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Circle Area Calculator

Calculate circle area, circumference, radius, and diameter with exact π and decimal working.

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How to Use the Circle Area Calculator – Area, Radius, Diameter

1Select your known dimension: Radius (r), Diameter (d), Circumference (C), or Area (A).
2Enter the numeric value into the dimension input box.
3View the calculated area, circumference, radius, and diameter simultaneously.
4Review the worked step-by-step geometry formulas using π.

Formula & How It Works

Circle Geometry Formulas & Relations

Area = π × r² = (π ÷ 4) × d² | Circumference = 2 × π × r

For any circle, area is proportional to the square of its radius multiplied by π (pi ≈ 3.14159265). Circumference is the linear boundary distance equal to 2πr or πd.

Worked Examples

Standard Radius Input

Input: Radius: 5 units

Explanation: Area = π × 5² = 25π ≈ 78.5398. Circumference = 2 × π × 5 = 10π ≈ 31.4159.

Result: Area: 78.5398 sq units | Circumference: 31.4159 units | Diameter: 10 units

Circular Dining Table by Diameter

Input: Diameter: 4 feet

Explanation: Radius = 4 / 2 = 2 ft. Area = π × 2² = 4π ≈ 12.5664 sq ft.

Result: Area: 12.5664 sq ft | Circumference: 12.5664 ft | Radius: 2 ft

Tree Trunk Girth (Circumference)

Input: Circumference: 62.83 inches

Explanation: Radius = C / (2π) = 62.83 / 6.28318 = 10.00 inches.

Result: Radius: ~10.00 inches | Diameter: ~20.00 inches | Area: ~314.16 sq in

Unit Circle Benchmark

Input: Radius: 1 unit

Explanation: Unit circle has radius 1, giving area π and circumference 2π.

Result: Area: 3.1416 sq units (π) | Circumference: 6.2832 units (2π)

Frequently Asked Questions

What is the formula for the area of a circle?▼

The formula is Area = π × r², where r is the radius of the circle and π (pi) is approximately 3.14159.

How do you find the area of a circle with diameter?▼

Divide the diameter by 2 to find the radius, then square the radius and multiply by π: Area = π × (d/2)².

What is the difference between radius and diameter?▼

The radius is the distance from the center of the circle to its edge. The diameter is the full distance across the circle passing through the center (Diameter = 2 × Radius).

What is circumference?▼

Circumference is the total linear perimeter or distance around the outer boundary of the circle (Circumference = 2πr = πd).

Can I enter the circumference to find the area?▼

Yes, our calculator allows you to select 'Circumference' as the input to derive area and radius.

Does this tool work completely offline?▼

Yes, all geometric arithmetic runs locally in your web browser with zero server latency.

Last reviewed & updated: 2026-11-01

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