Square Feet Formula: Complete Reference
Every square footage formula you'll ever need, with worked examples, unit notes, and common pitfalls.
Last updated:Tip: If you only have the diameter, divide by 2 to get the radius.
L-shape = two rectangles sharing a corner.
Add one row per rectangle and we'll sum them.
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.
Square Feet Formula — Rectangle
A = L × W
Where L is length and W is width, both in feet. Example: 12 × 10 = 120 sq ft.
Square Feet Formula — Square
A = S × S = S²
Where S is the side length in feet. Example: 10² = 100 sq ft.
Square Feet Formula — Circle
A = π × r²
Where r is the radius in feet. π (pi) ≈ 3.14159265.
Derivation: a circle's area was first calculated by Archimedes, who inscribed polygons inside the circle with more and more sides. As the number of sides increases, the polygon's area approaches π × r².
From diameter: radius = diameter / 2, so A = π × (d/2)² = π × d² / 4.
Square Feet Formula — Triangle
A = (b × h) / 2
Where b is the base, h is the perpendicular height. Crucial: height is the line perpendicular to the base going to the opposite vertex — not the slant length of either side.
Example: base 14 ft, height 9 ft → 14 × 9 / 2 = 63 sq ft.
Heron's formula (when you only have side lengths)
If you have the three sides a, b, c but not the height:
- Compute semi-perimeter s = (a + b + c) / 2.
- A = √( s × (s−a) × (s−b) × (s−c) ).
Example: sides 5, 6, 7. s = 9. A = √(9 × 4 × 3 × 2) = √216 ≈ 14.70 sq ft.
Square Feet Formula — Trapezoid
A = ((a + b) / 2) × h
Where a and b are the two parallel sides, h is the perpendicular distance between them.
Square Feet Formula — Parallelogram
A = b × h
Same as a rectangle, but the "height" is the perpendicular distance between the two parallel sides, not the slant.
Square Feet Formula — Regular Polygon
For a polygon with n sides, each of length s:
A = (n × s²) / (4 × tan(π / n))
Easier version if you know the apothem (distance from center to edge midpoint): A = (perimeter × apothem) / 2.
Square Feet Formula — Ellipse
A = π × a × b
Where a is the semi-major axis and b is the semi-minor axis.
Composite Shapes (Rooms & Buildings)
For any shape that isn't in the list above:
- Decompose into rectangles (and triangles when needed).
- Apply the matching formula to each sub-shape.
- Add the areas together.
The Irregular calculator does this 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, meters × 3.2808, etc.).
- Compute in sq ft.
- Convert to other units after (× 0.0929 for sq m, ÷ 9 for sq yd).
Frequently Asked Questions
What is the formula for square footage?
For a rectangle: L × W. For a circle: π × r². For a triangle: (b × h) / 2. Each shape has its own formula — see the list above.
How do you calculate square feet from a circle?
Square the radius, then multiply by π. For a 10-foot-radius circle: π × 10² = 314.16 sq ft.
Does the triangle formula work for all triangles?
Yes — (base × height) / 2 works for every triangle, as long as you use the perpendicular height (not the slant length).
Is the formula the same for square yards?
Yes. The same formulas give square yards if you measure in yards, or square meters if you measure in meters. Then convert to square feet by multiplying (or use our converters).