Circle calculator
Enter one measurement of a circle, get the other three.
How do I find the area of a circle?
Area = π × r², where r is the radius. A circle with a 5 ft radius has an area of 3.14159 × 25 = 78.54 ft².
How do I find the circumference?
Circumference = 2 × π × r, or π × d. A 5 ft radius gives 2 × 3.14159 × 5 = 31.42 ft around.
How do I get the diameter from the circumference?
Divide by π: a tree trunk 94.25 inches around is 94.25 ÷ 3.14159 = 30 inches across.
Is one 12-inch pizza bigger than two 8-inch pizzas?
Yes. A 12-inch pizza is 113.1 in² (π × 6²); two 8-inch pizzas are 2 × π × 4² = 100.5 in². Area grows with the square of the size.
What is π?
The ratio of any circle's circumference to its diameter, about 3.14159265. The calculator uses the full precision of your device, not 3.14.
How do I find the radius if I only know the area?
Turn A = πr² around: r = √(A ÷ π). A circular patio of 100 ft² has a radius of √(100 ÷ π) = 5.64 ft and a diameter of 11.28 ft. In the calculator, choose Area as the value you know.
How do I find the area from the diameter?
Halve the diameter first, then square: A = π × (d ÷ 2)². A patio 10 ft across has r = 5 ft and an area of 78.54 ft². The same thing in one step is A = πd² ÷ 4.
Why does my textbook answer differ in the last digits?
Textbooks usually round π to 3.14 (or use 22/7). With r = 2.5 ft the OpenStax answer is 19.625 ft², while the full value of π gives 19.635 ft², a difference of about 0.05%. Both are right for the rounding they use.
The formulas and what they assume
The radius r runs from the center to the edge and the diameter is d = 2r. The circumference is C = 2πr = πd and the area is A = πr² (OpenStax Prealgebra 2e, section 9.5). Run backwards, r = C ÷ 2π and r = √(A ÷ π). Choose in the calculator which of the four quantities you know and it returns the other three in your unit, with the area in square units. The formulas describe a perfect circle; for an oval use the ellipse calculator.
Worked example: a round sandbox
OpenStax Example 9.41 is a circular sandbox with a radius of 2.5 feet. Its circumference is 2π × 2.5 = 15.71 ft and its area is π × 2.5² = 19.63 ft². The book prints 19.625 because it rounds π to 3.14. In Example 9.43 the circumference is 47.1 cm and the question runs the other way: the diameter is 47.1 ÷ π = 14.99 cm, which the book rounds to 15 cm.
Common mistakes
The classic one is typing a diameter where the radius belongs: a patio 10 ft across has an area of 78.54 ft², but 10 entered as the radius gives 314.16 ft², four times too much, because area grows with the square of the size. Mixing units is the second: with the radius in inches the area comes out in square inches, and one square foot is 144 square inches, not 12. Finally, do not round π early: rounding it to 3.14 in the middle of a long calculation passes a small error into every later step.
Sources: OpenStax, Prealgebra 2e, section 9.5 “Solve Geometry Applications: Circles and Irregular Figures” (properties of circles, Examples 9.41 and 9.43). Related tools: area calculator, ellipse calculator, arc length calculator and circle equation calculator. How we check our calculators.