By This area calculator finds the area of eight common shapes: square, rectangle, triangle, parallelogram, trapezoid, rhombus, circle and ellipse. Choose the shape, enter the measurements, and it shows the formula, the numbers substituted in, and the area. For squares, rectangles and rhombuses it also gives the perimeter, and for circles the circumference. Circle and ellipse answers are given exactly in terms of \( \pi \) as well as in decimals.
It’s free, works on phones, and needs no sign-up.
How to use the area calculator
- Pick the shape. The menu says which letters each shape uses: for a trapezoid, a and b are the two parallel sides and h is the height.
- Enter the measurements, all in the same unit. Leave unused boxes as they are; the calculator only reads the ones the shape needs.
- Press Find area. The answer is in square units: if you entered centimetres, the area is in cm².
Area formulas
| Shape | Formula | Letters |
|---|---|---|
| Square | \( A = a^2 \) | a = side |
| Rectangle | \( A = ab \) | length and width |
| Triangle | \( A = \frac12bh \) | base and perpendicular height |
| Parallelogram | \( A = bh \) | base and perpendicular height |
| Trapezoid | \( A = \frac12(a + b)h \) | parallel sides a, b; height h |
| Rhombus | \( A = \frac12d_1d_2 \) | the two diagonals |
| Circle | \( A = \pi r^2 \) | radius |
| Ellipse | \( A = \pi ab \) | semi-major and semi-minor axes |
Every formula is explained, with a picture of why it works, in the area formulas guide.
Worked example: a rectangle
A room is 8 m long and 5 m wide (the values loaded above). Its area is \( 8 \times 5 = 40 \) m² and its perimeter is \( 2(8 + 5) = 26 \) m. That’s how much flooring and how much skirting board you need.
Worked example: a trapezoid
A trapezoid has parallel sides 6 cm and 10 cm and height 4 cm:
$$A = \tfrac12(6 + 10)\times4 = 32 \text{ cm}^2$$
Averaging the two parallel sides and multiplying by the height is the idea behind the formula.
Worked example: a circle
A circle of radius 3 cm has area \( \pi\cdot3^2 = 9\pi \approx 28.27 \) cm² and circumference \( 2\pi\cdot3 = 6\pi \approx 18.85 \) cm. If you know the diameter or circumference instead, use the circle calculator.
Tips and common mistakes
- Use the perpendicular height. For triangles, parallelograms and trapezoids, h is measured at a right angle to the base, not along a slanted side. If you only know the side lengths of a triangle, use Heron’s formula or the triangle calculator.
- Radius, not diameter. \( \pi r^2 \) needs the radius. A 10 cm pizza has radius 5 cm.
- Mixed units. Convert everything to one unit first. A 2 m by 50 cm rectangle is \( 2 \times 0.5 = 1 \) m², not 100.
- Squared units. Area is always in square units; doubling every length multiplies the area by 4.
Areas of curved regions
For regions bounded by curves, such as the area under a parabola, there’s no fixed formula: you add up thin strips with an integral. See area between curves, Riemann sums and the definite integral calculator.
Related guides
- Area Formulas for Every Shape
- Volume Formulas and Surface Area
- The Pythagorean Theorem
- Area Between Curves
Further reading
- Area (Wikipedia) — definitions, units and formulas for common shapes.
- List of formulas in elementary geometry (Wikipedia) — areas, perimeters and volumes in one table.
FAQ
How do you calculate area?
Multiply the right measurements for the shape: length × width for a rectangle, \( \frac12 \) × base × height for a triangle, and \( \pi r^2 \) for a circle.
What is the formula for the area of a rectangle?
\( A = \text{length} \times \text{width} \).
What units is area measured in?
Square units, such as m², cm², ft² or in², matching the units of the lengths you used.
How do I find the area of an irregular shape?
Split it into rectangles, triangles and circles, find each area, and add them. For shapes bounded by curves, use integration.