How do you calculate the square footage of a circle?

Multiply pi (about 3.14159) by the radius squared: area = π × radius². Measure the radius in feet from the center of the circle to the edge, square it, then multiply by 3.14159. A circle with a 10 ft radius is 3.14159 × 100 ≈ 314 sq ft.

What is the difference between radius and diameter?

The diameter is the full distance across a circle through its center; the radius is half of that, measured from the center to the edge. The area formula uses the radius, so if you measured the diameter, divide it by 2 first. A 20 ft diameter means a 10 ft radius.

How do you find the square footage of a semicircle?

Calculate the full circle's area with π × radius², then divide by 2, because a semicircle is exactly half a circle. For a semicircle with a 10 ft radius, that's 3.14159 × 100 = 314.16, halved to about 157 sq ft.

How do I calculate a circle's area if I only know the diameter?

Divide the diameter by 2 to get the radius, then use area = π × radius². You can also do it in one step: area = π × (diameter ÷ 2)². For a 20 ft diameter, the radius is 10 ft, so the area is 3.14159 × 100 ≈ 314 sq ft.

Circle Square Footage Calculator

Fórmula y guía

Cómo se calcula

A circle's area depends only on its radius — the distance from the center to the edge. Because the radius is squared, small measuring errors grow quickly, so measure carefully and work from the center outward.

1Measure the radius in feet — the straight-line distance from the center of the circle to its edge.
2If you only have the diameter (edge to edge through the center), divide it by 2 to get the radius.
3Square the radius by multiplying it by itself (radius × radius).
4Multiply that result by pi (3.14159) to get the area in square feet.

Radius	10 ft
Radius squared (10 × 10)	100 sq ft
× pi (3.14159)	≈ 314.16 sq ft
Total area	≈ 314 sq ft

Precisión y supuestos

Measure the radius from the exact center of the circle to the edge; being off-center understates the area.
If you measured the diameter (all the way across), divide it by 2 before squaring — never square the diameter itself.
For a semicircle (half a circle), calculate the full circle area and halve it.
For a ring or annulus (a circle with a hole, like a round pool with a deck), find each circle's area and subtract the inner from the outer.

Consejos y reglas clave

Radius vs. diameter: the radius is half the diameter, and the formula π × radius² uses the radius, so always convert first.
Pi (π) is approximately 3.14159; using 3.14 is close enough for most projects, but the extra digits improve accuracy on large circles.
A semicircle is exactly half the area of the full circle — calculate π × radius² and divide by 2.
For a ring, subtract the inner circle's area from the outer circle's area to get only the covered band.

How to calculate the square footage of a circle

The square footage of a circle is its surface area measured in square feet, and it comes from one clean formula: area = π × radius². Pi is a constant, roughly 3.14159, and the radius is the distance from the center of the circle to its edge. Because the radius is squared, the area grows fast as the circle widens — doubling the radius quadruples the area — so an accurate radius is the whole game.

To measure, find the center of the circle and run a tape straight out to the edge; that length in feet is your radius. Square it (multiply it by itself), then multiply by 3.14159. For a round patio with a 10 ft radius, that's 10 × 10 = 100, then 100 × 3.14159 ≈ 314 sq ft. The calculator above does this instantly — enter a radius and read the result, or switch to diameter if that's easier to measure.

Radius, diameter, and the mistakes to avoid

The single most common error is squaring the diameter instead of the radius. The diameter is the full distance across the circle through the center, and the radius is exactly half of it. If you measured across a round space and got 20 ft, that's the diameter — divide by 2 to get a 10 ft radius before you square anything. Squaring the diameter would give roughly four times the true area.

Diameter is often the easier field measurement because you don't have to locate the exact center; you just stretch the tape across the widest point. That's fine — just remember area = π × (diameter ÷ 2)². If your round space is really a pool, the same math gives the water surface area, and for straight-sided spaces the triangle calculator handles the angled shapes a circle can't.

Semicircles, rings, and turning area into cost

Not every round shape is a full circle. A semicircle — a half-round patio or bay window nook — is exactly half a circle, so calculate the full area with π × radius² and divide by 2. A ring or annulus, like a circular walkway around a fountain or the deck around a round pool, is a circle with a smaller circle removed: work out the outer circle's area, work out the inner circle's area, and subtract the inner from the outer to get just the band you're covering.

Once you have the square footage, turning it into a materials order or a budget is a short step. Multiply the area by your price per square foot with the square footage cost calculator to estimate what a round patio, garden, or pool project will actually cost.

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