From the radius
A = π × r²
The reference formula: the radius squared, times π.
Area of a Circle Calculator
Calculate the area of a circle, meaning the surface enclosed by it, from its radius, diameter or circumference. The formulas A = πr², A = πd²/4 and A = C²/4π are explained with worked examples, and the result is shown in cm², m², in² or ft².
Area
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How does this tool work?
This calculator gives the area of a circle, strictly speaking the area of the disk it encloses, from whichever measurement you have: the radius, the diameter or the circumference. Use it to check geometry homework or to estimate the surface of a round table, a circular flower bed, an above-ground pool or a round concrete slab.
The area of a circle with radius r is A = π × r². The radius is squared, then multiplied by π ≈ 3.14159. Doubling the radius therefore multiplies the area by four: a circle with a 2 m radius covers 12.57 m², while one with a 4 m radius covers 50.27 m².
If you know the diameter d, the tool halves it before applying the formula, which is the same as A = π × d² ÷ 4. From the circumference C, it first recovers the radius, r = C ÷ (2π), which gives A = C² ÷ (4π). This is the most practical method in the real world: wrap a tape measure around a tree trunk, a column or a tank, with no need to locate the center.
The result is expressed in the square of the length unit you chose: centimeters give cm², meters give m², feet give ft² (square feet). The calculation uses the browser's value of π (about 15 significant digits); a textbook that uses π ≈ 3.14 gets a slightly smaller value, by about 0.05%.
Strictly speaking, a circle is the curved line and a disk is the flat region it surrounds. "Area of a circle" is the everyday shorthand for the area of the disk; the length of the line itself is the circumference, which has its own dedicated calculator.
How to use this tool
Pick the measurement you know
Radius, diameter or circumference: select the tab that matches the value you have.
Enter the value and its unit
Millimeters, centimeters, meters, kilometers, inches, feet or yards; both a dot and a comma work as the decimal separator.
Read the area
It is shown in the matching square unit and updates on every change, so you can compare several sizes quickly.
Formulas for the area of a circle
The same area can be calculated from three different measurements of the circle.
From the diameter
A = π × d² ÷ 4
Equivalent to the first one, since r = d ÷ 2.
From the circumference
A = C² ÷ (4π)
Handy when you measure around an object with a tape.
Radius from the area
r = √(A ÷ π)
The inverse formula, to find a dimension from a target area.
- A
- area of the disk, in square units (cm², m², ft²...)
- r
- radius: distance from the center to the circle
- d
- diameter, equal to 2r
- C
- circumference, the length of the circle, equal to 2πr
- π
- Archimedes' constant, about 3.14159
Example: r = 3 m, A = π × 9 = 9π ≈ 28.27 m².
Use cases
Geometry homework
Check the area of a circle, a semicircle or a composite figure, keeping radius and diameter clearly apart.
Garden and landscaping
Estimate the surface of a round flower bed, a circular patio or a pond to buy mulch, sod, pavers or a liner.
Construction and materials
Get the cross-sectional area of a round column, a duct or a pipe, then multiply by the height for a concrete volume.
Comparing sizes
Compare cake pans, pizzas, round screens or speakers: area grows with the square of the diameter, not in proportion to it.
Examples
From the radius
A = π × 5² = 25π ≈ 78.54 cm².
Input
r = 5 cmResult
A ≈ 78.54 cm²From the diameter
The radius is 0.6 m, so A = π × 0.36 ≈ 1.131 m².
Input
d = 1.2 m (round table)Result
A ≈ 1.131 m²From the circumference
r = 94.2 ÷ 2π ≈ 14.99 cm, then A = 94.2² ÷ 4π ≈ 706.1 cm²: that is the cross-section of the trunk.
Input
C = 94.2 cm (around a tree trunk)Result
A ≈ 706.1 cm²Above-ground pool cover
Radius of 2.285 m; π × 2.285² ≈ 16.40 m², plus an overhang for fastening the cover.
Input
d = 4.57 m (15 ft pool)Result
A ≈ 16.40 m²One 12-inch pizza or two 8-inch pizzas?
A single 12-inch pizza gives you more to eat than two 8-inch pizzas (2 × 50.27 in²).
Input
d = 12 in vs 2 × d = 8 inResult
113.1 in² vs 100.5 in²Tips and best practices
- Check whether the problem gives a radius or a diameter: mixing them up multiplies or divides the area by four.
- On a real object, measuring the circumference with a tape is often more accurate than trying to hit the diameter through the center.
- Area is measured in square units: 1 m² = 10,000 cm² (not 100), and 1 ft² = 144 in².
- For a semicircle or a quarter circle, divide the area you get by 2 or by 4.
- Keep π exact as long as possible (for example 25π cm²) and round only the final result.
Sources and references
- Weisstein E.W., Circle (opens in a new tab), Wolfram MathWorldPage in English
- Weisstein E.W., Pi (opens in a new tab), Wolfram MathWorldPage in English
Frequently asked questions
What is the formula for the area of a circle?
A = π × r², where r is the radius. With the diameter, A = π × d² ÷ 4; with the circumference, A = C² ÷ (4π). All three give the same result for the same circle.
How do you find the area of a circle with the diameter?
Divide the diameter by two to get the radius, then apply π × r². For a 10 cm diameter: radius 5 cm, area π × 25 ≈ 78.54 cm².
How do you find the radius from the area?
Divide the area by π, then take the square root: r = √(A ÷ π). An area of 50 m² corresponds to a radius of about 3.99 m.
What is the difference between the area and the circumference of a circle?
The area measures the surface of the disk and is expressed in square units (cm², m², ft²). The circumference measures the length of the outline, C = 2πr, and is expressed in length units (cm, m, ft).
Why is my result slightly different from my textbook's?
Textbooks often use π ≈ 3.14, while the tool uses π to about fifteen decimal places. For r = 10 cm, you get 314 cm² with 3.14 and 314.16 cm² with the precise value.
How do I get the area in m² when I measured in centimeters?
Enter the value in centimeters, then switch the unit selector to meters: the value is converted before the calculation. By hand, convert the radius to meters before squaring it, or divide the result in cm² by 10,000.
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