# Area of a Circle Calculator

Calculate the area of a circle from its radius, diameter, or circumference. See the formula A = πr² worked out step by step with all circle measurements.

## What this calculates

Find the area of any circle instantly. Enter the radius, diameter, or circumference you know and this calculator computes the area along with all other circle measurements.

## Inputs

- **I know the...** — options: Radius, Diameter, Circumference — Select which measurement you know.
- **Value** — The measurement of the selected property.

## Outputs

- **Area** — The area enclosed by the circle.
- **Radius** — Distance from center to edge.
- **Diameter** — Distance across the circle through the center.
- **Circumference** — The perimeter of the circle.

## Details

The area of a circle measures how much space the circle encloses. There are three common ways to calculate it depending on which measurement you have.

**From the radius:**

A = πr²

This is the most direct formula. If a circle has radius 7, its area is π(7²) = 49π = 153.938 square units.

**From the diameter:**

A = π(d/2)² = πd²/4

Since the diameter is twice the radius, divide it by 2 first. A circle with diameter 10 has area = π(5²) = 25π = 78.54 square units.

**From the circumference:**

A = C²/(4π)

First find the radius with r = C/(2π), then compute the area. If the circumference is 31.42, then r = 31.42/(2π) = 5.0, and A = π(25) = 78.54 square units.

**Practical uses:** Circle area calculations come up in pipe sizing, pizza comparisons, irrigation coverage, wheel and gear design, and any scenario where you need the surface area of a round object.

## Frequently Asked Questions

**Q: What is the formula for the area of a circle?**

A: The formula is A = πr², where r is the radius. For example, a circle with radius 4 has area = π(16) = 50.2655 square units. If you only know the diameter, use A = π(d/2)². If you know the circumference, use A = C²/(4π).

**Q: How do I find circle area from the diameter?**

A: Divide the diameter by 2 to get the radius, then use A = πr². For a circle with diameter 12: radius = 6, area = π(36) = 113.097 square units. The shortcut formula is A = πd²/4.

**Q: Why is pi used in circle calculations?**

A: Pi (approximately 3.14159) is the ratio of every circle's circumference to its diameter. It naturally appears in any formula involving circles because it captures the fundamental relationship between a circle's linear dimensions and its curved shape.

**Q: How does doubling the radius affect the area?**

A: Doubling the radius quadruples the area because area depends on the square of the radius. If a circle with radius 3 has area 28.27, a circle with radius 6 has area 113.10, which is exactly 4 times larger. This is why a 16-inch pizza is more than twice the food of an 8-inch pizza.

**Q: Can I find the area from the circumference?**

A: Yes. Use the formula A = C²/(4π). For example, if the circumference is 20, then A = 400/(4π) = 400/12.566 = 31.831 square units. This works because C = 2πr, so r = C/(2π), and substituting into A = πr² gives A = C²/(4π).

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Source: https://vastcalc.com/calculators/math/area-of-circle
Category: Math
Last updated: 2026-04-08