This area calculator finds the area of the common shapes — rectangle, square, triangle, circle, trapezoid and parallelogram. Pick a shape, enter its measurements, and get the area with the formula shown.
The Area Formulas in One Place
| Shape | Formula | Example (verified) |
|---|---|---|
| Rectangle | l × w | 12 × 9 = 108 |
| Square | side² | 8² = 64 |
| Triangle | ½ × base × height | ½ × 10 × 6 = 30 |
| Circle | πr² | π × 7² = 153.94 |
| Trapezoid | (a + b)/2 × h | (8 + 12)/2 × 5 = 50 |
| Parallelogram | base × height | 10 × 6 = 60 |
This calculator is part of our Math Calculators collection; circles and triangles also have dedicated deep-dives in the Circle Calculator and Triangle Calculator.
Area in Real Life
- Paint and flooring: rooms are rectangles (with cut-outs subtracted) — coverage per gallon or box is an area figure. (For 3-D rooms with walls and coats, our dedicated Paint Calculator and Tile Calculator go further.)
- Land: one acre = 43,560 square feet; irregular lots get decomposed into triangles and trapezoids.
- The scaling trap: doubling every length quadruples the area — why a 16-inch pizza is four 8-inch pizzas, and why big houses cost disproportionately more to heat and roof.
Units Reminders
- Area is always in square units: ft², m², cm². Convert lengths before multiplying, or convert areas with squared factors (1 m² = 10.764 ft², not 3.28).
- Heights must be perpendicular heights — the recurring parallelogram/trapezoid mistake is using a slanted side.
Related Tools
- Circle Calculator
- Triangle Calculator — Heron and types
- Perimeter Calculator — the boundary counterpart
Frequently Asked Questions
How do I calculate the area of a rectangle?
Multiply length by width: 12 × 9 = 108 square units.
What is the area of a triangle without the height?
If you know all three sides, use Heron’s formula — our Triangle Calculator does exactly that.
Why is trapezoid area the “average width × height”?
A trapezoid’s two parallel sides average to its effective width: (a + b)/2 × h. Two identical trapezoids also form a parallelogram of base (a + b), which proves the formula.
How do I find the area of an irregular shape?
Split it into rectangles, triangles and trapezoids, compute each, and add (subtracting any cut-outs). Surveyors and flooring installers work exactly this way.
What is the difference between area and perimeter?
Area measures the surface covered (square units); perimeter measures the boundary length (plain units). A fence needs perimeter; sod needs area.
Is this area calculator free?
Yes — free, instant, no sign-up.