Calculating Area: Formulas for Rectangle, Triangle, Circle
Area formulas for rectangles, triangles, trapezoids and circles, composite shapes such as L-shaped rooms, Pythagoras for sloping edges and unit conversion.
Math & Technology4 linked calculatorsReading time: 6 min.
Whether it is a room, a flower bed or a plot of land: every area can be broken down into a few basic shapes. With six formulas, the Pythagorean theorem and the right units, any everyday area calculation can be solved.
Key takeaways
- Rectangle: length times width. Triangle: base times height divided by 2. Circle: π times radius squared.
- Break irregular areas into rectangles and triangles, calculate them separately and add them up – subtract any cut-outs.
- If an edge is missing, the Pythagorean theorem helps: a² + b² = c².
- Before calculating, convert all measurements to the same unit, ideally metres.
- The are and the hectare are legal units in Germany for land areas: 1 hectare is 10,000 m².
Formulas for the basic shapes
The height is always perpendicular to the base – for slanted shapes it is not the length of the sloping side.
| Shape | Area A |
|---|---|
| Rectangle | A = a × b |
| Square | A = a² |
| Triangle | A = b × h ÷ 2 |
| Trapezoid | A = (a + c) ÷ 2 × h |
| Parallelogram | A = b × h |
| Circle | A = π × r² |
Examples: a room measuring 5 m × 4 m has 20 m². A round flower bed with a radius of 1.5 m has 7.07 m².
Calculate area and volume
Choose a shape, enter the dimensions – area, perimeter and volume with the formula.
Composite shapes
Irregular floor plans are broken into rectangles, triangles or parts of circles. Either add up the parts, or calculate one large rectangle and subtract the missing corners.
Example, an L-shaped room: the enclosing rectangle is 6 m × 4 m = 24 m², minus a missing corner of 2 m × 1.5 m = 3 m². Area: 21 m².
Floor area is not living space
For renting and buying in Germany, living space is what counts: under Section 4 WoFlV, areas under sloped ceilings count only by half or not at all depending on the clear height, and balconies usually by a quarter. For heating and ventilation, however, the volume of the room matters – use the room volume calculator for that.
Sloping edges with Pythagoras
In a right-angled triangle, a² + b² = c²: the squares of the two short sides (legs) add up to the square of the long side (hypotenuse). This gives you diagonals, rafters or stair lengths without measuring them.
Example, a gable roof: ridge height 3 m above the ceiling, half the house width 4 m. The rafter is then √(3² + 4²) = 5 m long (without the roof overhang).
Calculate Pythagoras
Hypotenuse or missing leg from two sides.
Converting area units
Area units grow with the square of length: 1 m is 100 cm, but 1 m² is 100 × 100 = 10,000 cm².
| Unit | in square metres |
|---|---|
| Square centimetre (cm²) | 0.0001 m² |
| Square metre (m²) | 1 m² |
| Are (a) | 100 m² |
| Hectare (ha) | 10,000 m² |
| Square kilometre (km²) | 1,000,000 m² |
Under Annex 1 of the German Units Ordinance, the are and the hectare are legal units, but only for the area of land plots and parcels.
Convert area units
Square metres, hectares, ares, square feet and acres.
Frequently asked questions
How do I calculate square metres?
How do I calculate the area of a triangle?
How do I calculate the area of a circle?
How many square metres are in a hectare?
Sources
Every figure in this article comes from these primary sources or from the linked calculators, which are based on the same sources.
- Units Ordinance (EinhV), Annex 1 – legal units (are, hectare) (accessed September 30, 2026)
- Section 4 WoFlV – how floor areas are counted (accessed September 30, 2026)
Full-Stack Developer & Founder of HEADON.pro
Full-stack developer and founder of HEADON.pro. Developer of Rechnerzentrale.