Area Calculator: Rectangle, Circle, Triangle & More

What does 96 sq ft mean?

It means a rectangle 12 ft by 8 ft covers 96 square feet — twelve feet one way and eight feet the other, multiplied. The area in square feet and the four conversions are five outputs, never the same number: the area is the number, and the conversions are the same area in other units — 13,824 sq in, 10.666667 sq yd, 8.918692 sq m and 0.002204 acres. A square foot is a square one foot on each side, so a 12 by 8 rectangle holds 96 of them, and a square yard is nine square feet, which is why the yard figure is the foot figure divided by nine.

Three things to check before you trust the number

The shape decides the formula, not the numbers. The same two numbers give a different area for every shape: 12 and 8 make 96 sq ft as a rectangle, 48 sq ft as a triangle, and 12 and 8 as the bases of a trapezoid with a height of 5 make 50 sq ft. Pick the shape first, then the dimensions.

Area grows with the square of the size. A circle of radius 5 ft is 78.54 sq ft, and a circle of radius 10 ft is 314.16 sq ft — twice the radius, four times the area. Doubling one side doubles the area, but doubling both sides quadruples it, and the calculator shows you exactly how much.

A zero dimension is a line, not a shape. A length of 0 gives an area of 0.00 sq ft, and a negative length is not a shape at all — the calculator says so plainly instead of giving you a number you cannot use.

Worked example

On the defaults: a rectangle 12 ft by 8 ft.

1. Multiply length by width: 12 × 8 = 96 sq ft.
2. Square inches: 96 × 144 = 13,824 sq in.
3. Square yards: 96 ÷ 9 = 10.666667 sq yd.
4. Square metres: 96 × 0.09290304 = 8.918692 sq m.
5. Acres: 96 ÷ 43,560 = 0.002204 acres.
6. A circle of radius 5 ft: π × 5 × 5 = 3.141593 × 25 = 78.54 sq ft (unrounded 78.539816).
7. Smallest length for 100 sq ft at 8 ft wide: 12.5 ft — at 12.5 ft the area is 100.00 sq ft, and at 12 ft it is 96.00 sq ft.
8. Smallest radius for a circle of 100 sq ft: 5.65 ft — at 5.65 ft the area is 100.29 sq ft (unrounded 100.287491), and at 5.64 ft it is 99.93 sq ft.

Every branch, checked

• Square of side 10 ft: Square of side 10 ft: Area 100.00 sq ft; 14,400.00 sq in; 11.111111 sq yd; 9.290304 sq m; 0.002296 acres. A square of side 10 ft — area 100.00 sq ft, the unit square ten times bigger.
• Circle of radius 5 ft: Circle of radius 5 ft: Area 78.54 sq ft; 11,309.73 sq in; 8.726646 sq yd; 7.296588 sq m; 0.001803 acres. A circle of radius 5 ft — area 78.54 sq ft, unrounded 78.539816 — pi times 25.
• Triangle, base 10 ft, height 6 ft: Triangle, base 10 ft, height 6 ft: Area 30.00 sq ft; 4,320.00 sq in; 3.333333 sq yd; 2.787091 sq m; 0.000689 acres. A triangle of base 10 ft and height 6 ft — area 30.00 sq ft, half of 10 times 6.
• Trapezoid, bases 8 ft and 12 ft, height 5 ft: Trapezoid, bases 8 ft and 12 ft, height 5 ft: Area 50.00 sq ft; 7,200.00 sq in; 5.555556 sq yd; 4.645152 sq m; 0.001148 acres. A trapezoid with bases 8 ft and 12 ft and height 5 ft — area 50.00 sq ft, the average base, 10, times the height.
• Parallelogram, base 9 ft, height 4 ft: Parallelogram, base 9 ft, height 4 ft: Area 36.00 sq ft; 5,184.00 sq in; 4.000000 sq yd; 3.344509 sq m; 0.000826 acres. A parallelogram of base 9 ft and height 4 ft — area 36.00 sq ft, the same as a 9 by 4 rectangle, slanted.
• Rectangle 20 ft by 15 ft: Rectangle 20 ft by 15 ft: Area 300.00 sq ft; 43,200.00 sq in; 33.333333 sq yd; 27.870912 sq m; 0.006887 acres. A rectangle 20 ft by 15 ft — area 300.00 sq ft.
• Circle of radius 10 ft: Circle of radius 10 ft: Area 314.16 sq ft; 45,238.93 sq in; 34.906585 sq yd; 29.186351 sq m; 0.007212 acres. A circle of radius 10 ft — area 314.16 sq ft, unrounded 314.159265 — four times the radius-5 circle.
• Triangle, base 7.5 ft, height 4.2 ft: Triangle, base 7.5 ft, height 4.2 ft: Area 15.75 sq ft; 2,268.00 sq in; 1.750000 sq yd; 1.463223 sq m; 0.000362 acres. A triangle of base 7.5 ft and height 4.2 ft — area 15.75 sq ft.
• Trapezoid, bases 5.5 ft and 9.5 ft, height 3 ft: Trapezoid, bases 5.5 ft and 9.5 ft, height 3 ft: Area 22.50 sq ft; 3,240.00 sq in; 2.500000 sq yd; 2.090318 sq m; 0.000517 acres. A trapezoid with bases 5.5 ft and 9.5 ft and height 3 ft — area 22.50 sq ft.
• Rectangle 1 ft by 1 ft: Rectangle 1 ft by 1 ft: Area 1.00 sq ft; 144.00 sq in; 0.111111 sq yd; 0.092903 sq m; 0.000023 acres. A rectangle 1 ft by 1 ft — area 1.00 sq ft, the unit square: 144 sq in, 0.111111 sq yd, 0.092903 sq m, 0.000023 acres.

The reverses, worked backwards

• Smallest length for a rectangle 8 ft wide to REACH at least 100 sq ft: 12.5 ft — at 12.5 ft the figures are Area 100.00 sq ft (unrounded 100.000000); 14,400.00 sq in; 11.111111 sq yd; 9.290304 sq m; 0.002296 acres; at the lower neighbor the figures are Area 96.00 sq ft (unrounded 96.000000); 13,824.00 sq in; 10.666667 sq yd; 8.918692 sq m; 0.002204 acres; at the upper neighbor the figures are Area 104.00 sq ft (unrounded 104.000000); 14,976.00 sq in; 11.555556 sq yd; 9.661916 sq m; 0.002388 acres — verdict: STEP.
• Smallest radius for a circle to REACH at least 100 sq ft: 5.65 ft — at 5.65 ft the figures are Area 100.29 sq ft (unrounded 100.287491); 14,441.40 sq in; 11.143055 sq yd; 9.317013 sq m; 0.002302 acres; at the lower neighbor the figures are Area 99.93 sq ft (unrounded 99.932806); 14,390.32 sq in; 11.103645 sq yd; 9.284061 sq m; 0.002294 acres; at the upper neighbor the figures are Area 100.64 sq ft (unrounded 100.642806); 14,492.56 sq in; 11.182534 sq yd; 9.350023 sq m; 0.002310 acres — verdict: STEP.
• Largest width for a rectangle 12 ft long to STAY at or below 100 sq ft: 8.3 ft — at 8.3 ft the figures are Area 99.60 sq ft (unrounded 99.600000); 14,342.40 sq in; 11.066667 sq yd; 9.253143 sq m; 0.002287 acres; at the lower neighbor the figures are Area 100.80 sq ft (unrounded 100.800000); 14,515.20 sq in; 11.200000 sq yd; 9.364626 sq m; 0.002314 acres; at the upper neighbor the figures are Area 98.40 sq ft (unrounded 98.400000); 14,169.60 sq in; 10.933333 sq yd; 9.141659 sq m; 0.002259 acres — verdict: STEP.
• Smallest side for a square to REACH at least 50 sq ft: 7.1 ft — at 7.1 ft the figures are Area 50.41 sq ft (unrounded 50.410000); 7,259.04 sq in; 5.601111 sq yd; 4.683242 sq m; 0.001157 acres; at the lower neighbor the figures are Area 49.00 sq ft (unrounded 49.000000); 7,056.00 sq in; 5.444444 sq yd; 4.552249 sq m; 0.001125 acres; at the upper neighbor the figures are Area 51.84 sq ft (unrounded 51.840000); 7,464.96 sq in; 5.760000 sq yd; 4.816094 sq m; 0.001190 acres — verdict: STEP.
• Smallest height for a triangle of base 10 ft to REACH at least 60 sq ft: 12 ft — at 12 ft the figures are Area 60.00 sq ft (unrounded 60.000000); 8,640.00 sq in; 6.666667 sq yd; 5.574182 sq m; 0.001377 acres; at the lower neighbor the figures are Area 57.50 sq ft (unrounded 57.500000); 8,280.00 sq in; 6.388889 sq yd; 5.341925 sq m; 0.001320 acres; at the upper neighbor the figures are Area 62.50 sq ft (unrounded 62.500000); 9,000.00 sq in; 6.944444 sq yd; 5.806440 sq m; 0.001435 acres — verdict: STEP.
• Largest radius for a circle to STAY at or below 80 sq ft: 5.04 ft — at 5.04 ft the figures are Area 79.80 sq ft (unrounded 79.801480); 11,491.41 sq in; 8.866831 sq yd; 7.413800 sq m; 0.001832 acres; at the lower neighbor the figures are Area 80.12 sq ft (unrounded 80.118467); 11,537.06 sq in; 8.902052 sq yd; 7.443249 sq m; 0.001839 acres; at the upper neighbor the figures are Area 79.49 sq ft (unrounded 79.485122); 11,445.86 sq in; 8.831680 sq yd; 7.384409 sq m; 0.001825 acres — verdict: STEP.

What the defaults assume

The defaults are a rectangle 12 ft by 8 ft — a small bedroom, near enough — and the conversions are the exact ones: 144 square inches in a square foot, 9 square feet in a square yard, 0.09290304 square metres in a square foot, and 43,560 square feet in an acre. They are a starting point, not a benchmark: your shape may be a circle or a trapezoid, and the right area for you is the one your measurements describe. Change the shape and the three numbers to your own and the calculator recomputes instantly. The shape decides the formula, not the numbers — pick it first.

These notes repeat in every explainer section because this page is built to be read start to finish: the defaults are one rectangle, not a standard; the shape decides the formula, not the numbers; area grows with the square of the size; and a zero dimension is a line, not a shape.

Output · formula · meaning

Who uses this

• A homeowner measuring a room for flooring — 12 ft by 10 ft is 120 sq ft, and the square-footage-calculator page adds the waste and the cost.
• A gardener working out how much lawn a circular bed covers — radius 5 ft is 78.54 sq ft of soil and seed.
• A student checking homework — a triangle of base 10 ft and height 6 ft is 30 sq ft, half of 10 times 6.
• A builder pricing a trapezoid-shaped patio — bases 8 ft and 12 ft, height 5 ft, 50 sq ft of pavers.

Accuracy & limitations

The calculator does the arithmetic exactly — the area is length times width, pi times radius squared, base times height over two, or the trapezoid average times the height, and the conversions use the exact factors 144, 9, 0.09290304 and 43,560 — and every figure on this page is checked against an independent model. What it cannot do is measure for you: a room that is not quite a rectangle needs measuring in pieces, and a curved wall needs the area-of-hemisphere-calculator page or a land survey. It also takes one shape at a time — an L-shaped room is two rectangles, not one. And the area is 103.13 sq ft, unrounded 103.125000, on fractional dimensions — the page prints the unrounded figure so the rounding does not mislead you.

Cite this calculator

Area = length × width for a rectangle; side × side for a square; π × radius × radius for a circle; base × height / 2 for a triangle; (base 1 + base 2) / 2 × height for a trapezoid; base × height for a parallelogram. On the defaults — a rectangle 12 ft by 8 ft — the area is 96 sq ft, 13,824 sq in, 10.666667 sq yd, 8.918692 sq m and 0.002204 acres. Smallest length for a rectangle 8 ft wide to reach at least 100 sq ft: 12.5 ft. Smallest radius for a circle to reach at least 100 sq ft: 5.65 ft. Largest width for a rectangle 12 ft long to stay at or below 100 sq ft: 8.3 ft. Smallest side for a square to reach at least 50 sq ft: 7.1 ft. Smallest height for a triangle of base 10 ft to reach at least 60 sq ft: 12 ft. Largest radius for a circle to stay at or below 80 sq ft: 5.04 ft. Source: Bright Side Kit, brightoolbox.com.

Frequently asked questions