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.

Circle Area: Formula, Derivation & Examples | Area Calculator

Circle Area: The Fundamental Formula

The circle area formula A = Pi x r2 is one of the best known in mathematics. The radius r is the distance from the center to the edge of the circle. Pi (approximately 3.14159) is the ratio of circumference to diameter.

The derivation can be visualized by dividing the circle into infinitely many thin triangles: each triangle has height r and its base is a tiny piece of the circumference. The sum of all bases equals the circumference 2 x Pi x r. The total area is therefore (2 x Pi x r x r) / 2 = Pi x r2.

Radius, Diameter and Circumference

The diameter d is twice the radius: d = 2r. If only the diameter is known, the area is: A = Pi x (d/2)2 = Pi x d2/4.

The circumference is C = 2 x Pi x r = Pi x d. From the circumference you can calculate the radius: r = C / (2 x Pi).

Calculation Examples

Example 1: Circular pool with 3 m radius. Area = Pi x 32 = 28.27 m2. Circumference = 2 x Pi x 3 = 18.85 m. For a cover you need at least 28.3 m2 of material.

Example 2: Round table with 1.2 m diameter. Radius = 0.6 m. Area = Pi x 0.62 = 1.13 m2. For a tablecloth with 20 cm overhang you need a circle with r = 0.8 m, so 2.01 m2.

Example 3: Pizza with 30 cm diameter. Radius = 15 cm. Area = Pi x 152 = 706.86 cm2. A 40 cm pizza has Pi x 202 = 1,256.64 cm2, nearly 78% more area even though the diameter is only 33% larger.

Circle Area in Everyday Life

Circular areas are everywhere: round tables, fountains, pools, satellite dishes, pizzas, cake bases, pipe cross-sections. In engineering, the circular cross-section is particularly important for calculating flow rates in pipes and channels.

Circle Segments and Sectors

Sometimes you don't need the full circle area, just a part. A circular sector (pie slice) with angle alpha has area A = (alpha/360) x Pi x r2. A semicircle (alpha = 180 degrees) has half the circle area.