Area and perimeter of plane shapes, volume of solids, and Pythagoras — seven calculators that write out the formula and substitute your numbers.
Area says how much space a shape covers and is given in square units. Perimeter is the length of its boundary, in ordinary units. The circle and rectangle calculators show both at once so they do not get mixed up.
In a triangle or a trapezium the height is the perpendicular distance to the base, not the length of a slanted side. Substituting a side for the height overstates the answer — the classic error in these questions.
The calculator uses the full value of π rather than the 3.14 approximation, so the answer is more precise than one worked out by hand. If a question wants the answer left “in terms of π”, take the formula from the Formula panel and skip the final multiplication.
Multiply π by the radius squared: A = π r². For a radius of 5 that is π · 25 ≈ 78.54.
The circumference is 2π r, twice π times the radius. For a radius of 5 that is about 31.42.
By Pythagoras: c = √(a² + b²). For legs of 3 and 4 the answer is exactly 5.
Area describes a flat shape and is measured in square units. Volume applies to a solid and is measured in cubic units.
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