The Square Footage Formula for Every Shape

The square footage formula almost everyone knows is length × width — and for a rectangular room, that’s the whole thing. But that formula only covers rectangles. Triangles, circles, trapezoids and L-shaped rooms each have their own, and they’re all variations on the same idea: multiply measurements together until you have an area.

This is the reference. Every shape’s formula, what to measure for each, and the calculator that runs it if you’d rather not do it by hand.

The formula that covers most rooms

For a rectangle, the formula is length × width, both in feet, giving an answer in square feet. A room 12 feet by 15 feet is 12 × 15 = 180 square feet. A square is the same formula with equal sides, so side × side — a 10-foot-square room is 10 × 10 = 100 square feet.

Most rooms are rectangles, or break down into rectangles, so this one formula does the bulk of the work. The others handle the shapes it can’t.

Every shape’s square footage formula

Shape	Formula	What to measure	Calculator
Rectangle	length × width	Both sides	Rectangle
Square	side × side	One side	Square
Triangle	½ × base × height	Base and its perpendicular height	Triangle
Triangle (3 sides)	√[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2	All three side lengths	Three-sides triangle
Circle	π × radius²	Radius (half the diameter)	Circle
Circle sector	(angle ÷ 360) × π × radius²	Radius and the angle	Sector
Trapezoid	½ × (base 1 + base 2) × height	The two parallel sides and the gap between them	Trapezoid
Parallelogram	base × height	Base and perpendicular height	Parallelogram
L-shape	split into two rectangles, then add	Both rectangles	L-shape

The second triangle formula is Heron’s formula, and it’s the one to reach for when you can measure the three sides of a triangle but can’t easily measure its height — which is most real triangular spaces.

Get the units right, whatever the shape

Every formula gives square feet only if the measurements go in as feet. Tape measures read feet and inches, so convert the inches first: divide them by 12 and add the decimal. So 8 feet 6 inches is 8.5 feet.

The mistake that ruins any of these formulas is mixing units — multiplying feet on one side by inches on the other, which lands you a figure twelve times out. If you’re working from inches, the inches-to-square-feet guide covers both ways to handle it.

Combining shapes for a real room

Real rooms rarely match one shape exactly, and that’s fine — you don’t need a single formula for a complicated space. Break the floor plan into pieces that each match a shape above, work out each one, and add them (or subtract, for a corner that’s been cut out).

A room with a bay window is a rectangle plus a trapezoid. A room with an angled corner is a rectangle minus a triangle. The multi-room calculator totals the pieces as you go, and the guide to measuring a room walks through the decomposition.

Three worked examples

Seeing the formulas run once makes them stick:

1. Rectangular bedroom, 11 × 13 ft: 11 × 13 = 143 square feet.
2. Triangular gable end, 20 ft base and 6 ft high: ½ × 20 × 6 = 60 square feet.
3. Round patio, 14 ft across: the radius is half the diameter, so 7 ft. π × 7² = 3.14159 × 49 = 154 square feet.

The mistakes that break the formulas

1. Using diameter instead of radius in the circle formula. The radius is half the diameter — miss that and your answer is four times too big.
2. Forgetting the ½ in the triangle and trapezoid formulas. Without it, you’ve calculated the surrounding rectangle, not the shape.
3. Measuring a slanted height instead of the perpendicular one. Triangle and parallelogram heights are the straight-up distance, not the sloped side.
4. Mixing feet and inches in a single multiplication. Convert everything to feet first.

Frequently asked questions

What is the formula for square footage?

For a rectangle, it’s length times width, with both measured in feet. That covers most rooms. Other shapes have their own versions — a triangle is half the base times the height, a circle is pi times the radius squared — but they all come down to multiplying measurements to get an area in square feet.

What’s the formula for the area of a triangle in square feet?

Half the base times the height: ½ × base × height, in feet. A triangle with a 12-foot base and a 5-foot height is ½ × 12 × 5 = 30 square feet. If you know the three side lengths but not the height, use Heron’s formula instead, which works straight from the sides.

How do you calculate the square footage of a circle?

Multiply pi (about 3.14159) by the radius squared. The radius is half the diameter, so measure across the circle and halve it first. A circle 10 feet across has a 5-foot radius, giving π × 5² = about 78.5 square feet. Using the diameter by mistake overstates the area fourfold.

Do all shapes use length times width?

No — that’s only the rectangle and square. Triangles, circles, trapezoids and sectors each have their own formula because they don’t have two clean sides to multiply. What they share is the goal: combine the measurements into an area. The table above lists the right formula for each.

How do you find the square footage of an odd or irregular shape?

Split it into shapes you do have formulas for. Almost any floor plan breaks into rectangles, triangles and parts of circles. Work out each piece, then add them together — or subtract, if a section has been cut away. A running total, by hand or in the multi-room calculator, keeps it straight.

The short version

Every square footage formula is a way of multiplying measurements into an area — length × width is just the simplest one.

• Rectangle and square: multiply the sides.
• Triangle: half the base times the height (or Heron’s formula from three sides).
• Circle: pi times the radius squared — radius, not diameter.
• Trapezoid and parallelogram have their own formulas; L-shapes split into rectangles.
• Convert inches to feet before multiplying, and break odd rooms into pieces.

Each shape above links to a calculator that applies its formula for you, and the main square footage calculator switches between them and converts the result to square yards, square meters and acres.