$Cuboid$

Cuboid

Find the volume, surface area and diagonal of a rectangular cuboid from its dimensions, and the height from the volume or diagonal.

What is known:

Length, width and height

Length, width and volume

Length, width and diagonal

Length a

Width b

Height c

Units:

Lengths are positive numbers (whole or decimal), angles are in degrees.

Test yourself

The rectangular cuboid calculator finds the volume, the total and lateral surface area, the base area and the diagonal from the three dimensions, as well as the missing dimension from the volume or the diagonal.

Cuboid formulas

Value	Formula
Volume	V = a · b · c
Total surface area	S = 2(ab + bc + ac)
Lateral surface area	S_lat = 2c(a + b)
Diagonal	d = √(a² + b² + c²)
Height from volume	c = V / (a · b)

Example. A box 6 × 4 × 3 dm.
V = 6 · 4 · 3 = 72 dm³ = 72 liters, S = 2 · (24 + 12 + 18) = 108 dm², d = √(36 + 16 + 9) ≈ 7.81 dm.

Volume in liters: 1 dm³ = 1 L, 1 m³ = 1000 L. Useful for the volume of an aquarium, a room or a box.

A rectangular cuboid is a prism whose faces are all rectangles. Its opposite faces are equal, and all four diagonals are equal and meet at one point. If all three dimensions are equal, it is a cube.