Circle Calculator
Find a circle's area, circumference, and diameter from its radius.
Try an example
78.5398
About this calculator
What Is a Circle?
A circle is the set of all points in a plane that are the same distance from a fixed point, called the center. That constant distance is the radius. This circle calculator works out the rest when you provide any one measurement: enter a radius, diameter, circumference or area and it returns the others.
Parts of a Circle
- Center: the point equally far from every point on the circle.
- Radius (r): the distance from the center to any point on the circle; half the diameter.
- Diameter (d): the longest distance across, passing through the center; twice the radius.
- Circumference (C): the distance around the circle.
- Arc: a portion of the circumference — a minor arc is shorter than half and a major arc longer than half.
- Chord: a line segment joining two points on the circle; a chord through the center is a diameter.
- Sector and segment: a "pizza slice" bounded by two radii and an arc, and the region between a chord and its arc.
Worked Example
A circle with radius 5 has a diameter of 10, a circumference of about 31.42, and an area of about 78.54.
Circle Formulas
- Diameter: d = 2r
- Circumference: C = 2πr = πd
- Area: A = πr² = πd² ÷ 4
- Radius from circumference: r = C ÷ 2π
- Radius from area: r = √(A ÷ π)
A circle with radius 5 has a diameter of 10, a circumference of about 31.42 and an area of about 78.54.
About Pi
π (pi) is the ratio of any circle's circumference to its diameter — about 3.14159 — and it is an irrational number, meaning its decimal digits never end or repeat. It appears throughout geometry, trigonometry, physics and statistics. For everyday work, 3.14 or 3.1416 is usually accurate enough.
Everyday Uses
Circles come up when you size a pizza, a round table or a pipe, work out how far a wheel travels in one turn, or plan a circular garden bed. Estimate the volume of material for a round slab with the Concrete Calculator, compare tire sizes with the Tire Size Calculator, or work with right triangles inside circles using the Pythagorean Theorem Calculator.
Worked example
A circle with radius 5 has a diameter of 10, a circumference of about 31.42, and an area of about 78.54.
Frequently asked questions
What if I only know the diameter or circumference?
Divide the diameter by 2, or divide the circumference by 2π, to get the radius — then enter that into the calculator.
Why does area use r² but circumference uses r?
Area scales with the square of the radius because it measures a two-dimensional space, while circumference is a one-dimensional distance around the edge — this is also why doubling the radius quadruples the area but only doubles the circumference.
