How to use the circle area and circumference calculator
- In I know the, pick Radius (r), Diameter (d), Area (A) or Circumference (C).
- Type the number in Value. It must be greater than 0.
- Optional: choose a Unit such as cm or ft, the Decimal places, or a Value of π of 3.14 or 22/7 if your class uses one.
- Read the area, circumference, radius and diameter. In terms of π gives the exact answer, and the lines below it show the working.
The formulas
For a circle with radius r and diameter d, the circumference is C = 2πr = πd and the area is A = πr². The diameter is d = 2r. Going the other way, r = C ÷ (2π) and r = √(A ÷ π). Combining them gives A = C² ÷ (4π), which is how the tool finds the area when you only know the circumference. π is the ratio of any circle's circumference to its diameter. See Wolfram MathWorld, Circle for the full set of relations.
Worked example with the default values
I know the Radius (r), Value = 5, no unit, 4 decimal places:
- d = 2r = 2 × 5 = 10
- C = 2πr = 2 × π × 5 = 31.4159
- A = πr² = π × 5² = 78.5398
- In terms of π: Area = 25π, circumference = 10π
Start from the area instead: for A = 100, r = √(100 ÷ π) = 5.6419 and C = 35.4491. Start from the circumference: for C = 10, r = 10 ÷ (2π) = 1.5915 and A = 7.9577. With π set to 3.14, the default radius of 5 gives an area of 78.5. With 22/7 it gives 78.5714.
Real uses
- Comparing pizzas. A 12-inch pizza (diameter) has 113.0973 in² of area. A 14-inch pizza has 153.938 in², about 36 percent more.
- A round garden bed. A bed with a 3 m radius covers 28.2743 m², and its edge is 18.8496 m long.
For a rectangular space, use the rectangle area calculator. For 3D shapes built on a circle, try the cylinder volume and sphere volume calculators, and use the area converter to change area units.
Limits and edge cases
- The unit applies to the value you enter. If you choose Area with the unit cm, enter square centimeters.
- The In terms of π line is exact. The decimal results are rounded to the places you choose.
- Zero, negative numbers and text show a message next to the field instead of a result.
- For a radius above about 1e154 the area overflows, and that row reads "too large to show".
Frequently asked questions
How do I find the area of a circle from the diameter?
Halve the diameter to get the radius, then use A = πr². Choose Diameter, enter the value, and the area appears at once. For a diameter of 10, the radius is 5 and the area is π × 5² = 78.5398.
How do I find the radius from the circumference?
Divide the circumference by 2π: r = C ÷ (2π). Choose Circumference in the I know the menu and enter the value. For C = 10, r = 10 ÷ (2π) = 1.5915.
How do I leave the answer in terms of pi?
Choose Radius or Diameter and read the line marked In terms of π. For a radius of 5, the area is 25π and the circumference is 10π, so you can write the exact answer without rounding.
Is circumference the same as perimeter?
Yes. Circumference is the perimeter of a circle, the distance all the way around it. Area measures the space inside the circle, so it is given in square units such as cm² or ft².
Sources: Wolfram MathWorld, Circle.