Square Footage Formulas by Shape

The master table

All measurements in feet; all results in square feet.

Shape	Formula	Example	Result
Square	s²	12 ft side	144 ft²
Rectangle	L × W	20 × 12 ft	240 ft²
Triangle	(b × h) ÷ 2	base 20, height 9	90 ft²
Triangle (3 sides)	Heron’s formula	12, 15, 18 ft	89.29 ft²
Circle (diameter)	π × d² ÷ 4	d = 10 ft	78.54 ft²
Circle (radius)	π × r²	r = 5 ft	78.54 ft²
Semicircle	π × d² ÷ 8	d = 10 ft	39.27 ft²
Ellipse / oval	π × a × b ÷ 4	16 × 10 ft	125.66 ft²
Trapezoid	((a + b) ÷ 2) × h	8 & 12, height 5	50 ft²
Parallelogram	b × h	base 14, height 8	112 ft²
Rhombus	(d₁ × d₂) ÷ 2	diagonals 10, 8	40 ft²
Regular pentagon	1.720 × s²	s = 6 ft	61.94 ft²
Regular hexagon	2.598 × s²	s = 4 ft	41.57 ft²
Regular octagon	4.828 × s²	s = 5 ft	120.71 ft²
Annulus (ring)	π × (D² − d²) ÷ 4	D 26, d 20 ft	216.77 ft²
L-shape	Total − notch	300 − 48	252 ft²
Border	Outer − inner	300 − 176	124 ft²

Rectangles and squares

Area = Length × Width

The one everyone knows. Worth noting that for a square you only need one measurement, since all sides are equal: a 12 ft square room is 12² = 144 ft².

Calculator: the main sqft calculator or the room calculator.

Triangles

Area = (Base × Height) ÷ 2

The height must be perpendicular to the base — the straight-line distance from the base to the opposite corner, not the length of a sloping side. Using a sloping side is the most common triangle error and always overstates the area.

If you cannot measure a perpendicular, measure all three sides and use Heron’s formula:

1. Semi-perimeter: s = (a + b + c) ÷ 2
2. Area: √(s × (s−a) × (s−b) × (s−c))

For sides of 12, 15 and 18 ft: s = 22.5, giving √(22.5 × 10.5 × 7.5 × 4.5) = 89.29 ft².

Calculator: triangle sqft calculator.

Circles and curves

Area = π × diameter² ÷ 4 or equivalently π × radius²

Measure the diameter if you have the choice. Finding the exact centre of a circle to measure a radius is error-prone, and any error gets squared.

Fractions of a circle are simple: a semicircle is half the full area, a quarter circle is a quarter. A ring — a circular path around a pool, say — is the outer circle minus the inner circle.

Calculator: circle sqft calculator.

Trapezoids

Area = ((Side A + Side B) ÷ 2) × Height

A trapezoid has one pair of parallel sides. Average those two, then multiply by the perpendicular distance between them.

These show up in bay windows, angled corner lots and roof sections more often than you would expect.

Regular polygons

For a regular polygon with n equal sides of length s, the general formula is:

Area = (n × s²) ÷ (4 × tan(π ÷ n))

In practice it is easier to use the pre-computed multiplier:

Sides	Multiplier	Area for s = 5 ft
5 (pentagon)	1.7205	43.01 ft²
6 (hexagon)	2.5981	64.95 ft²
8 (octagon)	4.8284	120.71 ft²
10 (decagon)	7.6942	192.36 ft²

Multiply the side length squared by the figure in the table.

Technique 1 — additive splitting

The most useful skill in the whole subject: any complicated shape is a set of simple ones.

An L-shaped room is two rectangles. A room with a bay window is a rectangle plus a trapezoid. A garden with a rounded end is a rectangle plus a semicircle.

Draw the divisions on a sketch first, label each piece, calculate them separately, then add.

Technique 2 — subtractive measuring

Sometimes it is easier to measure a bounding shape and take away what is missing.

For an L-shaped room 20 × 15 ft with an 8 × 6 ft notch: 300 − 48 = 252 ft².

For a patio with a circular planter in the middle: patio area minus circle area.

For a room with a chimney breast: full rectangle minus the breast footprint.

Best practice is to use both. Calculate additively, then check subtractively. If the two disagree, you have mis-measured — and you have caught it before ordering materials.

Genuinely irregular shapes

For an area with no straight edges at all — a curved garden bed, a natural pond, an oddly shaped lot — there are three practical options:

1. Triangulate. Every straight-sided polygon divides completely into triangles. Break the boundary into straight segments, then into triangles, and sum them.
2. Grid overlay. Sketch the area on graph paper at a known scale, count the full squares, and estimate the partial ones. Crude but surprisingly accurate.
3. Satellite measurement. For anything outdoors, tracing the boundary on a map is faster and more accurate than a tape measure — see measuring square footage on Google Maps.