Square Footage of a Circle
Area of a circular room, patio or pad from its diameter, with the radius step shown as its own line rather than folded away inside a single formula step.
A circular patio is priced by area but poured by volume, and the area is where people go wrong: doubling the diameter quadruples the area. A 12 ft circle is 113 sq ft; a 24 ft circle is 452, not 226.
With diameter 12 ft, number of identical areas 1, waste factor 10 percent, price per square foot 0 usd, square footage comes to 124.4 sq ft — area to order. It is reached in 9 steps, the last of which is 113.09734 * (1 + 10 / 100), and each one is printed on the page with its numbers filled in. The formula is the one published by ANSI Z765 residential square footage measurement standard, not an approximation fitted to it.
Formula and sources checked · How we check
- The three sides close into a triangle
1- Area of the openings
2 * 3 * 530 sq ft- Area per shape
113.097 sq ft- Total area
113.09734 * 1113.097 sq ft- Area to order
113.09734 * (1 + 10 / 100)124.407 sq ft- Same area in square meters
124.40707 * 0.09290311.558 sq m- Same area in square yards
124.40707 / 913.823 sq yd- Same area in acres
124.40707 / 435600.003 acres- Material at that price
124.40707 * 0$0
Several at once
A job is rarely one of anything. Work out the first, add it, change the figures and add the next — the list keeps what each line was, and totals them.
How do you measure a circle you cannot cross?
Run a tape around the outside for the circumference and divide by π to get the diameter. On a round patio that is a more reliable measurement than guessing where the centre is, and it produces exactly the number this calculator asks for.
What about a ring or a border?
Work out the full circle, then the inner circle, and subtract. A 3 ft path around a 12 ft patio is 254 sq ft less 113, so 141 — not the 113 the outer figure alone suggests, and nothing like the 36 that pacing the path gives.
The formula
- The three sides close into a triangle
heron > 0 ? 1 : 0 - Area of the openings
openings * opening_w * opening_h - Area per shape
shape_rect * (length * width) + shape_wall * max(0, length * width - openings_area) + shape_border * ((length + 2 * border_width) * (width + 2 * border_width) - length * width) + shape_trapezoid * ((top_width + bottom_width) / 2 * trap_height) + shape_circle * (pi * pow(diameter / 2, 2)) + shape_annulus * (pi * (pow(diameter / 2, 2) - pow(min(inner_diameter, diameter) / 2, 2))) + shape_triangle * (base * tri_height / 2) + shape_triangle_sides * sqrt(heron) - Total area
area * rooms - Area to order
subtotal * (1 + waste / 100) - Same area in square meters
total * 0.09290304 - Same area in square yards
total / 9 - Same area in acres
total / 43560 - Material at that price
total * price
Formula from ANSI Z765 residential square footage measurement standard, NIST Office of Weights and Measures.
The same calculator, other cases
Undecided? The Square Footage Calculator carries every case behind one control.