Article — Square Footage Calculator
Square footage calculator: rectangle, triangle, circle, trapezoid
Square footage is the area of a flat surface measured in square feet. The basic formula is length × width for rectangles, half base times height for triangles, π times radius squared for circles, and ((base1 + base2) ÷ 2) × height for trapezoids. One square foot equals 144 square inches, 0.0929 square metres, or 0.0000229 acres. A typical US home is 1,800 to 2,200 ft²; a tennis court is 2,106 ft²; an acre is 43,560 ft².
This calculator handles all four common shapes with a single shape selector. Inputs accept feet, inches, yards, metres, or centimetres. Output shows square feet, square metres, square yards, square inches, square centimetres, and acres. For complex spaces, decompose into rectangles, triangles, and trapezoids, calculate each, and add the results.
The square footage formula
Square footage for a rectangle is length × width. The math is dimensionless: any consistent unit works, but feet times feet yields square feet. A 12 ft × 10 ft room is 120 ft². A 30 ft × 40 ft lot is 1,200 ft². The same numbers in metres give square metres instead — 12 m × 10 m = 120 m², which is 1,292 ft² because the metre is bigger than the foot.
Rectangle = L × W most roomsTriangle = ½ × b × h gables, cornersCircle = π × r² pools, silosTrapezoid = ½ × (b₁ + b₂) × h sloped roofs, lots1 ft² = 144 in² = 0.0929 m² conversionsThe constants are exact. The ½ in triangle and trapezoid math comes from the fact that a triangle is half a rectangle of the same base and height; a trapezoid is the average of two parallel rectangles. The π in circle math is irrational — 3.14159... infinitely — but for practical work, four decimal places is more than enough.
Square footage by shape
Rectangle is the workhorse shape. Almost every room, every flooring order, every paint estimate is a rectangle calculation. The other three shapes appear in specific cases: triangles for roof gables and irregular corners, circles for round pools and silos, trapezoids for sloped roofs and trapezoidal lot edges.
- Rectangle = length × width; covers 90% of indoor measurements
- Triangle = ½ base × height; use perpendicular height, not slant
- Circle = π × radius²; the radius is half the diameter, square first
- Trapezoid = average parallel sides × perpendicular distance between them
- Parallelogram = base × perpendicular height (same as rectangle math)
- Regular polygon = ½ × perimeter × apothem (specialised case)
For shapes that do not fit any of the standard formulas, the right approach is decomposition. Split the area into pieces that match a formula, calculate each, and add. A hexagonal patio splits into six triangles. An oval splits into a rectangle plus two semicircles. The arithmetic gets long, but the answer is exact.
Square footage of L-shaped rooms
L-shaped rooms are the most common irregular case in residential floor plans. The approach is to draw a horizontal line through the L to create two rectangles, calculate each, and add. The choice of where to split does not change the answer — any decomposition works as long as the pieces fit together without overlap.
Same decomposition logic applies to T-shaped rooms (three rectangles), bay windows (rectangle plus trapezoid), and angled corners (rectangle plus triangle). The square footage of any polygon can be computed by triangulation, dividing it into triangles from a common vertex and summing the areas. Surveyors use this method for irregular lots; CAD software automates it.
Square footage for flooring orders
Flooring is ordered by the box, with each box covering a specific square footage. Always order 10 to 15% more than the room area to allow for cuts, mistakes, and future repairs. For diagonal layouts or herringbone patterns, increase the overage to 15 to 20%.
Round up to the next whole box. If a 200 ft² room needs 17.4 boxes (at 12 ft²/box) you order 18 boxes for 216 ft². Keep the leftover sealed in case a plank gets damaged later. Manufacturers change dye lots between production runs, so a matching replacement box bought two years later may be visibly different.
For tile, the overage is higher because tiles break during cutting and a partial tile from a broken whole gets wasted. Plan 15% extra for standard layouts and 20 to 25% for diagonal, herringbone, or large-format tile work. Pre-spaced mosaic sheets need less overage because the small format hides cutting losses.
Square footage for paint coverage
Paint is sold in gallons that cover a specified square footage at one coat. Standard interior latex covers 350 to 400 square feet per gallon. Most rooms need two coats, so divide wall square footage by 175 to 200 to find the gallons required.
Wall square footage is not the same as floor square footage. For a 12 × 10 ft room with 8 ft ceilings, walls total 2 × (12 × 8) + 2 × (10 × 8) = 352 ft² of wall, minus window and door openings (about 40 ft² for typical residential). Net paintable area is roughly 310 ft², which needs 1 gallon for two coats. Add the ceiling (120 ft²) and you need another gallon for that surface.
The square foot as a unit was standardised in the 1959 International Yard and Pound Agreement, when the US, UK, Canada, Australia, New Zealand, and South Africa agreed to define the foot as exactly 0.3048 metres. Before that, the US foot and the UK foot differed by about 6 parts per million — small enough that nobody noticed in residential work but enough to cause errors in surveying and engineering. The unified definition meant the square foot became exactly 0.09290304 m², a defined value with no measurement uncertainty.
Square footage vs square metres
The conversion is 1 ft² = 0.0929 m², or 1 m² = 10.764 ft². A 1,500 ft² US home is 139 m²; a 100 m² European apartment is 1,076 ft². The metre is roughly 3.28 times longer than the foot, so the square metre is 3.28² = 10.76 times bigger than the square foot.
For mental math, the rule of thumb is 1 m² ≈ 11 ft² (close to exact: 10.76). To convert ft² to m² in your head, divide by 11; multiply by 10 or 11 to reverse. The error is under 2%, which is well within the noise of typical room measurements.
Common square footage mistakes
The most frequent square footage error is mixing units. Multiplying feet by inches gives an answer in foot-inches, not square feet — divide by 12 to fix it.
A 12-inch square is 1 ft² — but in square inches, that same square is 12 × 12 = 144 in². The factor of 144 (not 12) is the source of constant confusion. To convert ft² to in², multiply by 144. To convert in² to ft², divide by 144. The factor is the square of the linear conversion, which most people forget under time pressure.
A round patio with a 10 ft diameter has a 5 ft radius. Using the diameter in the area formula gives 4 times the correct answer (10² × π = 314, versus the correct 5² × π = 79). Always halve the diameter first. The same trap appears with circular pools, fire pits, and grain silos.
Why realtor square footage differs
Realtor square footage figures often differ from a measurement you take yourself. The reason is what counts as living space. The American National Standards Institute (ANSI Z765-2021) defines finished above-grade living space as the standard for US single-family homes, excluding basements, garages, attics, and unheated porches. Most regional MLS systems follow this standard, but enforcement varies.
Below-grade space (basements) is reported separately. Decks, patios, and outdoor structures are excluded. Open stairwells count once, not twice. The 2,200 ft² in a listing may exclude a 600 ft² finished basement — the actual usable square footage is 2,800. Always read the listing detail or ask for the appraisal report when square footage is a critical purchase factor.