Box Volume Calculator

Length

Width

Height

Result

Volume47.25
Litres (if metres)47,250
Surface area80.9
Space diagonal6.673829
Base area17.5
Total edge length44.8

Length times width times height

Volume, surface area, space diagonal and total edge length for a rectangular box or a room.

The simplest solid formula there is, and the most used: room volume for ventilation and heating, box volume for shipping, load volume for a move.

The space diagonal answers a different question — whether something will fit. It is the longest straight line inside the box, and it comes from Pythagoras with three terms under the root instead of two.

What this calculator shows

Volume in cubic units and in litres
Total surface area for wrapping, painting or lining
The space diagonal and the combined length of all twelve edges

What to keep in mind

All corners are right angles. An oblique box needs the perpendicular height rather than the slanted edge.
Litres assume metre inputs, since a cubic metre is a thousand litres.

FAQs

Why calculate room volume?

For ventilation, air conditioning and heating capacity. A rough heating rule is 100 watts per square metre with ceilings up to three metres.

How do I estimate load volume for a move?

Add the volumes of every box and item. Movers quote in cubic metres, and a standard 60 by 40 by 40 cm box is just under a tenth of one.

What is the space diagonal?

The longest line inside the box, corner to opposite corner. It is the root of the sum of the three squared dimensions — Pythagoras in three dimensions.

How many litres in a cubic metre?

Exactly a thousand. A cubic centimetre is a millilitre, which makes the conversions easy in both directions.

Worked example

A 5 by 3.5 room with a 2.7 ceiling

Input: 5 × 3.5 × 2.7 m

Output: 47.25 m³, diagonal 6.67 m

Note: Room volume drives ventilation sizing: a living room wants roughly one air change an hour, so about 47 cubic metres.

Useful links

All tools in Math & Statistics

Box Volume Calculator

Result

Related tools

Cylinder Calculator

Square Footage Calculator

Pythagorean Theorem Calculator

Useful links