Area in simple words
Area is how much flat space a shape covers. Think of covering a floor with square tiles: the area is how many tiles you need. That is why area is measured in square units, such as square meters (m²) or square feet (ft²).
Each shape has its own rule. For a rectangle you multiply the length by the width. A triangle is half of a rectangle, so you multiply the base by the height and halve it.
Example: a rug is 5 m long and 3 m wide. Its area is 5 × 3 = 15 square meters, so 15 tiles of 1 m × 1 m would cover it.
Pick your shape, type the sizes and the calculator shows the rule with your numbers put in, step by step.
Worked example for every shape
Each row substitutes sample dimensions (in meters) into the formula the calculator uses, so you can check a result by hand. Use the Solve for option above to work backward from a known area, perimeter, diagonal or surface area.
| Shape | Inputs | Formula with numbers | Result |
|---|---|---|---|
| Rectangle | Length 5 m, Width 3 m | A = 5 × 3 | 15 m² |
| Square | Side 4 m | A = 4² | 16 m² |
| Triangle — base and height | Base 6 m, Perpendicular height 4 m | A = 6 × 4 ÷ 2 | 12 m² |
| Triangle — three sides | Side a 3 m, Side b 4 m, Side c 5 m | s = (3 + 4 + 5) ÷ 2 = 6; A = √(6 × 3 × 2 × 1) | 6 m² |
| Circle | Radius 2 m | A = π × 2² | 12.566371 m² |
| Ellipse | Semi-major axis 3 m, Semi-minor axis 2 m | A = π × 3 × 2 | 18.849556 m² |
| Trapezoid | Parallel side a 8 m, Parallel side b 5 m, Perpendicular height 4 m | A = (8 + 5) × 4 ÷ 2 | 26 m² |
| Parallelogram | Base 6 m, Perpendicular height 4 m | A = 6 × 4 | 24 m² |
| Parallelogram — two sides and angle | Side a 6 m, Side b 4 m, Angle between sides in degrees 30 | A = 6 × 4 × sin 30° | 12 m² |
| Trapezoid — four sides | Longer base a 10 m, Shorter base b 4 m, Leg c 5 m, Leg d 5 m | a − b = 6; h = 2·√(s(s−5)(s−5)(s−6)) ÷ 6; A = (10 + 4) × h ÷ 2 | 28 m² |
| Rhombus | Diagonal 1 6 m, Diagonal 2 8 m | A = 6 × 8 ÷ 2 | 24 m² |
| Circular sector | Radius 3 m, Angle in degrees 60 | A = π × 3² × 60 ÷ 360 | 4.712389 m² |
| Regular polygon | Number of sides 6, Side length 2 m | A = 6 × 2² ÷ (4 × tan(π ÷ 6)) | 10.392305 m² |
| Stadium (rectangle with semicircle ends) | End radius 1 m, Straight side length 4 m | A = π × 1² + 2 × 1 × 4 | 11.141593 m² |
| Annulus (ring) | Outer radius 5 m, Inner radius 3 m | A = π × (5² − 3²) | 50.265482 m² |
Formula and method
Select the shape and enter its dimensions. Lengths are converted to meters before applying the shape formula. Rectangle area is lw, triangle area is bh/2, circle area is πr² and regular polygon area is ns²/(4 tan(π/n)). A triangle entered by three sides uses Heron’s formula.
Worked example
A 5 m by 3 m rectangle has area 15 m², approximately 161.458656 ft². A triangle with base 5 m and perpendicular height 3 m has half that area, 7.5 m².
Inputs and limitations
Height is perpendicular to the base, not the sloping side. Ellipse inputs are semi-axes, not full diameters. For a ring the outer radius must exceed the inner radius. Linear conversion factors must be squared to convert areas.