Circle Area Calculator
Enter the radius and the calculator returns the diameter, circumference and area A = πr². Handy for sizing a round table, cutting a circular pizza, or any back-of-napkin geometry problem where π × r² is too much to do in your head.
How circle area is calculated
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1
Enter the radius
Any unit: cm, inches, metres. Lengths keep the unit you entered; the area is expressed in that unit squared.
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2
Other measurements derive
From the radius: diameter = 2r and circumference = 2πr, then the area follows from A = πr².
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3
Area formula applied
A = πr², with π taken to 15 significant digits internally. Results are displayed rounded to 4 decimal places.
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4
Read the results
Diameter, circumference and area in a single panel. The values update as you type.
The formulas
- Radius from diameter: r = d / 2
- Radius from circumference: r = C / (2π)
- Diameter: d = 2r
- Circumference: C = 2πr = πd
- Area: A = πr² = π(d/2)² = C² / (4π)
Reference values
| Radius | Diameter | Circumference | Area |
|---|---|---|---|
| 1 | 2 | 6.283 | 3.142 |
| 2 | 4 | 12.566 | 12.566 |
| 5 | 10 | 31.416 | 78.540 |
| 10 | 20 | 62.832 | 314.159 |
| 15 | 30 | 94.248 | 706.858 |
| 20 | 40 | 125.664 | 1,256.637 |
| 25 | 50 | 157.080 | 1,963.495 |
| 50 | 100 | 314.159 | 7,853.982 |
| 100 | 200 | 628.319 | 31,415.927 |
Everyday applications
- Pizza: a pizza with radius 7 in (diameter 14 in) has an area of about 154 in²; one with radius 5 in (diameter 10 in) about 79 in². The bigger one is roughly twice the pizza, because area scales with the square of the radius.
- Paint coverage: a circular ceiling with radius 1.5 m has an area of 7.07 m². At 12 m² per litre, one litre is enough for a single coat.
- Rugs / round tables: a round rug with radius 2.5 ft covers 19.63 sq ft; one with radius 2 ft covers 12.57 sq ft, 36% less.
- Garden irrigation: a sprinkler with a 6 m radius covers about 113 m² in a circle.
Why area scales with radius squared
Doubling the radius does not double the area, it quadruples it. A pizza with radius 8 in is (8/7)² = 1.31 times the area of one with radius 7 in: 31% more pizza at the same price per square inch.
Sectors and segments
If you need the area of a pie-slice (sector):
- A = (θ/360) × πr² for degrees
- A = (θ/2) × r² for radians
This calculator always computes the full circle. For a sector or segment, apply the formulas above with your angle.
Frequently Asked Questions
Internally 15 significant digits (the double-precision limit of the calculation). Results are displayed rounded to 4 decimal places.
Any. The calculator is unit-agnostic: enter the radius and read the result in the same unit squared (radius in cm → area in cm²).
Not directly, a circle is 2D. For a cylinder, multiply the circle area by the height. For a sphere, use V = (4/3)πr³ in a separate volume calculator.
Ellipse area = π × a × b (semi-major axis × semi-minor axis). Not the same formula; use a dedicated ellipse calculator if your shape isn’t perfectly round.
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