Circle Calculator

What is a Circle Calculator?

This tool calculates the key measurements of a circle — area, circumference, and diameter — from any single known value (radius, diameter, area, or circumference). It's useful for geometry homework, construction and design projects (like sizing round tables, pipes, or garden beds), and any situation where you need to quickly work out circular measurements without manually rearranging formulas.

Formulas Used

Area = π × r²  |  Circumference = 2 × π × r  |  Diameter = 2 × r, where r is the radius and π (pi) is approximately 3.14159. If you start from diameter, radius is simply diameter ÷ 2. If you start from area or circumference, the calculator rearranges these formulas to solve for the radius first.

How to Use This Tool

Enter any one known value — radius, diameter, area, or circumference — and the calculator instantly derives the other three measurements using the standard circle formulas.

Examples

Example 1: A circle with radius 5 cm has an area of π × 5² ≈ 78.54 cm², a circumference of 2 × π × 5 ≈ 31.42 cm, and a diameter of 10 cm.

Example 2: A circle with diameter 20 cm has a radius of 10 cm, an area of π × 10² ≈ 314.16 cm², and a circumference of 2 × π × 10 ≈ 62.83 cm.

Frequently Asked Questions

What is pi (π) and why is it used? Pi is the ratio of a circle's circumference to its diameter, approximately 3.14159, and it is constant for every circle regardless of size, which is why it appears in every circle formula.

What's the difference between area and circumference? Area measures the space enclosed inside the circle (in square units), while circumference measures the distance around the outer edge of the circle (in linear units).

Can I calculate a circle from its area alone? Yes — the calculator rearranges the area formula to solve for radius first (r = √(Area ÷ π)), then derives diameter and circumference from that.

Is this useful for real-world projects? Yes, common uses include calculating pipe or drum sizes, sizing a circular garden bed, determining how much material is needed to cover a round surface, or basic construction planning.

Does unit choice matter? No — the formulas work the same regardless of unit (cm, inches, meters, feet); just be sure to interpret the output in the same unit you entered.