Area of Circle Calculation & Formula

This calculator finds the area of a circle from its radius, diameter, or circumference. Enter the value you know, and the area is returned in the same unit system (square meters, square feet, etc.). The first result is the area; the second is the radius if you started from a diameter or circumference.

Formula

The area of a circle is given by the formula:

A = π × r²

• A — area, in square units (m², cm², ft², etc.)
• π (pi) — approximately 3.14159, the ratio of a circle’s circumference to its diameter
• r — radius, the distance from the center to the edge, in the same linear unit as the area’s square unit

If you have the diameter d instead, use A = π × (d/2)². If you have the circumference C, use A = C² / (4π).

Worked Example

Using the default radius of 5 meters:

1. Square the radius: 5² = 25
2. Multiply by π: 25 × 3.14159 ≈ 78.54

The area is approximately 78.54 square meters. The circumference is 2 × π × 5 ≈ 31.42 meters. The calculator’s output shows the same values.

When to Use This Calculation

Circle area calculations appear in many everyday tasks:

• Finding the surface area of a round table, rug, or garden bed
• Estimating paint or material needed for a circular surface
• Calculating the cross-sectional area of a pipe or wire
• Working with pizza sizes, circular pools, or manhole covers

The formula works for any circle, regardless of size, as long as you have one accurate measurement.

Common Mistakes and How to Avoid Them

The most frequent error is mixing up radius and diameter. The radius is half the diameter. If a problem gives you a diameter of 10 cm, the radius is 5 cm — using 10 as the radius gives an area four times too large.

Another mistake is forgetting to square the radius before multiplying by π. The order matters: r² first, then multiply by π. Also, be consistent with units. If you measure the radius in inches, the area is in square inches; if you want square feet, convert the radius to feet first (divide inches by 12).

Rounding too early can also skew results. Keep π as 3.14159 or use the π button on a calculator until the final step, then round to the needed precision.

Limits of the Formula

The formula A = πr² is exact for a perfect Euclidean circle. Real-world objects may not be perfectly round, so the result is an approximation of the true surface area. For very large circles (like the Earth), the curvature of the sphere means the planar formula is only accurate for small patches. For most practical purposes — from pizza to roundabouts — the formula is accurate to far more decimal places than your measurements justify.

Also note that the area is always positive. If you get a negative result, check your input; a negative radius is physically meaningless.

How to Measure the Radius

If you don’t have the radius given, measure the diameter (the distance across the circle through the center) and divide by 2. For a physical object, you can often measure the diameter with a ruler or tape measure. For a circle drawn on paper, you can measure the diameter directly. If you only have the circumference (the distance around the circle), divide it by 2π to get the radius. For example, a circle with a circumference of 31.4 cm has a radius of about 5 cm.

Frequently Asked Questions

How do I find the area if I only have the diameter?

Divide the diameter by 2 to get the radius, then use A = πr². Or directly use A = π(d/2)². For a diameter of 10 cm, the radius is 5 cm, so the area is π × 25 ≈ 78.54 cm².

What is the area of a circle with a radius of 1?

The area is exactly π, approximately 3.14159 square units. This is a useful reference: a circle with radius 1 has an area equal to π.

Why is the formula πr² and not something like 2πr?

2πr is the circumference, not the area. The area formula comes from calculus (integration) or from the geometric insight that a circle can be rearranged into a rectangle of length πr and height r. The area is the product: πr × r = πr².

Can I use this calculator for a semicircle?

Yes. Calculate the full circle area, then divide by 2. For a semicircle with radius 5 m, the full area is 78.54 m², so the semicircle area is 39.27 m².

What if my radius is in inches but I want square feet?

Convert the radius to feet first (divide inches by 12), then square and multiply by π. For example, a radius of 24 inches is 2 feet, so the area is π × 2² = 12.57 ft². Do not compute in inches and then try to convert square inches to square feet by dividing by 12; you must divide by 144 (12²).

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in r | Radius | m | 5 | 0
out area | Area | m² | pi * r^2 | 2
out circum | Circumference | m | 2 * pi * r | 2