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

Radius	Diameter	Area	Circumference
3	6	28.27	18.85
5	10	78.54	31.42
10	20	314.16	62.83

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.

Everyday circle problems

Why area grows faster than size

Area depends on the square of the radius, so doubling the radius multiplies the area by four. A 16-inch pizza has an area of about 201 square inches, while a 12-inch pizza has about 113, so it is almost 78% more pizza, not 33% more. Compare areas, not widths, when judging value.

Distance and wheels

The circumference of a wheel is the distance it travels in one full turn. A bicycle wheel with a 0.7 m diameter covers π × 0.7 ≈ 2.2 m per revolution, so about 455 turns cover a kilometre.

Quick conversions between measurements

Known value	Find	Formula
Diameter	Radius	r = d ÷ 2
Circumference	Diameter	d = C ÷ π
Area	Radius	r = √(A ÷ π)

More questions

Which value of pi does the calculator use? It uses the full-precision value of pi available in your browser, not a rounded 3.14, so results are more accurate.

Do units matter? Use the same unit for every value. Lengths come out in that unit, and areas come out in that unit squared.