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.

Plot Area: How to Calculate Irregular Shapes | Area Calculator

Calculating Irregular Plot Areas

Very few properties are perfect rectangles. Most have irregular shapes with angled boundaries, rounded corners or indentations. Three methods help with area calculation.

Method 1: Triangle Decomposition

The simplest method is breaking the property into triangles. Measure the sides of each triangle and calculate areas using Heron's formula. Add all partial areas together.

Practical approach: Choose a corner point as base and draw diagonals to all non-adjacent corners. A pentagon is thus divided into three triangles, a hexagon into four.

Example: A property has the shape of an irregular quadrilateral with sides 20 m, 25 m, 18 m and 22 m and a diagonal of 30 m. The two triangles yield the total area.

Method 2: Shoelace Formula (Gauss Area Formula)

When coordinates of all vertices are known (e.g., from a survey plan or GPS), you can calculate the area exactly. The formula is: A = |Sum(xi x yi+1 - xi+1 x yi)| / 2, where indices cycle through.

This method is also called the Shoelace algorithm and is particularly well suited for implementation in spreadsheets or programming code.

Method 3: GPS-Based Surveying

Modern GPS apps (e.g., GPS Fields Area Measure or Google Earth) allow you to simply walk the property boundaries. The app records the path and automatically calculates the enclosed area. Accuracy with smartphone GPS is about 3-5 m, with differential GPS (DGPS) under 1 cm.

Plot Area vs. Building Footprint vs. Living Space

Important distinction: Plot area is the total ground area according to the cadastral office. Building footprint (relevant for GRZ/site coverage ratio) is the horizontal projection of the building. Living space (per WoFlV) is the usable area inside the building.

Cadastral Map and Land Registry

The official plot area is recorded in the land registry and cadastral map. You can request an extract from the cadastral office showing the exact area and boundary courses. In case of discrepancies between your own measurement and the official record, the official area generally prevails.

Partial Areas in Zoning Plans

Zoning plans specify site coverage ratio (GRZ) and floor area ratio (GFZ). A GRZ of 0.3 on an 800 m2 plot means: a maximum of 240 m2 may be built on. Calculating the buildable area therefore requires precise knowledge of the plot area.