How do I calculate the area of a circle?

Use A = πr², where r is the radius. Square the radius, then multiply by pi.

How do I calculate circumference?

Use C = 2πr if you know the radius, or C = πd if you know the diameter.

What is the radius of a circle?

The radius is the distance from the center of the circle to any point on the edge.

What is the diameter of a circle?

The diameter is the distance across the circle through the center. It is twice the radius.

What is the formula for circle area?

The circle area formula is A = πr².

What is the formula for circumference?

The circumference formula is C = 2πr or C = πd.

How do I find radius from area?

Use r = √(A ÷ π). Divide the area by pi, then take the square root.

How do I find radius from circumference?

Use r = C ÷ 2π. Divide the circumference by two times pi.

Why is area written in square units?

Area measures two-dimensional space, so it uses square units such as cm², m², or in².

What value of pi should I use?

For most everyday calculations, π ≈ 3.14159 is accurate enough. This calculator uses JavaScript’s built-in Math.PI value.

Circle Calculator | Area, Circumference, Radius & Diameter

Choose known value

Enter radius

Unit

Decimal precision

Show exact π formUseful for symbolic answers.

Formula-aware · Unit labels · Updated May 2026

Area

78.54 units²

Space inside the circle.

Circumference

31.42 units

Distance around the circle.

Radius

5 units

Center-to-edge distance.

Diameter

10 units

Edge-to-edge through the center.

Formula used

r is known directly

A radius of 5 means the diameter is 10 because diameter is twice the radius.

The circumference is about 31.42 units, which is the distance around the circle.

The area is about 78.54 units², which measures the space inside the circle.

Area uses square units, while circumference uses regular length units.

Changing the radius has a squared effect on area because the formula uses r².

Your selected input mode is radius, so the calculator first finds the radius.

Circle Formulas

Diameter

d = 2r

Radius from diameter

r = d ÷ 2

Circumference

C = 2πr

Circumference from diameter

C = πd

Area

A = πr²

Radius from circumference

r = C ÷ 2π

Radius from area

r = √(A ÷ π)

Variable Explanations

r

Radius: distance from the center to the edge.

d

Diameter: distance across the circle through the center.

C

Circumference: distance around the circle.

A

Area: space inside the circle.

π

Pi: approximately 3.14159.

Units

Radius, diameter, and circumference use length units; area uses square units.

Circle Diagram and Visual Explanation

Radius

The radius goes from the center to the edge.

Diameter

The diameter passes through the center from edge to edge.

Circumference

The circumference is the outside boundary.

Area

The area is the inside region of the circle.

Worked Examples

Find area and circumference from radius 5

Formula: A = πr² and C = 2πr

Substitution: A = π × 5², C = 2π × 5

Answer: A ≈ 78.54, C ≈ 31.42

Radius is used directly in both formulas.

Find radius and area from diameter 12

Formula: r = d ÷ 2, A = πr²

Substitution: r = 12 ÷ 2 = 6, A = π × 6²

Answer: r = 6, A ≈ 113.10

Always halve the diameter before using the area formula.

Find radius from circumference 31.4

Formula: r = C ÷ 2π

Substitution: r = 31.4 ÷ 2π

Answer: r ≈ 5.00

Circumference is the distance around the circle.

Find radius from area 50

Formula: r = √(A ÷ π)

Substitution: r = √(50 ÷ π)

Answer: r ≈ 3.99

Area must be divided by pi before taking the square root.

Compare area when radius doubles

Formula: A = πr²

Substitution: If r doubles, r² becomes 4 times larger

Answer: Area becomes 4× larger

Area grows with the square of the radius.

Use units correctly

Formula: C uses length units, A uses square units

Substitution: r = 5 cm

Answer: C ≈ 31.42 cm, A ≈ 78.54 cm²

Circumference is length; area is space.

Radius, Diameter, Circumference, and Area

Radius

Half the diameter and the key value used in most circle formulas.

Diameter

Twice the radius and the full width through the center.

Circumference

The perimeter of the circle, or the distance around it.

Area

The space inside the circle. It grows with the square of the radius.

Common Circle Calculation Mistakes

Confusing radius and diameter.

Using diameter in the area formula without halving it first.

Forgetting square units for area.

Rounding π too early in a multi-step calculation.

Entering a negative radius or negative area.

Mixing units without converting them first.

Assuming doubling the radius only doubles the area.

Understanding Your Results

Area

The space inside the circle.

Circumference

The distance around the circle.

Radius

The distance from the center to the edge.

Diameter

The distance from edge to edge through the center.

Exact π form

The symbolic answer before decimal approximation.

Frequently Asked Questions

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