How to use the area calculator
Select the shape, choose the unit you measured in, and enter the dimensions. The headline result is in square units of that measurement (cm², m², in² or ft²); the rows convert it to square meters, square feet and hectares or acres. Heights are always the perpendicular distance from the base to the opposite side or vertex, which for a parallelogram is shorter than the slanted side.
Area formulas
| Shape | Formula | Example |
|---|---|---|
| Square | A = a² | a = 4 → 16 |
| Rectangle | A = l × w | 5 × 3 → 15 |
| Triangle (base, height) | A = ½ b h | b = 6, h = 4 → 12 |
| Triangle (three sides) | A = √(s(s − a)(s − b)(s − c)), s = (a + b + c) ÷ 2 | 3, 4, 5 → 6 |
| Circle | A = π r² | r = 5 → 78.54 |
| Semicircle | A = ½ π r² | r = 4 → 25.13 |
| Ellipse | A = π a b | a = 5, b = 3 → 47.12 |
| Trapezoid | A = (a + b) ÷ 2 × h | 3, 5, h = 4 → 16 |
| Parallelogram | A = b × h | b = 6, h = 4 → 24 |
| Regular polygon | A = n s² ÷ (4 tan(180° ÷ n)) | hexagon, s = 2 → 10.39 |
| Circle sector | A = θ ÷ 360 × π r² | r = 10, 60° → 52.36 |
Worked example: a raised garden bed
A bed against a fence is a trapezoid: 3 m along the fence, 5 m along the path, and the two edges are 4 m apart. Area = (3 + 5) ÷ 2 × 4 = 16 m². To fill it 30 cm deep you need 16 × 0.3 = 4.8 m³ of soil, which the volume calculator converts to liters or cubic feet if the supplier quotes those. For a quick imperial check, 16 m² ÷ 0.09290304 = 172.2 ft².
Heron's formula: a triangle from three sides
When you know the three side lengths but not a height — a triangular lot, a sail, a gable measured along its edges — use Heron's formula. Add the sides and halve the sum to get the semi-perimeter s, then take the square root of s(s − a)(s − b)(s − c). For sides 7, 8 and 9: s = 12 and A = √(12 × 5 × 4 × 3) = √720 = 26.83. The calculator refuses sides that break the triangle inequality (any side equal to or longer than the other two together), because no triangle can be built from them.
Which shape should I pick?
- Rooms, floors, walls, fields: rectangle, or split an L-shape into two rectangles — the square footage calculator does this for several rooms at once.
- Round tables, pools, pizzas, pipes: circle; halve a measured diameter. An oval table is an ellipse.
- Gables, roof ends, pennants: triangle — base and height if you can measure straight up from the base, otherwise the three edges with Heron.
- Lots with two parallel sides: trapezoid. Many city lots and driveways are this shape.
- Gazebos, stop signs, tiles: regular polygon — a hexagonal gazebo with 8 ft sides covers 166.3 ft².
- Pie slices, fan-shaped patios, sprinkler coverage: sector with the angle in degrees.
Unit conversions used here
Area scales with the square of the length factor: 1 foot is 0.3048 m, so 1 ft² is 0.09290304 m² exactly. An acre is 43,560 ft² = 4,046.8564224 m² (a square about 208.71 ft on a side), and a hectare is 10,000 m², about 2.471 acres. Other unit pairs are in the unit converter.
Frequently asked questions
How do I find the area of a circle from its diameter?
Halve the diameter to get the radius, then square it and multiply by π. A 12-inch pizza has r = 6, so A = π × 36 = 113.1 in². Equivalently A = π d² ÷ 4.
What is the difference between the height and the side of a triangle?
The height is the perpendicular distance from the base to the opposite corner, measured at a right angle to the base. Only in a right triangle does a side double as the height. If you know only the three sides, switch to the three-sides option, which uses Heron's formula.
How many square feet are in a square meter?
10.7639 ft². One meter is 3.28084 feet, and area uses the square of that factor. A 120 ft² room is 11.15 m².
Why does the calculator say my three sides cannot form a triangle?
For a triangle to exist, every side must be shorter than the sum of the other two. Sides of 2, 3 and 6 fail because 2 + 3 = 5 is less than 6 — the two short sides cannot reach each other. Check for a typo or a mixed unit.
How do I calculate the area of an irregular shape?
Divide it into shapes from the list — rectangles, triangles, trapezoids, half circles — compute each and add them, subtracting any cut-outs.
Last updated: October 9, 2026