Work out area, perimeter, volume and surface area — with the formula, your numbers substituted and a diagram of the shape. Units can be mixed: enter centimetres, get metres, hectares and acres.
an L-shaped room, a plot with a cut-out: add the parts, subtract the openings
Example
1
20 m²
2
7.5 m²
12
approximate layout, not a drawing
Total area
27.5m²
S = S1 + S2 = 20 + 7.5 = 27.5 m²
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About the formulas
Area is measured in square units and volume in cubic ones, which is why converting between them is not what it seems: a square metre holds not a hundred square centimetres but ten thousand. The formulas for most shapes are simple, but it is easy to mix up where the height goes and where the side does — so this page shows the formula, the substitution and the diagram together.
Area and perimeter
Flat
S = πr² · P = 2πr
Area is how much room a shape takes up, perimeter is the length of its boundary. For a circle they are πr² and 2πr, for a rectangle a×b and 2(a+b).
Volume and surface
Solid
V = πr²h
Volume is how much fits inside, surface area is how much material covers the outside. For a cylinder they are πr²h and 2πr(r+h).
Height, not side
Common mistake
S = ½ a·h
For a triangle and a trapezoid the formula takes the height — a perpendicular, not a slanted side. If you only know the sides, use Heron’s formula.
Square units
Conversion
1 m² = 10,000 cm²
Converting area squares the factor, converting volume cubes it. That is why a square metre holds ten thousand square centimetres and a cubic metre a million cubic ones.
Hectares and sotkas
Land
1 ha = 10,000 m²
A hectare is 10,000 m², about 2.47 acres. In Russia land is also measured in sotkas, hundredths of a hectare: a “six-sotka” plot is 600 m².
Irregular shapes
Composite
add and subtract
An irregular shape is split into simple parts: rectangles are added, while openings, alcoves and columns are subtracted.
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Frequently asked
For a rectangular room, multiply length by width: 5 × 4 m is 20 m². If the room is L-shaped or otherwise irregular, split it into rectangles in the composite shape section, add their areas and subtract columns, alcoves and boxing. You can mix units — length in metres and width in centimetres — and everything is converted to one unit automatically.
The area of a circle is pi times the radius squared: S = πr². For a radius of 5 cm that is 3.1416 × 25 ≈ 78.54 cm². If you know the diameter, the radius is half of it — putting the diameter into the formula gives an area four times too large. The tool shows the formula with your numbers substituted, so every step is visible.
Divide by 10,000. A metre has a hundred centimetres, but area is two-dimensional, so the factor is squared: 100 × 100 = 10,000 cm² in one square metre. That makes 2500 cm² equal to 0.25 m², not 25. Volume works the same way, only cubed: a cubic metre holds a million cubic centimetres. The tool converts automatically and shows several units at once.
A hectare is 10,000 m² — a square one hundred metres on each side — and about 2.47 acres. Russians also measure land in sotkas, hundredths of a hectare: one sotka is 100 m², so a six-sotka plot is 600 m². When an area exceeds a hundred square metres, the tool adds hectares and acres to the answer, and the composite shape handles plots with cut-outs.
Multiply the base area by the height: V = πr²h. A barrel with a 30 cm radius and 90 cm height holds 3.1416 × 900 × 90 ≈ 254,469 cm³, about 254 litres — the tool shows litres on its own. Surface area, 2πr(r + h), is calculated separately: you need it when the material for the walls and lids matters, not what fits inside.
Yes. Switch on the inverse calculation, pick what you know — area, perimeter or volume — and which size to find. The tool rearranges the formula, for example r = √(S / π) for a circle, and shows the working with your numbers. Where no general rearrangement exists, the answer is found numerically, and it is labelled as such. A forward check closes the solution.