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.

How do I calculate an irregular area online?

Choose “Custom shape” in the calculator. Sketch the area on the grid or start from a template (e.g. L-shape). Then type in the measured side lengths and angles. The calculator finds the exact area and perimeter with the shoelace formula. The last side closes the shape automatically – measure it as a check.

Area Calculation: All Formulas at a Glance | Area Calculator

Area Calculation: What You Need to Know

Area calculation is one of the most fundamental mathematical operations and we encounter it daily: when renovating, buying property, laying carpet or calculating wall paint. This guide explains all the important formulas and shows when to use each one.

Area measurements are always in square units: square meters (m²), square centimeters (cm²), square kilometers (km²) or hectares (ha). The unit depends on context: rooms in m², properties in m² or ha, countries in km².

Rectangle: The Most Common Shape

The rectangle formula is the simplest and most frequently used. With length $a$ and width $b$ :

A = a \cdot b

A room 5 m long and 4 m wide has an area of 20 m². Most rooms, properties and objects can be calculated as rectangles or combinations of rectangles.

For the perimeter and the diagonal (using the Pythagorean theorem):

P = 2 \cdot (a + b) \qquad d = \sqrt{a^2 + b^2}

Square: Special Case of the Rectangle

A square is a rectangle with equal sides $a$ :

A = a^2 \qquad P = 4a \qquad d = a\sqrt{2} \approx 1.414 \cdot a

A 10 m square therefore has an area of 100 m².

Triangle: Base Times Height Divided by Two

The standard triangle formula with base $b$ and height $h$ is:

A = \frac{b \cdot h}{2}

The height must be perpendicular to the chosen base. In a right triangle, the two legs directly serve as base and height.

If all three sides $a$ , $b$ and $c$ are known, Heron's formula helps. First calculate the semi-perimeter $s$ , then the area:

s = \frac{a + b + c}{2} \qquad A = \sqrt{s\,(s-a)\,(s-b)\,(s-c)}

This formula is especially useful in surveying when the height cannot be measured directly.

Circle: Pi Times Radius Squared

The circle area is calculated from the radius $r$ . If only the diameter $d$ is known, use $r = d/2$ :

A = \pi r^2 = \frac{\pi d^2}{4}

The circumference is:

C = 2\pi r = \pi d

The constant $\pi \approx 3.14159$ is an irrational number with infinitely many non-repeating decimals.

Example: A circle with 3 m radius has area $\pi \cdot 3^2 \approx 28.27\ \text{m}^2$ and circumference $2\pi \cdot 3 \approx 18.85\ \text{m}$ .

Trapezoid: Two Parallel Sides

A trapezoid has two parallel sides $a$ (top) and $b$ (bottom) and a height $h$ between them. The area is the average of the two parallel sides multiplied by the height:

A = \frac{a + b}{2} \cdot h

Trapezoids commonly appear in property plots that are wider on one side. Example: a = 10 m, b = 16 m, h = 20 m gives:

A = \frac{10 + 16}{2} \cdot 20 = 260\ \text{m}^2

Parallelogram: Shifted Rectangle

The area of a parallelogram with base $b$ and height $h$ is:

A = b \cdot h

Important: the height is the perpendicular distance between the parallel sides, not the side length itself. A parallelogram with base 8 m and height 5 m has area 40 m², regardless of how much it's slanted.

Ellipse: Oval Area

The ellipse is a generalized circle with two different semi-axes $a$ (horizontal) and $b$ (vertical):

A = \pi \cdot a \cdot b

If both semi-axes are equal ( $a = b = r$ ), you get the circle formula. The perimeter of an ellipse cannot be calculated exactly with a simple formula. Ramanujan's approximation gives good results:

P \approx \pi \left( 3(a+b) - \sqrt{(3a+b)(a+3b)} \right)

Converting Units: m², cm², km² and More

In area conversions, the factor gets squared: $1\ \text{m} = 100\ \text{cm}$ , so $1\ \text{m}^2 = 100 \cdot 100\ \text{cm}^2 = 10{,}000\ \text{cm}^2$ . Key conversions: 1 km² = 1,000,000 m², 1 ha = 10,000 m², 1 m² = 10.764 ft², 1 acre = 4,047 m².

Calculating Irregular Areas

Not every area can be directly calculated with a formula. Three methods help: First, decomposition into simple shapes (rectangles, triangles) whose individual areas you add up. Second, the Shoelace formula when vertex coordinates are known. Third, GPS-based surveying where you walk the boundaries.

Practical Everyday Applications

Wall paint: paint needed = wall area ÷ coverage per liter. Tiles: area + 10% waste. Property tax: calculation based on plot area in m². Rental contract: living space per WoFlV determines rent per m².

Area Calculation: All Formulas at a Glance