Why use this calculator
Area is the number that sets the cost of almost every surface job in a house or garden. Paint, tiles, flooring, turf, membrane, mesh and mulch are all priced per square metre or square foot, so a measurement error of five per cent is a five per cent error in the bill, repeated across every material in the quote.
The mistakes are consistent and avoidable: measuring the sloping side of a triangle instead of its perpendicular height, using the diameter where the formula wants the radius, and forgetting that a ten per cent allowance for cuts and breakages is not optional in any tiling or flooring job.
This calculator handles the four shapes that cover nearly every real room and garden bed, and reports the diagonal so you can check on site whether the corners are actually square before ordering anything.
How to use it
- Choose the shape first, because the inputs change with it and the wrong shape is the most expensive mistake available here.
- For a rectangle, measure the two sides at both ends rather than once, since rooms are rarely as square as they look, and enter the longer figure as the length.
- For a circle, enter the radius, which is half the width across the widest point, not the full diameter.
- For a triangle, the height is the perpendicular distance from the base to the opposite corner, measured at right angles to the base and never along the sloping side.
- For a trapezoid, enter the two parallel sides and the perpendicular distance between them.
- Keep every measurement in the same unit and the area will come back in that unit squared.
What each result means
- Area
- The enclosed surface in square units of whatever unit you measured in. Metres in gives square metres out.
- Area including 10% waste allowance
- The quantity to actually order for tiles, flooring, turf or paint, covering cuts, breakages and pattern matching.
- Perimeter
- The distance around the outside, which sets skirting, edging, coving and fencing quantities.
- Diagonal
- Corner to corner distance. Measure both diagonals on site; if they differ, the room is not square and cuts will show.
- Circumference
- The distance around a circle, used for edging a round bed, a pond or a paved circle.
- Diameter
- The full width of the circle across its centre, which is twice the radius you entered.
- Radius
- The distance from the centre to the edge, restated so you can confirm you did not enter the diameter by mistake.
- Base
- The triangle side the perpendicular height was measured against, restated so you can confirm the pairing is right.
- Height
- The perpendicular height used in the calculation, which is not the sloping side of the shape.
- Average of the parallel sides
- The mean of the trapezoid's two parallel sides, which is the effective width used in the area formula.
The formula
Four expressions cover the shapes offered.
A rectangle
A = L × W
A circle
A = πr²
A triangle
A = ½ × b × h
A trapezoid
A = ((a + b) ÷ 2) × h, the average of the two parallel sides a and b multiplied by the perpendicular height h between them
How this number is used in practice
Tilers, floorers and painters all work from area but apply different allowances to it, and knowing which is which prevents both shortfalls and expensive surplus. Tiling normally adds ten per cent for cuts and breakage, rising to fifteen for a diagonal or herringbone layout and more for a large format tile in a small room, because every cut wastes most of a tile.
Flooring adds five to ten per cent depending on plank length and pattern. Paint is different again: coverage is usually quoted between ten and fourteen square metres per litre per coat, and almost every job needs two coats, so the area matters twice.
Room geometry is rarely as clean as a plan suggests. Older buildings routinely have walls out of square by twenty or thirty millimetres over a few metres, which is why the diagonal matters. Measure both diagonals of a rectangular room and compare them: equal diagonals mean the corners are square, and a difference of more than about five millimetres means you should set the floor out from a centre line rather than from a wall, or the taper will be visible along one edge.
For irregular rooms, split the plan into rectangles and triangles, compute each separately and add them, which is exactly how a quantity surveyor does it.
Land and property area follow their own conventions. A hectare is ten thousand square metres and an acre is 4,047 square metres, so an acre is roughly 0.405 of a hectare and a hectare is about two and a half acres. Property measurement standards published by professional bodies define exactly which areas count as internal floor area, which is why an advertised floor area and a measured one often differ: balconies, garages, voids and wall thicknesses are treated differently under different standards.
Worked examples
A 10 by 5 rectangular room
Area 50.0000, perimeter 30.0000 and a diagonal of 11.1803, with 55.0000 to order once a 10% allowance is added.
A circular patio with a 5 metre radius
Area 78.5398 square metres and a circumference of 31.4159 metres for the edging.
A triangular garden bed, 10 along the base and 5 high
Area 25.0000, half what the equivalent rectangle would be.
A trapezoidal block, parallel sides of 10 and 6, height 5
Area 40.0000, which is the 8.00 average width multiplied by the height.
When people use it
- Ordering flooring, tiles or turf with the right waste allowance included
- Estimating how much paint a wall or ceiling needs before buying it
- Checking whether a room is actually square by comparing measured and calculated diagonals
- Sizing a garden bed, patio or lawn area for mulch, soil or seed
- Breaking an irregular floor plan into simple shapes to total the area
Tips
- Measure each dimension at both ends. Rooms are rarely square, and using the shorter figure prevents an expensive shortfall at the far wall.
- For a triangle, the height is perpendicular to the base, never the sloping side. Using the slope overstates the area every time.
- A circle takes the radius, not the diameter. Entering the diameter by mistake gives four times the correct area.
- Add ten per cent for cuts and breakage on tiles and flooring, and fifteen for diagonal or herringbone layouts where offcuts are unusable.
- Compare both diagonals of a rectangular room on site. A difference above about five millimetres means setting out from a centre line, not a wall.
- For irregular shapes, split the plan into rectangles and triangles, calculate each and add them. That is how professional take-offs are done.
- Paint coverage is usually ten to fourteen square metres per litre per coat, and most jobs need two coats, so double the area before converting to litres.
What it assumes, and where it stops being accurate
- The shape is a flat, regular figure with straight or perfectly circular edges. Real rooms with bays, alcoves and chimney breasts must be split up.
- Every dimension is in the same unit, and the calculator has no idea which unit that is. It returns the same unit squared.
- The waste allowance is a flat ten per cent, which suits straight-laid tiles and flooring. Diagonal and large-format layouts need more.
- It is not accurate for sloping ground or curved surfaces. The area of a sloping lawn is larger than its plan area.
- Wall openings, doors and windows are not deducted, which matters for paint but not for flooring.
- Property measurement standards define floor area differently by jurisdiction, so this figure will not always match an advertised one.
Terms used on this page
- Perimeter
- The total distance around the outside of a shape, which sets edging, skirting and fencing quantities.
- Perpendicular height
- The distance from a base to the opposite point measured at right angles, which is what area formulas require.
- Waste allowance
- Extra material ordered above the measured area to cover cuts, breakages and pattern matching.
- Hectare
- Ten thousand square metres, roughly 2.47 acres, the standard metric unit for land area.
Questions people ask
- How do I calculate the area of an irregular shape?
- Split it into rectangles, triangles and part circles, calculate each separately and add the results. That is exactly how a quantity surveyor produces a take-off. For a room with a bay window, treat the main floor as a rectangle and the bay as a trapezoid, and remember to include the depth of any alcove that will be covered by the same material.
- How much extra material should I order?
- Ten per cent above the measured area is the standard allowance for straight-laid tiles and flooring, covering cuts, breakages and a few spares for later repairs. Diagonal, herringbone and large format layouts need fifteen per cent or more, because each cut wastes most of a piece. Pattern matched materials such as patterned carpet need an allowance based on the repeat length.
- How many square metres are in an acre?
- An acre is 4,047 square metres, which is about 0.405 hectares, and a hectare is 10,000 square metres or roughly 2.47 acres. An acre was historically the area one person could plough in a day with a yoke of oxen, which is why it is not a round number in any metric unit.
- Why is the height of a triangle not the sloping side?
- Because the area formula multiplies the base by the distance the shape rises perpendicular to it. The sloping side is always longer than the perpendicular height, so using it overstates the area, sometimes substantially on a shallow triangle. Drop a line at right angles from the apex to the base line, and measure that.
- How do I check a room is square?
- Measure both diagonals from corner to corner. In a true rectangle they are identical, and this calculator reports the diagonal a perfect rectangle of your dimensions would have. If your two measured diagonals differ by more than about five millimetres, set the floor or tile layout out from a centre line so the taper is split across both edges.
- How much paint will an area need?
- Divide the area by the coverage on the tin, usually ten to fourteen square metres per litre, then multiply by the number of coats, which is almost always two. A twenty square metre wall at twelve square metres per litre needs about 1.7 litres per coat, so about 3.3 litres for two coats before any allowance for touch-ups.
Use this with
Area Calculator answers one part of the question. These pick up where it stops: Paint Calculator, Flooring Calculator, Tile Calculator, Mulch, Soil and Gravel Calculator and Concrete Volume Calculator.
Where these figures come from
This calculation is jurisdiction-neutral arithmetic. No country-specific rules are applied.
- Royal Institution of Chartered Surveyors. Property measurement standards and area definitions
- NIST Office of Weights and Measures. Legal units of length and area used in trade
Area Calculator produces an estimate for general information. It is not financial, tax, medical, legal or engineering advice. read the full disclaimer. Spotted a wrong number? Report it and it gets fixed. The form picks up this calculator and the inputs you used.