Circle Area and Circumference Calculator

Math Geometry • Basic Shapes and Properties

Written by STEM Calculators Team Published January 21, 2026 Updated February 24, 2026

Instantly compute circle area and circumference from a radius or diameter.

Inputs accept 1e-3, pi, e, sqrt(2), sin(), cos(), tan(), ln(), log(), abs(). Use * for multiplication.

Choose “Given”, enter a value, then click Calculate.

Circle diagram (pan/zoom enabled)

Tip: use the mouse wheel / pinch to zoom the circle.

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Theory

Circle basics

A circle is the set of points at a fixed distance from a center. That fixed distance is the radius \(r\). The diameter \(d\) spans the circle through the center.

Radius–diameter relationship

\[ d = 2r,\qquad r=\frac{d}{2}. \]

Area

The area (surface enclosed) of a circle grows with the square of the radius:

\[ A = \pi r^2. \]

Circumference

The circumference (distance around the circle) is:

\[ C = 2\pi r = \pi d. \]

Units: if \(r\) is in cm, then \(A\) is in cm\(^2\) and \(C\) is in cm.

Common checks & tips

\(r>0\) and \(d>0\) are required for a valid circle.
If you know \(d\), compute \(r=d/2\) first, then apply \(A=\pi r^2\) and \(C=2\pi r\).
Doubling the radius multiplies the area by 4, but only doubles the circumference.

Frequently Asked Questions

How do I calculate the area and circumference of a circle from the radius?

Use A = pi x r^2 for area and C = 2 x pi x r for circumference. Enter r in the calculator to get both results with the working steps.

How do I use the diameter to find circle circumference and area?

Convert diameter to radius with r = d/2, then use A = pi x r^2 and C = 2 x pi x r. Equivalently, circumference can be computed directly by C = pi x d.

Why are the units for area squared?

Area measures surface size, so its unit is length squared. For example, if the radius is in cm, the area is in cm^2 while circumference is in cm.

Can I use pi or scientific notation in the inputs?

Yes. The calculator accepts entries like pi, sqrt(2), and 1e-3, and it evaluates them before applying the circle formulas.

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Frequently Asked Questions

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