Circle Area & Circumference Calculator
Circle Area & Circumference Calculator
A circle is defined entirely by its radius - the distance from the center to any point on the edge. Enter the radius, and this calculator finds the area, circumference (the distance around the circle), and diameter, along with a diagram and the full step-by-step working.
Both formulas scale directly with the same radius but in different ways — area grows with the radius squared (πr²) while circumference grows linearly (2πr) — which is why doubling a circle's radius quadruples its area but only doubles the distance around its edge, a distinction that trips people up in geometry problems involving scaling. If you only know the diameter rather than the radius, simply halve it first — the diameter is always exactly twice the radius by definition, for any circle.
- Area = πr², so a circle with radius 5 has an area of π × 5² ≈ 78.54 square units.
- Circumference = 2πr, for the same circle that's 2 × π × 5 ≈ 31.42 units - this is the distance you'd walk if you traced the circle's edge exactly once.
- If you only know the diameter, halve it to get the radius (r = d/2) before using these formulas - a common source of errors is plugging the diameter directly into the area formula.
How do I find the area of a circle?
Use Area = πr², where r is the radius. A circle with radius 5 has an area of π × 5² ≈ 78.54.
What's the difference between circumference and perimeter?
They mean the same thing - the total distance around the shape - but "circumference" is the term used specifically for circles, while "perimeter" is used for polygons.
Circle Area & Circumference Calculator
A circle is defined entirely by its radius - the distance from the center to any point on the edge. Enter the radius, and this calculator finds the area, circumference (the distance around the circle), and diameter, along with a diagram and the full step-by-step working.
Both formulas scale directly with the same radius but in different ways — area grows with the radius squared (πr²) while circumference grows linearly (2πr) — which is why doubling a circle's radius quadruples its area but only doubles the distance around its edge, a distinction that trips people up in geometry problems involving scaling. If you only know the diameter rather than the radius, simply halve it first — the diameter is always exactly twice the radius by definition, for any circle.
- Area = πr², so a circle with radius 5 has an area of π × 5² ≈ 78.54 square units.
- Circumference = 2πr, for the same circle that's 2 × π × 5 ≈ 31.42 units - this is the distance you'd walk if you traced the circle's edge exactly once.
- If you only know the diameter, halve it to get the radius (r = d/2) before using these formulas - a common source of errors is plugging the diameter directly into the area formula.
How do I find the area of a circle?
Use Area = πr², where r is the radius. A circle with radius 5 has an area of π × 5² ≈ 78.54.
What's the difference between circumference and perimeter?
They mean the same thing - the total distance around the shape - but "circumference" is the term used specifically for circles, while "perimeter" is used for polygons.