How it works
A circle's area only ever depends on its radius, so whichever of radius, diameter or circumference you start from, the first step is always to work back to the radius — then area follows in one step.
area = π × radius²
Worked example
A circle with radius 5.
- Square the radius: 5² = 25.
- Multiply by π: π × 25 = 78.54.
The area is 78.54.
Common questions
Why does area use radius squared, not diameter?
The πr² formula comes directly from integrating a circle's area in terms of its radius. Diameter-based versions exist (area = π × (d/2)²) but they're the same formula after substituting d/2 for r — squaring the radius is simply the more direct route.
How does this differ from the Circumference Calculator?
Same three starting values (radius, diameter, circumference), different output — this page always returns area (a squared measurement); the Circumference Calculator always returns the distance around the circle (a plain length).
What if I only know the circumference?
Pick "Circumference" from the chips and enter it directly — this calculator works back to the radius first (radius = circumference ÷ 2π), then squares it, exactly as if you'd measured the radius yourself.