Box formulas
- Volume = length × width × height
- Surface area = 2 × (lw + lh + wh)
- Space diagonal = √(l² + w² + h²), the longest straight line inside the box
Worked examples
A box 2 m × 3 m × 4 m holds 24 m³ and has 52 m² of surface. Its longest diagonal is about 5.39 m, the longest pole that fits inside.
An aquarium 60 × 30 × 40 cm holds 72,000 cm³ = 72 litres (divide cm³ by 1,000). A concrete slab 5 m × 4 m × 0.10 m needs 2 m³ of concrete; order a few percent extra.
Shipping
Couriers charge by "dimensional weight": length × width × height in cm divided by a factor such as 5,000. A 40 × 30 × 20 cm parcel has 24,000 cm³ ÷ 5,000 = 4.8 kg of volumetric weight.
How this works
The page multiplies the three dimensions for the volume, adds the areas of the six faces (three pairs) for the surface area, and uses the three-dimensional Pythagorean theorem for the space diagonal. Results carry your unit, cubed for volume and squared for area. Everything runs in your browser.
Frequently asked
What is the volume of a cube?
Side³: a 10 cm cube holds 1,000 cm³, exactly 1 litre.
How many litres in a box?
Volume in cm³ ÷ 1,000, or in m³ × 1,000.
How do I calculate concrete for a slab?
Length × width × thickness, all in meters, gives m³. Add 5–10% for waste.
What is the space diagonal?
The straight line from one corner to the opposite corner through the inside.
Sources
Reviewed Oct 17, 2026 · test vectors fixtures/calculators/math/volume/box/