Area calculator for every common shape
This area calculator works out the area of squares, rectangles, triangles, circles, ellipses, trapezoids, parallelograms, rhombuses, irregular four-sided shapes, sectors and regular polygons. Choose a shape, type the measurements and you get the answer immediately, with the formula filled in with your numbers and a labelled diagram that shows exactly which length is which.
Measurements can be in millimetres, centimetres, metres, kilometres, inches, feet, yards or miles, and the result is converted to every common area unit — from square centimetres and square feet to acres and hectares. That makes it as useful for geometry homework as for working out flooring, paint, turf, a room in square feet or a plot of land in India, the US or the UK.
How to use the Area Calculator
- Choose the shape. For triangles, pick the version that matches what you know: base and height, three sides, or two sides and the angle between them.
- Choose the unit your measurements are in.
- Enter the measurements shown in the diagram — the labels a, b, h, r and so on match the input boxes.
- Read the area in the result panel, with the formula and working underneath.
- Check the extra values (perimeter, diagonal, angles) and the conversion table for other units such as ft², acres or hectares.
Area Calculator features
13 shapes in one tool
Three ways to find a triangle’s area, a four-sided plot with unequal sides, sectors and any regular polygon.
Labelled diagrams
Each shape has a small diagram with your values on it, so you never mix up the slanted side and the height.
Formula with working
See the general formula and the substituted calculation, ready to copy into homework.
Every area unit
Results in mm², cm², m², km², in², ft², yd², acres, hectares, square miles, guntha and cents at once.
Extra measurements
Perimeter, diagonals, circumference, arc length, apothem and interior angles where they apply.
Checks your input
Impossible triangles and out-of-range angles are caught with a clear explanation.
Area formulas for common shapes
Area measures how much flat surface a shape covers, in square units. If the lengths are in metres, the area is in square metres (m²); if they are in feet, it is in square feet (ft²). Always use the same unit for every measurement before applying a formula.
| Shape | Formula | Example |
|---|---|---|
| Square | A = a² | a = 5 → 25 |
| Rectangle | A = l × w | 8 × 5 → 40 |
| Triangle | A = ½ × b × h | ½ × 10 × 6 → 30 |
| Triangle (3 sides) | A = √(s(s − a)(s − b)(s − c)), s = (a + b + c)/2 | 3, 4, 5 → 6 |
| Circle | A = πr² | r = 5 → 78.54 |
| Ellipse | A = πab | a = 6, b = 4 → 75.40 |
| Trapezoid | A = ½(a + b)h | ½(6 + 10) × 4 → 32 |
| Parallelogram | A = b × h | 10 × 6 → 60 |
| Rhombus / kite | A = d₁ × d₂ / 2 | 10 × 6 / 2 → 30 |
| Quadrilateral | Heron(AB, BC, AC) + Heron(CD, DA, AC) | 30, 40, 30, 40, AC 50 → 1,200 |
| Sector | A = (θ/360) × πr² | r = 6, θ = 90° → 28.27 |
| Regular polygon | A = n s² / (4 tan(180°/n)) | hexagon, s = 2 → 10.39 |
Worked example: a triangle from three sides
Suppose a triangular garden bed has sides of 7 m, 8 m and 9 m, but you cannot measure its height. Heron’s formula needs only the sides. First find the semi-perimeter: s = (7 + 8 + 9) / 2 = 12. Then A = √(12 × (12 − 7) × (12 − 8) × (12 − 9)) = √(12 × 5 × 4 × 3) = √720 ≈ 26.83 m², which is about 288.8 ft².
Heron’s formula only works if the three lengths can actually make a triangle: the two shorter sides must add up to more than the longest one. The calculator checks this “triangle inequality” for you. For right-angled triangles, the Pythagorean theorem calculator finds a missing side first.
Common mistakes when calculating area
- Using the slanted side instead of the height. For triangles, parallelograms and trapezoids, the height is measured at right angles to the base, not along the sloping edge.
- Mixing units. A room 4 m by 350 cm must be written as 4 m × 3.5 m. Convert first, or use the length converter.
- Converting area like length. 1 m = 100 cm, but 1 m² = 10,000 cm², because both dimensions are scaled. The same applies to feet: 1 yd² = 9 ft². The area converter handles these directly.
- Confusing radius and diameter. The circle formula uses the radius — half the diameter. Use the “I know the” option to enter whichever you have.
- Forgetting waste for real projects. For tiles, flooring and paint, add 5–10% to the calculated area to allow for cutting and mistakes.
Area Calculator FAQ
How does the area calculator work?
Pick a shape and unit, then enter the measurements shown in the diagram. The area calculator applies the standard formula for that shape, shows the working and converts the result into every common area unit.
How do I find the area of a triangle without the height?
If you know all three sides, use Heron’s formula (choose “Triangle — three sides”). If you know two sides and the angle between them, use A = ½ab sin C (choose “Triangle — two sides + angle”).
How do I calculate square feet?
Measure the length and width in feet and multiply them: a 12 ft × 15 ft room is 180 ft². If you measured in metres, enter the metres and read the ft² value from the conversion table.
How many square feet are in an acre and a hectare?
One acre is 43,560 ft² (about 4,047 m²). One hectare is 10,000 m², which is about 2.471 acres or 107,639 ft².
What is the formula for the area of a circle?
A = πr², where r is the radius. A circle with a diameter of 10 cm has a radius of 5 cm and an area of π × 25 ≈ 78.54 cm².
Can I calculate the area of an irregular shape?
For a four-sided shape with unequal sides, choose “Quadrilateral” and add one diagonal — four sides alone do not fix the area. Otherwise split the shape into rectangles, triangles and sectors and add the areas. For land plots, maps and units such as bigha, use the land area calculator.