Circle Calculator
Calculate area, circumference, and diameter
Circle Formulas
Frequently Asked Questions
How do you calculate the area of a circle from the diameter?
First find the radius: r = d/2. Then apply A = πr². For a circle with diameter 10: r = 5, so A = π × 25 ≈ 78.54 square units. The calculator accepts either radius or diameter — entering one automatically updates the other.
What is the circumference of a circle?
Circumference C = 2πr = πd, where r is radius and d is diameter. For r = 5: C = 2 × π × 5 ≈ 31.42 units. This is the total length of the circle’s boundary. It represents the distance you would travel walking exactly once around the circle.
What is the relationship between radius and diameter?
The diameter is always exactly twice the radius: d = 2r. Equivalently, r = d/2. The diameter is the longest possible chord — a straight line passing through the center connecting two points on the circle. Entering either value in the calculator automatically computes the other.
Why does the circle area formula use π?
Pi (π) is the constant ratio of any circle’s circumference to its diameter — approximately 3.14159. It appears in the area formula A = πr² because the area of a circle was proven by Archimedes to be equivalent to a right triangle with legs equal to the radius and circumference.
What happens if I enter a radius of zero in the circle calculator?
A radius of zero gives area = 0 and circumference = 0, which is mathematically correct — a circle with zero radius is a single point with no enclosed area. Negative radii have no geometric meaning; the calculator will compute with the absolute value but physical interpretation requires a positive radius.