Square Feet Formula: Complete Reference

The Universal Principle

Area is a two-dimensional measurement. Every square-footage formula boils down to multiplying two lengths in feet together. When you see π, divide, or sum, it's still the same idea under the hood. The classical way to see it is grid counting: lay a 1 ft × 1 ft grid over the shape and count the squares — every formula below is a shortcut for that count.

Master Table

Quadrilaterals Most Formula Pages Skip

Rhombus

A rhombus is a parallelogram with all four sides equal. Its diagonals cross at right angles and bisect each other, which splits the shape into four right triangles — so A = (d1 × d2) / 2. With d1 = 12 ft and d2 = 8 ft: (12 × 8) / 2 = 48 sq ft.

You can also use the parallelogram rule b × h: a rhombus with 5 ft sides and a 4 ft perpendicular height is 20 sq ft. The two routes only agree when the height really is perpendicular — using the slanted side instead of the height is the standard mistake here, exactly as on a trapezoid.

Kite

A kite has two pairs of adjacent equal sides, and its diagonals still meet at right angles, so the same (d1 × d2) / 2 applies: d1 = 10 ft, d2 = 6 ft → 30 sq ft. What changes is which diagonal is which — one diagonal is the axis of symmetry, and only that one is bisected. For area it does not matter; for laying out a garden bed with strings it does.

Circle Parts: Sector, Segment, Annulus

Sector

A sector is a pie slice bounded by two radii and the arc. Scale the whole circle by the angle: A = (θ / 360) × π × r². For θ = 90° and r = 6 ft: (90 / 360) × π × 36 = 28.27 sq ft. If the site gives you arc length s rather than degrees, use A = (s × r) / 2 — the same relationship, no angle needed.

Segment

A segment is what a straight chord cuts off, so it is the sector minus the triangle between the two radii. Taking the 90° slice above: the triangle is ½ × 6 × 6 = 18 sq ft, so the segment is 28.27 − 18 = 10.27 sq ft. This is the shape of a curved garden bed cut off by a straight path, and the reason "just use the sector" over-orders the soil.

Annulus

An annulus is a ring: outer circle minus inner circle, A = π × (R² − r²). With R = 10 ft and r = 6 ft: π × (100 − 36) = 201.06 sq ft. A paved ring around a tree, a circular drive wrapping a courtyard, or the border of a stamped patio is this shape — and note it is not the same as circumference × width, which is only an approximation that gets worse as the ring gets thick.

Triangle Without a Height

Two routes when no perpendicular is available:

• Two sides and the included angle: A = (a × b × sin C) / 2. Sides of 24 ft and 25 ft enclosing 60° give (24 × 25 × sin 60°) / 2 = 300 × 0.866025 = 259.81 sq ft. Cross-check by recovering the height: 24 × sin 60° = 20.78 ft on a 25 ft base, and ½ × 25 × 20.78 = 259.8 sq ft ✓.
• Three sides, no angles (Heron): s = (a + b + c) / 2, then A = √(s(s − a)(s − b)(s − c)). For 5, 6, 7 ft: s = 9, A = √(9 × 4 × 3 × 2) = √216 ≈ 14.70 sq ft.

A caution worth repeating: Heron's result is only as good as the three tapes. A triangle whose sides nearly sum to a straight line (say 5, 6, 10.9) has an area of about 2.6 sq ft, and a half-inch error on any one side moves it by double-digit percentages.

Worked Examples

Example 1 — a room in feet

A 12 ft × 10 ft room: A = L × W = 12 × 10 = 120 sq ft, which is 120 ÷ 9 = 13.33 sq yd and 120 × 0.09290304 = 11.15 sq m.

Example 2 — an inches-based product up to coverage

A tile measuring 8 in × 36 in: area = 8 × 36 = 288 sq in. Since 1 sq ft = 144 sq in, one tile covers 288 ÷ 144 = exactly 2 sq ft. A box of 8 tiles covers 16 sq ft; 16 boxes cover 16 × 16 = 256 sq ft. Add the waste allowance after converting, not before: 256 sq ft with 10% is 281.6 sq ft, so order 18 boxes (288 sq ft), not 17.

Example 3 — solve for height (inverse)

You know the area of a triangular bed (120 sq ft) and its base (12 ft) but not how deep it must be. Rearrange A = (b × h) / 2 to h = 2 × Area / b, which is the way to solve for height from a known area: 2 × 120 / 12 = 20 ft. The same rearrangement family:

• Rectangle depth: W = A / L
• Trapezoid height: h = 2 × A / (a + b)
• Circle radius from area: r = √(A / π)
• Annulus outer radius from area: R = √((A / π) + r²)

The calculator above does not run backwards — it takes dimensions and returns area — so keep these four inverse forms on the sketch.

Composite Shapes (Rooms & Buildings)

For any shape that isn't in the table:

1. Decompose into rectangles (and triangles when needed).
2. Apply the matching formula to each sub-shape.
3. Add the areas together — or subtract the holes.

Two rules that keep the sum honest: the pieces must be non-overlapping, and every dimension must come from the same tape run, not from a plan plus a guess. Subtracting (outer rectangle minus cut-outs) is often more accurate than adding slivers, because errors in a long outer run are proportionally smaller. The Irregular calculator does the addition interactively.

Unit Handling in Formulas

Every formula above expects both inputs in the same unit. If your inputs are mixed:

• Convert everything to feet first (inches ÷ 12, yards × 3, meters × 3.28084, centimeters ÷ 30.48).
• Compute in sq ft.
• Convert to other units after (× 0.09290304 for sq m, ÷ 9 for sq yd, ÷ 43,560 for acres).

Do not confuse a length conversion with an area conversion: 1 in = 1/12 ft, but 1 sq in = 1/144 sq ft = 0.006944 sq ft. That single slip is the most common error in formula references — a widely-cited conversion table lists "1 square inch = 0.00064516 square foot", which is actually the square-meter value; the correct figure is 0.006944.

Frequently Asked Questions

Sources and How to Check This Page

• The area and length conversions used here are fixed by definition in NIST Special Publication 811, Appendix B.9.1: 1 in = 2.54 cm, 1 ft = 0.3048 m, hence 1 sq in = 6.4516 cm² and 1 sq ft = 0.09290304 m². Note the direction of that last pair — the frequently-misprinted figure 0.00064516 belongs to square meters per square inch, not square feet.
• π and the geometry need no external authority: every example on this page is reproducible by hand. Check the rhombus against its four right triangles (½ × 6 × 4 × 4 = 48), the sector against the whole circle (π × 36 = 113.10, one quarter of which is 28.27), and the segment against its triangle (28.27 − 18 = 10.27).
• The international foot used by these formulas is fixed at exactly 0.3048 m per Federal Register 85 FR 62698, which deprecated the US survey foot as of December 31, 2022. Surveying-derived lot dimensions older than that date may still be in survey feet, where the ratio to meters is 1200⁄3937 rather than 0.3048.
• What this page does not claim: it lists formulas, not manufacturer coverage rates or material allowances; the widget above implements the rectangle, square, circle, triangle, trapezoid, L-shape and irregular rows only, so Rhombus, Kite, Sector, Segment, Annulus, Ellipse and regular-polygon areas must be computed by hand or decomposed into the supported shapes.

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