.27
= 16π
r = 5
78.54
= 25π
r = 6
113.1
= 36π
r = 7
153.94
= 49π
r = 8
201.06
= 64π
r = 9
254.47
= 81π
r = 10
314.16
= 100π
r = 12
452.39
= 144π
r = 15
706.86
= 225π
r = 20
1,256.6
= 400π
r = 25
1,963.5
= 625π
r = 50
7,854
= 2,500π
r = 100
31,415.9
= 10,000π
Worth knowing
Rules and facts worth remembering
A few properties make circle area quicker to reason about — and harder to get wrong.
2r → 4A
Area scales with the square
Scale the radius by a factor and the area scales by that factor squared. Triple the radius and the area is nine times bigger.
A in unit²
The answer is always squared units
Length in, area out — so the unit is squared. Centimetres give cm²; feet give ft². Keep the unit attached or the number is meaningless.
½ π r² · ¼ π r²
Semicircles and sectors
A half or quarter circle uses the same πr², then takes that fraction. A sector of angle θ is θ ÷ 360 of the full area.
A = π r² > s²×?
The most area per perimeter
For a fixed perimeter, the circle encloses more area than any other shape. That is why bubbles, tanks, and pipes are round.
ring = π(R² − r²)
The area of a ring
An annulus — a washer or a circular path — is the big circle minus the small one: π(R² − r²).
3.14 ≠ π
Rounding π early bites
Using 3.14 instead of full π drifts the answer by about half a percent. Keep π symbolic until the final step.
Pitfalls
Common mistakes to avoid
Almost every wrong answer traces back to one of these three slips.
d ÷ 2 first
Using the diameter as the radius
The most frequent error. If a problem gives the width across, halve it before squaring — forgetting to do so makes the area four times too big.
(πr)² ✗
Squaring the wrong thing
The formula is π × r², not (π × r)². Square only the radius, then multiply by π.
unit²
Dropping the square on the unit
The result is an area, so its unit must be squared. Writing “cm” instead of “cm²” quietly mislabels the answer.
FAQ
Common questions
The area of a circle is A = πr², where r is the radius and π is roughly 3.14159. Square the radius, then multiply by π. For a radius of 5, the area is π × 25 ≈ 78.54 square units.
First halve the diameter to get the radius (r = d ÷ 2), then apply A = πr². You can also fold it into one step: A = π × (d ÷ 2)² = πd² ÷ 4. For a diameter of 10, the radius is 5, so the area is about 78.54 square units.
Recover the radius from the circumference with r = C ÷ (2π), then use A = πr². A direct shortcut is A = C² ÷ (4π). For a circumference of about 31.42, the radius is 5, giving an area near 78.54 square units.
Reverse the formula: r = √(A ÷ π). Divide the area by π, then take the square root. For an area of 78.54, that is √(78.54 ÷ π) = √25 = 5. Switch the calculator's mode to 'Area' to do this automatically.
π is the ratio of a circle's circumference to its diameter — the same for every circle. It is an irrational number that begins 3.14159265… and never ends or repeats. This calculator uses the full precision of π, not a rounded 3.14.
Area measures a two-dimensional region, so it grows with the square of the size. Double the radius and the area becomes four times larger (2² = 4), not twice as large. That squaring is exactly why a 16-inch pizza has far more than twice the food of an 8-inch one.
The area is always in square units of whatever unit you measured with. Measure the radius in centimetres and the area is in cm²; measure in feet and it is in ft². The calculator labels the answer with the squared unit and also shows common conversions.
Find the full circle's area with A = πr², then take the fraction you need. A semicircle is half (πr² ÷ 2) and a quarter circle is a quarter (πr² ÷ 4). The radius stays the same — you only scale the final area.
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Ugo CharlesBuilt and fact-checked against our editorial standards · Last updated June 2026
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