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Area and volume calculator for common shapes

Area and perimeter of ten plane figures, volume and surface of eight solids, with the formula shown and whatever is not determined flagged.

Parameters

Note

Enter all dimensions in the same unit; the area comes out in its square, the volume in its cube.

Result

Volume

226.195

Formula
V = πr²h, A = 2πr(r + h)
P = 18.8h = 8r = 3
Total surface area
207.345
Lateral surface area
150.796
Base circumference P
18.8496

Calculation, assumptions and sources

OverviewEighteen shapes: square, rectangle, triangle, circle, ellipse, trapezoid, parallelogram, rhombus, circular sector and regular polygon; cube, box, sphere, cylinder, cone, pyramid, torus and spherical cap.

Eighteen shapes: square, rectangle, triangle, circle, ellipse, trapezoid, parallelogram, rhombus, circular sector and regular polygon; cube, box, sphere, cylinder, cone, pyramid, torus and spherical cap. Every result comes with its formula and, for solids, with the lateral and total areas. A quantity the given dimensions do not determine (the perimeter of a triangle known by its base and height) is flagged.

Method & formulasdisc: A = πr², circumference: P = 2πr
disc: A = πr², circumference: P = 2πrsphere: V = 4πr³/3, A = 4πr²cylinder: V = πr²h, cone: V = πr²h/3pyramid: V = (base area) × h / 3

A cone or a pyramid has one third of the volume of the straight solid with the same base and height. The area of the sphere, 4πr², is the derivative of its volume with respect to the radius.

Lateral area vs total area
the lateral area excludes the bases, the total area includes them.
Slant height of a cone
the distance from apex to base edge, l = √(r² + h²). The lateral area is πrl.
Spherical cap
the portion of a ball cut off by a plane. Its curved surface is 2πRh and depends only on its height h (Archimedes).
Validity domainOnly the ellipse perimeter is approximate: Ramanujan’s formula, relative error below 5·10⁻⁵.

Only the ellipse perimeter is approximate: Ramanujan’s formula, relative error below 5·10⁻⁵. Shapes are ideal; irregular polygons and truncated cones are not covered.

Scaling of area and volumeDoubling a dimension multiplies the area by 4 and the volume by 8.

Doubling a dimension multiplies the area by 4 and the volume by 8. A 40 cm pizza has the area of four 20 cm pizzas.