How do you calculate square meters?

For a rectangle, multiply length × width (both in meters). A room of 5 m × 4 m has an area of 20 m². For irregular shapes, divide them into simple forms (rectangles, triangles) and add the partial areas.

How do you calculate circle area?

Circle area = π × r² (Pi times radius squared). If you only know the diameter, halve it first: r = d / 2. Example: A circle with radius 3 m has area π × 3² = 28.27 m².

What is the difference between area and perimeter?

Area measures the content of a flat shape (e.g. in m²) — how much space it covers. Perimeter is the length of the outer boundary (in m). For a 3 × 4 m rectangle, the area is 12 m² and the perimeter is 14 m.

How do you convert m² to cm²?

1 m² = 10,000 cm² (because 1 m = 100 cm, so 100 × 100 = 10,000). Multiply the area in m² by 10,000. Conversely: cm² divided by 10,000 gives m². Similarly: 1 m² = 1,000,000 mm².

How do you calculate triangle area?

Triangle area = (base × height) / 2. The height is perpendicular to the base. Example: base 6 m, height 4 m → area = (6 × 4) / 2 = 12 m². Alternatively: use Heron's formula when all three sides are known.

One hectare (ha) = 10,000 m² = 100 m × 100 m. It is mainly used in agriculture and forestry. For comparison: a football field is about 0.714 ha (7,140 m²). 1 km² = 100 ha.

How do you calculate living space?

Per the German WoFlV regulation: rooms with ceiling height above 2 m count 100%. Areas with 1–2 m height (e.g. under sloped ceilings) count 50%. Below 1 m does not count. Balconies and terraces are typically counted at 25%.

How do you calculate trapezoid area?

Trapezoid area = ((a + b) / 2) × h, where a and b are the two parallel sides and h is the height (perpendicular distance). Example: a = 4 m, b = 8 m, h = 5 m → area = ((4 + 8) / 2) × 5 = 30 m².

π (Pi) is the ratio of a circle's circumference to its diameter — a mathematical constant with the value ≈ 3.14159. Pi is irrational (infinitely many non-repeating decimals) and appears in formulas for circle area (πr²), circumference (2πr) and ellipse area (πab).

How do you calculate irregular shapes?

Calculate irregular areas by decomposing them into simple partial shapes (rectangles, triangles, circle segments) and summing them up. For plots, the Shoelace formula (Gauss area formula) helps: enter the vertex coordinates and get the exact area. Modern GPS apps calculate the area automatically when walking the property boundaries.

Living Space Calculation (WoFlV): The Correct Method | Area Calculator

Calculating Living Space Under WoFlV

The German Living Space Ordinance (WoFlV) from January 1, 2004 provides binding rules for how the living space of a rental apartment or house is calculated in Germany. It replaced the older Second Calculation Ordinance (II. BV) and is the standard for rental agreements.

Correct living space calculation is important: it determines the base rent amount, utility cost allocation, and deviations of more than 10% can be grounds for rent reduction.

Basic Rules of WoFlV

Rooms with a clear height of at least 2 meters count fully (100%) toward living space. Rooms with a clear height between 1 and 2 meters (typical under sloped ceilings) count at half (50%). Rooms below 1 meter height are not considered.

Balconies, loggias, roof gardens and terraces are typically counted at 25%. In particularly desirable locations or with premium finishes, the share can increase to up to 50%.

What Counts as Living Space?

Living space includes: all living rooms (bedrooms, kitchen, bathroom, toilet, hallway within the apartment), storage rooms within the apartment, conservatories (heated at 100%, unheated at 50%), and home offices.

What Doesn't Count?

Not counted as living space: cellars, laundry rooms, heating rooms, garages, attics (if not converted), drying rooms outside the apartment, stairs (more than 3 steps), and chimney protrusions over 0.1 m2.

Practical Example: Attic Apartment

An attic apartment has a floor area of 60 m2. Of this, 40 m2 has ceiling height above 2 m (counts at 100% = 40 m2). 15 m2 has height between 1 and 2 m (counts at 50% = 7.5 m2). 5 m2 has height below 1 m (doesn't count). The living space per WoFlV is: 40 + 7.5 = 47.5 m2, even though the floor area is 60 m2.

Getting Your Living Space Verified

If you suspect the living space stated in your rental contract is incorrect, you can have it measured by a certified surveyor. Costs range from 150 to 400 euros. With a deviation of more than 10%, you can reduce your rent retroactively.

Digital Tools

Modern laser distance measurers with area calculation functions greatly simplify surveying. Some apps can even recognize floor plans from photos and calculate the area automatically. For sloped ceilings, measure the height at several points and mark the 1 m and 2 m lines.