Area Calculator
Calculate the area of rectangles, circles, triangles, trapezoids, ellipses and parallelograms. Shows formula and step-by-step working
Enter values to calculate area
The Six Shape Formulas in One Place
Most area problems boil down to one of six formulas. A rectangle is length Γ width. A triangle is Β½ Γ base Γ height (the half is what trips people up). A circle is ΟrΒ². A trapezium uses ((a + b) / 2) Γ h, where a and b are the parallel sides. An ellipse is Ο Γ a Γ b, with a and b as the semi-axes. A parallelogram, despite the slanted look, is just base Γ height (perpendicular height, not the slanted side).
The most common mistake is using the slanted edge of a triangle or parallelogram as the height. Height always means perpendicular distance between the base and the opposite side or vertex. If you only have the slanted edge, you need a bit of trigonometry first; the [Trigonometry Calculator](/trigonometry-calculator) will give you the perpendicular component from the angle.
Working Out Skirting Board, Tiles, or Flooring
Most real-world area maths comes from buying enough material to cover a room. Measure the floor as a rectangle, then add 10% for cuts and waste. If the room is L-shaped, split it into two rectangles, work out each one, and add them together. Awkwardly shaped rooms (a bay window, a chimney breast notch) are easiest to handle by triangulating: break them into rectangles and triangles, calculate each area, then sum.
When the perimeter matters, not the area (skirting board, coving, edging tape), you want length around the outside, which is just the sum of the sides. Do not confuse the two; ordering 30 m of skirting because the floor is 30 mΒ² is how people end up two trips deep into the local DIY shop.
Common Shape Formulas
| Shape | Formula | Example |
|---|---|---|
| Rectangle | l Γ w | 5 Γ 3 = 15 |
| Triangle | Β½ Γ b Γ h | Β½ Γ 6 Γ 4 = 12 |
| Circle | Ο Γ rΒ² | Ο Γ 5Β² β 78.54 |
| Trapezium | ((a + b) / 2) Γ h | ((4 + 6) / 2) Γ 3 = 15 |
| Ellipse | Ο Γ a Γ b | Ο Γ 4 Γ 2 β 25.13 |
| Parallelogram | b Γ h | 6 Γ 4 = 24 |
Frequently Asked Questions
How do I find the area of an irregular shape?
Split it into shapes you recognise. Most awkward floor plans break cleanly into two or three rectangles plus a triangle for any diagonal corner. Calculate each piece, add the results. For genuinely curved outlines, the grid method works: overlay a grid, count full squares, then estimate partial squares as halves.
Why does the triangle formula have a Β½ in it?
A triangle is exactly half of the rectangle that surrounds it (with the same base and height). That is where the Β½ comes from. Drawing it out helps: a triangle inscribed in a rectangle, base Γ height, divided by two.
Should I use metres or feet?
Use whatever units the materials are sold in. UK flooring and carpet are normally priced per square metre, so work in metres. American or imported timber and some DIY products are priced per square foot. The calculator switches between the two so you can match the supplier.
What is the difference between perimeter and area?
Perimeter is the distance around the outside (used for skirting, fencing, edging). Area is the space inside (used for paint, tiles, carpet). They use different formulas and come in different units: perimeter in metres or feet, area in square metres or square feet.
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