The Area Formulas
Example — a 5 m × 3 m rug
Area = 5 × 3 = 15 m². In square feet that is 15 × 10.764 = 161.5 ft² — the number a flooring store will ask for. Every shape above is the same idea: multiply two lengths (with π or a ½ where the shape curves or tapers), and the answer is always in square units. If your triangle measurements are sides and angles rather than base and height, the triangle calculator finds its area from those too.
Square Feet, Acres and Hectares: Which Unit When?
Match the unit to the job:
| Unit | Equals | Used for |
|---|---|---|
| Square foot (ft²) | 144 in² | Rooms, flooring, paint coverage (US) |
| Square meter (m²) | 10.764 ft² | Rooms and land almost everywhere else |
| Acre | 43,560 ft² (4,047 m²) | Land, farms, lots (US/UK) |
| Hectare | 10,000 m² (2.471 acres) | Land, agriculture (metric world) |
A US football field including end zones is 57,600 ft² — about 1.32 acres. A hectare is roughly two American football fields without the end zones... close enough for a sanity check, never for a deed. Converting a single length before you start? The unit converter handles it — just remember to square its factor for area.
How Much Material Do I Need? Area in Real Jobs
Area is how paint, tile, turf and flooring are sold. Three everyday runs:
- Paint: one gallon covers ~350 ft² per coat. A 12 × 10 ft room with 8 ft ceilings has 352 ft² of wall — one gallon per coat, two gallons for the usual two coats.
- Flooring: add 10% waste for cuts (15% for diagonal layouts). A 15 m² room needs 16.5 m² of boards — the percentage calculator makes that waste markup a two-second job.
- Turf/seed: seed bags are rated by coverage — measure the lawn as rectangles and triangles, add them, and buy to the total.
Irregular shape? Split it into rectangles, triangles and half-circles, measure each piece (the tape measure calculator tames the fractions), calculate each piece above, and add. That is exactly how surveyors do it.
Common Area Mistakes
- Using the diameter in πr². Halve it first — the error is 4×, not 2×.
- Forgetting the ½ in triangles and trapezoids.
- Mixing units: 5 ft × 30 in is not 150 of anything. Convert first (30 in = 2.5 ft, so 12.5 ft²).
- Converting area with a length factor: 1 m = 3.28 ft, but 1 m² = 10.76 ft² — square the factor.
- Slant height for triangles: the height must be perpendicular to the base.
The Bottom Line
Area is always two lengths multiplied — everything else is a shape-specific twist: π for curves, ½ for tapers, an average of the two parallel sides for a trapezoid. Pick the shape above, keep your units consistent, and read the answer in whichever square unit your project uses. Checking the π and power work by hand? A scientific calculator covers both.