Area Calculator
Find the area of 2D shapes including rectangles, triangles, circles, parallelograms, and trapeziums — with the exact formula, substitution and step-by-step working shown.
Area calculator
Step by step calculations
Choose a shape, enter measurements and press Calculate to see the step by step formula and working.
Area Calculator Explained
Core concepts, classroom applications, and plain-English explanations for all audiences.
When would you actually use this?
Every time you buy flooring, carpet or paint, you're calculating area. A living room that's 4.5 m × 3.8 m has an area of 17.1 m². Carpet is sold per m², so you need this number before you can even get a quote — and you'd add 10% for cuts and waste.
Worked example
"You want to paint one wall. The wall is 5.2 m wide and 2.4 m high, with a door (2.1 m × 0.9 m) you don't need to paint. How much area needs paint?"
Wall area: 5.2 × 2.4 = 12.48 m²
Door area: 2.1 × 0.9 = 1.89 m²
Result: 12.48 − 1.89 = 10.59 m²
Most emulsion covers 10–12 m² per litre — so 1 litre per coat, with 2 coats needed.
Why does the triangle formula have ½?
Any triangle is exactly half a rectangle with the same base and height. Draw a rectangle, cut it diagonally — you always get two identical triangles. That's why A = ½ × b × h. The height must be perpendicular to the base, not the slant side.
Mistake to avoid
Using the slant height for a triangle instead of the perpendicular height. The height in the formula is always the shortest distance from the apex down to the base line — measured at a right angle.
Area formulas
Rectangle
A = l × w
Here, 'l' stands for the length of the rectangle and 'w' stands for its width. You multiply these two dimensions together to find the area.
Square
A = s²
A square is a special type of rectangle where all four sides are equal in length. 's' represents the length of one side. Squaring the side means multiplying it by itself (s × s).
Triangle
A = ½ × b × h
For a triangle, 'b' is the length of its base, and 'h' is its perpendicular height. The perpendicular height is the straight vertical distance from the base to the opposite vertex (corner), forming a right angle with the base. It's not the length of a slanted side.
Circle
A = π × r²
In a circle, 'r' is the radius (the distance from the centre to any point on the circumference). 'π' (pi) is a special mathematical constant, approximately 3.14159. You square the radius (r × r) and then multiply by pi.
Parallelogram
A = b × h
For a parallelogram, 'b' is the length of its base, and 'h' is its perpendicular height. The perpendicular height is the straight vertical distance between the base and the opposite parallel side, measured at a right angle to the base.
Trapezium
A = ½ × (a + b) × h
A trapezium has one pair of parallel sides. 'a' and 'b' are the lengths of these two parallel sides. 'h' is the perpendicular height, which is the straight distance between the two parallel sides, measured at a right angle.
What is Area?
Area is the amount of two-dimensional space a shape or surface covers. Imagine painting a wall; the amount of paint you need depends on the wall's area. It's a measure of how much 'stuff' fits inside the boundaries of a flat shape.
Understanding area is crucial in many real-world situations, from calculating the size of a room for flooring to determining the amount of fabric needed for a project. On this page, you'll find formulas, explanations, and common mistakes to help you master area calculations for common shapes.
Common mistakes to avoid
- Calculating the area of a triangle or parallelogram using the length of a slanted side instead of the perpendicular height:The formula requires the perpendicular height (the height measured at a right angle to the base) to correctly represent the 'squashed' rectangle or parallelogram that the shape can be derived from. Always identify the perpendicular height, which forms a 90-degree angle with the base.
- Adding up all the sides of a shape when asked for its area:Perimeter is the distance around the outside of a shape, while area is the space it covers inside. They are different measurements with different units. Remember that area is about the space inside the shape, and perimeter is about the distance around it.
- Stating the area in units like 'cm' or 'm' instead of 'cm²' or 'm²':Area is a two-dimensional measurement, so its units must be squared to reflect this (e.g., square centimetres, square metres). Always include the correct squared units (e.g., cm², m², km²) when stating an area.
- Calculating the area of a triangle as base × height, or a trapezium as (a + b) × h:A triangle is essentially half of a rectangle/parallelogram, and a trapezium can be thought of as half of a parallelogram formed by two identical trapeziums. The ½ is crucial for these shapes. Always remember the '½' factor in the formulas for triangles and trapeziums.
- Calculating the area of a circle as π × 2r (pi times two times radius) or π × r (pi times radius):The formula requires the radius to be squared (r²), not multiplied by 2. π × 2r is the formula for the circumference (distance around) of a circle. Ensure you square the radius (r × r) before multiplying by π for the area of a circle.