Calculators
Circle Area & Circumference
Enter a circle's radius to get its area, circumference and diameter.
About the Circle Area & Circumference
The Circle Calculator works out a circle's radius, diameter, circumference and area from any one of them, in the unit you choose. It also gives the area of a semicircle and the largest square that fits inside, with a diagram of your circle.
What you can do with the Circle Area & Circumference
- Start from anything: Enter the radius, diameter, circumference or area.
- Your unit: Results in the unit you choose.
- Extras: Semicircle area and the largest square that fits inside.
- Diagram: A drawing of your circle with its measurements.
The formulas
Area = π × r², circumference = 2 × π × r and diameter = 2 × r, where r is the radius. If you only know the circumference, say you wrapped a tape around a tree, choose "Circumference" and the calculator works out the rest.
Area grows with the square
Doubling a circle's radius makes its area four times bigger. That's why an 18-inch pizza (about 254 square inches) has more pizza than two 12-inch pizzas put together (about 226 square inches).
Practical uses
Working out the area of a round table or garden bed, the length of edging needed around a circular path, the size of a round cake tin, or the cross-section of a pipe.
Related tools
Frequently Asked Questions
How do I find the radius from the circumference?
Choose "Circumference" and type it in. Manually: divide by 2π (about 6.283).
What value of π does this use?
The full precision value built into the browser, 3.141592653589793.
What units is the answer in?
The unit you pick, and square units for area, like cm² or ft².
How do I find the radius if I only know the area?
Divide the area by π and take the square root: r = √(A ÷ π). In this tool, choose Area under "I know the", type the area, and it works out the radius, diameter and circumference for you. For example, an area of 78.5398 cm² gives a radius of 5 cm.
Is the answer different if I use 22/7 instead of π?
Slightly. With 22/7, a circle of radius 7 cm has an area of exactly 154 cm², while full-precision π gives 153.938 cm². School textbooks often use 22/7 or 3.14, so expect a small difference in the last digits when you compare with a worked answer.
What happens to the area if I double the radius?
The area becomes four times bigger, because area depends on the radius squared. The circumference only doubles. That is why a 12-inch pizza (about 113.1 sq in) has 2.25 times the area of an 8-inch pizza (about 50.3 sq in), not 1.5 times.
How do I work out the circumference from the diameter?
Multiply the diameter by π, since circumference = π × d. A wheel or pipe with a 1 m diameter has a circumference of about 3.1416 m. Pick Diameter under "I know the" and the tool shows the circumference along with the radius and area.
Why does my answer look wrong after I measured with a tape?
The most common mistake is mixing up radius and diameter. A tape across the middle of a circle measures the diameter, which is twice the radius. If you type that number while Radius is selected, the area comes out four times too large, so pick Diameter instead.
What is the largest square that fits inside a circle?
Its side is the radius × √2, or about 1.4142 × r, because the square's diagonal equals the circle's diameter. For a radius of 5 cm the square is about 7.0711 cm a side. The tool lists this as "Square that fits inside" below the main results.
How do I find the area of a semicircle?
A semicircle is half a circle, so its area is π × r² ÷ 2. For a radius of 5 cm that is about 39.2699 cm². The tool shows the semicircle area automatically, which helps with arched windows, half-round tables or semicircular garden beds.
How do I find the area of a round plot or room in square feet?
Choose the feet unit, select Radius or Diameter, and enter the measurement in feet. The area is then shown in square feet. A circular plot with a 10 ft radius covers about 314.16 sq ft. Only the unit you pick is used, so measure everything in feet first.
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