Circle Calculator

How this is calculated

Whichever value you enter — radius, diameter, circumference, or area — is first converted to the radius, then used to compute all four measurements together.

Circle formulas

Every measurement of a circle can be derived from its radius, since the ratio between a circle's circumference and its diameter is the constant pi (π ≈ 3.14159).

Formulas

Example: a circle with a 5-unit radius has an area of π × 5² ≈ 78.54 square units and a circumference of 2 × π × 5 ≈ 31.42 units.

Quick reference table

Common pitfalls

• Confusing radius and diameter — the most common circle-math mistake; always check which one you actually have before applying a formula.
• Squaring the wrong value — area squares the radius, not the diameter; using the diameter directly in the area formula gives a result four times too large.
• Rounding pi too early — using 3.14 instead of a more precise value introduces small errors that compound in larger circles.

Tips

• If you only have the diameter, divide by 2 to get the radius before using any other formula.
• Area grows with the square of the radius, so doubling the radius quadruples the area — not just doubles it.

Frequently asked questions

What is the formula for the area of a circle? Area = π × r², where r is the radius. A circle with a 5-unit radius has an area of π × 5² ≈ 78.54 square units.

What is the circumference formula for a circle? Circumference = 2 × π × r, or equivalently π × d, where r is the radius and d is the diameter.

How do I find the radius from the area of a circle? Divide the area by π, then take the square root: r = √(Area ÷ π).

How do I find the area from the circumference? First find the radius by dividing the circumference by 2π, then apply the area formula: Area = π × r².

What is the relationship between radius and diameter? The diameter is always exactly twice the radius: d = 2r, and conversely r = d ÷ 2.

Why is pi used in circle formulas? Pi (π ≈ 3.14159) is the fixed ratio between any circle's circumference and its diameter — it appears in every circle formula because that ratio never changes, regardless of the circle's size.

Worked examples

Example 1 — Known radius: radius 7 → diameter 14, area ≈ 153.94, circumference ≈ 43.98.

Example 2 — Known diameter: diameter 20 (radius 10) → area ≈ 314.16, circumference ≈ 62.83.

Example 3 — Known area: area = 100 → radius = √(100 ÷ π) ≈ 5.64, circumference ≈ 35.45.