Area of a Circle Calculator
Enter any one measurement and the rest are worked out.
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- Radius—
- Diameter—
- Circumference—
- Area in terms of π—
- Half circle area—
- Quarter circle area—
How to use this circle calculator
- Tell it which measurement you have — radius, diameter, circumference or even the area itself.
- Enter the figure and pick a unit.
- Read the area, with the other three measurements listed underneath, plus the area expressed exactly in terms of π.
Working backwards from the area is genuinely useful: if you know a pizza is 1,018 cm², the calculator tells you it is 36 cm across.
The area of a circle formula
Area equals π multiplied by the radius squared. The radius is the distance from the centre to the edge, which is half the diameter. Using the diameter by mistake is far and away the most common error here, and because the radius is squared it makes the answer four times too large.
If you only have the diameter, either halve it first or use the equivalent form:
Where πr² comes from
Imagine slicing a circle into many thin wedges, like a pizza, then arranging them alternately point-up and point-down. They interlock into a shape that gets closer to a rectangle the thinner you slice.
That rectangle’s height is the radius. Its width is half the circumference, because half the wedge tips point one way and half the other. Half of 2πr is πr, so the area is πr × r, which is πr². Nothing is lost in the rearrangement, so that is the circle’s area.
All four circle formulas
| You know | Area | Circumference |
|---|---|---|
| Radius r | πr² | 2πr |
| Diameter d | πd² / 4 | πd |
| Circumference C | C² / (4π) | — |
| Area A | — | √(4πA) |
A worked example
A circle has a radius of 5 cm.
- Square the radius. 5² = 25
- Multiply by π. 25 × 3.14159 = 78.54 cm²
The exact answer is 25π cm². Leaving it in that form is more precise than any decimal, which is why exam answers are often written that way, and the calculator shows both.
The circumference of the same circle is 2 × π × 5 = 31.42 cm.
What π actually is
π is the ratio of any circle’s circumference to its diameter. Every circle, from a coin to a planet’s orbit, gives the same ratio: roughly 3.14159.
It is irrational, meaning its decimal expansion never ends and never repeats, so it cannot be written exactly as a fraction. 22/7 is a familiar approximation and is accurate to about two decimal places, which is close enough for most practical work but not for engineering.
Area scales with the square of the radius
This catches people out constantly. Double the radius and the area becomes four times larger, not twice. Triple it and the area is nine times larger.
| Radius | Circumference | Area |
|---|---|---|
| 5 cm | 31.4 cm | 78.5 cm² |
| 10 cm | 62.8 cm | 314.2 cm² |
| 15 cm | 94.2 cm | 706.9 cm² |
| 20 cm | 125.7 cm | 1,256.6 cm² |
This is why a 16 inch pizza is not slightly bigger than a 12 inch one but 78 percent bigger, and why two 12 inch pizzas give you less food than one 16 inch. Pizza is priced by diameter and eaten by area, which is the single most useful application of this formula in ordinary life.
Where circle area comes up
- Pipes and cables. Flow capacity depends on cross-sectional area, so doubling a pipe’s diameter quadruples what it can carry.
- Chip manufacturing. Silicon wafers are circular, and yield per wafer is driven by its area, which is why the industry moved from 200 mm to 300 mm wafers.
- Camera sensors and lenses. Light gathered is proportional to aperture area, so each full stop doubles the area rather than the diameter.
- Cooling fans. Airflow scales with blade sweep area, which is why a larger, slower fan moves the same air more quietly than a small fast one.
- Materials and cost. Circular tabletops, rugs, tank bases and manhole covers are all priced by area.
Frequently asked questions
What is the formula for the area of a circle?
The area equals pi times the radius squared, written A = pi r squared. If you only have the diameter, halve it first to get the radius, or use A = pi d squared divided by 4.
What is the area of a circle with radius 5?
It is about 78.54 square units, or exactly 25 pi. Square the radius to get 25, then multiply by pi.
Do I use the radius or the diameter?
The radius, which is half the diameter. Using the diameter by mistake makes the answer four times too large, because the radius is squared in the formula.
How do I find the area if I only know the circumference?
Divide the circumference by 2 pi to get the radius, then use A = pi r squared. You can also go directly with A = C squared divided by 4 pi.
How do I find the radius from the area?
Divide the area by pi, then take the square root. A circle of area 78.54 has a radius of the square root of 25, which is 5.
What happens to the area if I double the radius?
It becomes four times larger, not twice. Area grows with the square of the radius, so tripling the radius multiplies the area by nine.
What is pi?
Pi is the ratio of a circle’s circumference to its diameter, the same for every circle, and roughly 3.14159. It is irrational, so its decimals never end or repeat and it cannot be written exactly as a fraction.
Why is a 16 inch pizza so much bigger than a 12 inch one?
Because area grows with the square of the size. A 16 inch pizza has about 78 percent more area than a 12 inch one, so two 12 inch pizzas actually give you less food than a single 16 inch.