About the Area Calculator
Area is how much surface something covers. It is the number you need before you buy turf, order tiles, price a plot, mix concrete or work out how much paint a wall will drink.
Every shape has its own formula, and this page carries eight of them — rectangle, triangle, circle, trapezoid, parallelogram, ellipse, circle sector and regular polygon. Pick the shape, enter its measurements, and the working shows which formula was applied and why.
They look like eight unrelated things to memorise. They are not. Almost all of them come back to width × height, with the width adjusted for how the shape tapers:
- A rectangle has the same width all the way up, so it is just length × width.
- A parallelogram leans, but each horizontal slice is the same width, so it is base
× height too.
- A triangle tapers from full width to nothing, averaging half, so it is ½ × base ×
height.
- A trapezoid tapers from a to b, averaging (a + b)/2, so it is that average ×
height.
Three formulas, one idea. The circle is the genuine outlier, and π is the price of admission.
How to Use the Area Calculator
Choose the shape, enter its measurements, press Calculate.
Every measurement must be in the same unit. Enter metres and the answer is square metres; enter inches and it is square inches. The calculator never converts behind your back, because a silent conversion is worse than no conversion.
For the triangle, parallelogram and trapezoid, the height is perpendicular — measured at a right angle to the base, not along a sloping side.
The Formulas
Rectangle A = l × w
Square A = s²
Triangle A = ½ × b × h
Parallelogram A = b × h
Trapezoid A = ½ × (a + b) × h
Circle A = π r²
Ellipse A = π × a × b (the two semi-axes)
Sector A = π r² × (angle / 360°)
Regular polygon A = n s² / (4 tan(180°/n))Two of these are worth a closer look.
The parallelogram. Its area is base × height, exactly like a rectangle, and the lean makes no difference at all. Cut the triangle off one end and slide it to the other: you have a rectangle of the same base and height. Nothing was added or taken away. People expect a leaning shape to hold less, and it does not.
The ellipse. πab is the circle formula with the single radius replaced by the two semi-axes. A circle is just an ellipse that has not been stretched — set a = b = r and πab becomes πr². (The ellipse's perimeter is a far harder problem, with no exact elementary formula at all, which is a story for the perimeter calculator.)
The One Thing Everyone Gets Wrong About Area
Doubling the size does not double the area. It quadruples it.
Area involves two dimensions at once, so scaling a shape by a factor of k multiplies its area by k². This holds for every shape on this page, whatever its formula.
| Scale each length by | Area becomes | |----------------------|--------------| | ×½ | a quarter | | ×2 | four times | | ×3 | nine times | | ×10 | a hundred times |
The consequences are everywhere once you look:
- A 16-inch pizza is not a third bigger than a 12-inch one. It is 1.78 times
bigger.
- Doubling the radius of a round patio needs four times the gravel.
- A room 20% larger in each direction has 44% more floor to cover, not 20%.
- Halving a tarpaulin's dimensions leaves a quarter of the shade.
This single fact causes more material-ordering errors than all the arithmetic slips combined, which is why this calculator states the scaling on every result.
Step-by-Step Example
A room with a bay. Main floor 4.2 × 3.6 m, plus a semicircular bay of radius 1.1 m.
Rectangle: 4.2 × 3.6 = 15.12 m²
Semicircle: π × 1.1² × (180/360) = 3.8013 × 0.5 = 1.9007 m²
Total: 17.02 m²Order about 10% over for cuts and waste, so around 18.7 m².
A gable wall. A triangle on a 6 m base, 2.4 m to the apex.
A = ½ × 6 × 2.4 = 7.2 m²Note what happens if you use the sloping rafter instead of the vertical height. A 30° pitch makes the rafter 2.77 m, giving 8.31 m² — 15% too much paint, and the error grows with the pitch.
A tapered garden bed. Parallel sides of 8 and 14 m, 5 m apart.
Average width = (8 + 14) / 2 = 11 m
A = 11 × 5 = 55 m²Irregular Shapes
Almost nothing in a real building is one clean shape, and there is no formula for "L-shaped room". The method is always the same:
- Split the outline into rectangles, triangles and part-circles.
- Calculate each piece separately.
- Add them up, and subtract anything that is a hole — a stairwell, a
chimney breast, a window in a wall you are painting.
An L-shaped room is two rectangles. A room with a bay is a rectangle plus a semicircle. A gable wall is a rectangle plus a triangle. Sketch it, put a number on each piece, and add.
The only real skill is choosing splits whose dimensions you can actually measure.
Understanding Your Result
The area is in square units of whatever you entered.
The formula used names exactly which rule was applied, so you can check it is the one you meant.
The shape line describes what the calculator understood, including special cases it noticed — that your rectangle is a square, or that your ellipse is really a circle.
The scaling line gives the area at double, triple and half the size, for the reason set out above.
The units line is a reminder that every input must share one unit.
When Should You Use This Calculator?
Flooring, carpet and tiles. Area gives quantity; add an allowance for cuts.
Paint. Wall area minus doors and windows, then divide by the coverage on the tin.
Turf, seed, mulch and gravel. Sold by area, or by volume once you add a depth.
Land and property. Price per square metre needs the square metres first.
Fabric and sheet goods. Curtains, upholstery, plywood, plasterboard.
Solar panels. Roof area sets how many will fit.
Ponds and pools. Surface area drives evaporation, cover size and chemical dosing.
Homework. Every shape here is a standard exercise, and the working shows the method rather than only the answer.
Common Mistakes
Using a sloping side as the height. The height is perpendicular to the base. A slanted side is always longer, so the area always comes out too big.
Adding dimensions instead of multiplying. 4 m and 3 m give 12 m², not 7. The units tell you: metres × metres = square metres.
Using the diameter in πr². The formula wants the radius. Putting the diameter in makes the answer four times too large, and it is the most common circle error by a wide margin.
Mixing units. Centimetres against metres is wrong by 100 in length and 10,000 in area. Convert everything first.
Converting squared units by the linear factor. A square metre is 10,000 square centimetres, not 100. The conversion factor gets squared along with the unit.
Assuming equal perimeters mean equal areas. A 1 × 12 rectangle and a 6 × 7 rectangle have the same perimeter and areas of 12 and 42.
Applying the regular-polygon formula to an irregular one. It assumes every side and angle is equal. An irregular polygon needs its corners measured individually.
Ordering exactly the calculated area. Always add a waste allowance — conventionally 10% for straightforward layouts and more for diagonal patterns or awkward rooms.