What area measures
Area is the amount of flat surface inside a shape, measured in square units. One square foot is a square 1 ft on each side. Because area multiplies two lengths, unit conversions are squared: 1 ft = 12 in, so 1 ft² = 144 in², and 1 m² ≈ 10.7639 ft².
Formulas
| Shape | Formula | Variables |
|---|---|---|
| Rectangle | l × w | l = length, w = width |
| Square | s² | s = side |
| Circle | π r² | r = radius (half the diameter) |
| Triangle | ½ b h | b = base, h = perpendicular height |
| Trapezoid | (a + b) ÷ 2 × h | a, b = parallel sides, h = distance between them |
| Parallelogram | b h | b = base, h = perpendicular height |
| Ellipse | π a b | a, b = semi-axes (half of each width) |
Worked examples
Circular patio, 12 ft across
Radius = 12 ÷ 2 = 6 ft. Area = π × 6² = 36π ≈ 113.10 ft². In square meters: 113.097 × 0.09290304 ≈ 10.51 m².
Trapezoid garden bed
Parallel sides of 6 m and 10 m, 4 m apart. Area = (6 + 10) ÷ 2 × 4 = 32 m², about 344.4 ft².
Triangular gable wall
Base 24 ft, peak height 6 ft. Area = ½ × 24 × 6 = 72 ft².
Practical uses
Area figures are used to estimate flooring, sod, paint, fabric, roofing and fertilizer, and to compare lot or room sizes. For rooms made of rectangles, the square footage calculator adds several areas together; for materials, see the flooring and paint calculators.
Common mistakes
- Entering a diameter where a radius is required, which makes a circle's area four times too large.
- Using a slanted side instead of the perpendicular height for triangles and parallelograms.
- Converting area by the linear factor (multiplying ft² by 12 instead of 144 to get in²).
- Mixing units between measurements. All inputs here share the unit you select.
Assumptions and limitations
Shapes are treated as ideal flat figures. Real surfaces may be irregular or sloped; divide them into simpler shapes and add the areas. Unit conversions use exact definitions (1 ft = 0.3048 m; 1 acre = 4,046.8564224 m²) per NIST Special Publication 811.
Frequently asked questions
Why do I need the height of a triangle and not its side?
The area formula uses the perpendicular height, measured at a right angle from the base to the opposite corner. A slanted side is longer than the height and would overstate the area.
I measured a circle's diameter. What do I enter?
Enter half the diameter as the radius. A circle 10 ft across has a radius of 5 ft and an area of π × 5² ≈ 78.54 ft².
How do I find the area of an L-shaped room?
Split it into rectangles, find each area, and add them. The square footage calculator does this for several rectangles at once.