A room 5 m by 3 m
Fifteen square metres, with a perimeter of 16 m and a diagonal of just over 5.8 m.
The diagonal is the figure to check before ordering anything rigid — a sheet of plywood does not care about the floor area.
Area calculator
Nine shapes, each with its own set of measurements, and a result you can read in square metres, square feet, hectares or acres. Every dimension takes whatever unit you measured in.
Result
Fill in the fields to see your result.
How it works
Most area formulas are one idea in disguise: a length multiplied by a perpendicular width. A rectangle multiplies them directly. A triangle is half a rectangle, so it halves the product. A parallelogram leans over but keeps the same base and perpendicular height, so its area is unchanged — which is why the slanted side never appears in the formula.
Circles break the pattern because they have no straight edges to multiply. Their area comes from pi, the constant relating a circle’s width to its boundary, and it grows with the square of the radius: double the radius and the area quadruples. A sector is simply a fraction of that circle, cut by the angle at the centre.
Where you know three sides but no height, Heron’s formula gets the area from the sides alone. It is more than two thousand years old and still the shortest route from a surveyor’s three measurements to the area they enclose.
Formulas used
Rectangle, triangle, parallelogram
L × W b × h ÷ 2 b × h
Circle, sector, ellipse
π r² r² θ ÷ 2 π a b
- θ
- angle at the centre, in radians
Heron’s formula
A = √(s(s − a)(s − b)(s − c))
- s
- half the perimeter, (a + b + c) ÷ 2
Regular polygon
A = n × c² ÷ (4 × tan(π ÷ n))
- n
- number of sides
- c
- length of one side
Worked examples
A circle of radius 2 m
The area is π × 4, about 12.57 m², and the circumference is 12.57 m as well — a coincidence that only happens at this radius.
Double the radius to 4 m and the area becomes 50.27 m²: four times as much, not twice.
A room measured in feet
Twelve feet by ten gives 120 square feet, which the panel also reports as 11.15 m².
Enter one dimension in feet and the other in metres if that is how you measured — the conversion happens before the multiplication.
Assumptions and limits
- Shapes are flat and regular as described.
- The polygon has equal sides and equal angles.
- The ellipse perimeter uses Ramanujan’s approximation, accurate to better than one part in ten million.
- Angles for the sector are converted to radians before use.
Frequently asked questions
Can I mix units between dimensions?
Yes. Each measurement has its own unit selector, and everything is converted to metres before the formula runs.
That is genuinely useful when a plan gives one figure in centimetres and another in metres, which is more common than it should be.
How do I find the area of an irregular room?
Split it into rectangles and triangles, work out each one, and add them. An alcove or a bay window is usually one extra rectangle.
For a shape with a curved wall, treat the curve as a sector of a circle and add that piece separately.
Why does the parallelogram ignore its slanted side?
Because area depends on perpendicular height, not on how far the shape leans. Slide the top of a rectangle sideways and you get a parallelogram of exactly the same area.
Measuring along the slope instead of straight up will overstate the area, sometimes badly.
How many square feet are in a square metre?
About 10.764. The number surprises people who expect around 3.28, which is the figure for a plain metre.
Squaring a conversion squares its factor: 3.2808 × 3.2808 = 10.764. The same trap catches cubic units, where the factor is cubed.
Updated
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