VolLab

Rectangular Prism (Box) Volume Calculator

The most common volume calculation there is.

Length

Width

Height

Volume

160

Surface area: 184
Space diagonal: 10.247

What you entered

Length: 8Width: 5Height: 4

1
Volume = l × w × h
8 × 5 × 4= 160
2
Surface area = 2(lw + lh + wh)
2 × (40 + 32 + 20)= 184
3
Space diagonal
√(8² + 5² + 4²)= 10.247

Result

Volume: 160

A 8 × 5 × 4 box has a volume of 160 and a surface area of 184.

Rectangular prism volume, surface area and space diagonal

Volume is length times width times height. Surface area sums the six faces, and the space diagonal runs corner to opposite corner.

Dimensions	Volume	Surface area	Space diagonal
2 x 3 x 4	24.00	52.00	5.3852
5 x 4 x 3	60.00	94.00	7.0711
10 x 5 x 2	100.00	160.00	11.3578
6 x 6 x 6	216.00	216.00	10.3923
12 x 8 x 4	384.00	352.00	14.9666

The 6 x 6 x 6 row shows volume and surface area both at 216, which happens for a cube of side 6 exactly as it does in the cube calculator - s cubed equals 6 s squared only when s is 6. Compare rows two and three: both are moderate boxes but the flatter 10 x 5 x 2 has far more surface area per unit of volume, which is why compact shapes lose less heat and need less packaging material. The space diagonal is the longest straight line that fits inside, which is the figure that decides whether a long object fits in a box.

Same idea as rectangle area, one dimension up

A box's volume is just its footprint area (length × width) multiplied by height — the natural 3D extension of a rectangle's 2D area formula.

Used constantly in shipping and storage

Box volume determines shipping costs, storage capacity, and material needed for packaging — it's one of the most frequently needed real-world geometry calculations.

Frequently asked questions

How do I calculate the volume of a box?

Volume = length × width × height. A box 12×8×6 inches has volume 576 cubic inches. For shipping, carriers often use dimensional weight: (L×W×H) / 5000 (cm) or / 139 (inches) to estimate billable weight.

How do I convert cubic inches to gallons?

1 US gallon = 231 cubic inches. Divide cubic inches by 231. A container 12×10×20 inches = 2,400 in³ ÷ 231 = 10.4 gallons. For liters: 1 liter = 61.024 in³, so divide by 61.024.

What is the surface area of a box?

SA = 2(lw + lh + wh). A 12×8×6 box: SA = 2(96 + 72 + 48) = 2 × 216 = 432 square inches. This tells you how much cardboard, wrapping paper, or paint is needed to cover all six faces.