Rectangular Prism Calculator

Background.

Most of the boxes in daily life are rectangular prisms: a shipping carton, a fish tank, a brick, a shoebox, a room. Three measurements describe each of them completely — length, width and height, meeting at right angles — and from those three come the answers people usually need: how much it holds, how much material covers it, and the longest straight line that fits inside.

Volume is the product of the three edges, so it is the number for capacity: how much water a tank takes, how much soil fills a raised bed, how much air a room holds. Measure in centimetres and the volume is in cubic centimetres, and every 1,000 of those is a litre. A 60 × 30 × 36 cm tank holds 64,800 cm³, or 64.8 litres, filled to the brim.

Surface area adds up the six faces, which come in three matching pairs. It answers covering questions — cardboard for a box, paint for a crate, insulation for a tank. Real jobs rarely need all six faces: a room's walls get painted but not its floor, a raised bed has no lid. Treat the figure as the total and subtract whatever you will not cover.

The space diagonal runs from one corner to the opposite corner through the middle of the box. It is the longest rod, pole or umbrella that will lie inside, and it comes from applying Pythagoras twice. The default 3 × 4 × 12 box shows this neatly: its base diagonal is 5 and its diagonal through the box is 13.

The shape is treated as solid, with exact right angles. No wall thickness is subtracted, so an inside capacity needs inside measurements.

What is rectangular prism calculator?

A rectangular prism, also called a cuboid or simply a box, is a solid with six rectangular faces in which every corner is a right angle. Opposite faces are identical, so the whole shape is fixed by three edge lengths: length, width and height. A cube is the special case with all three equal. Volume, surface area and the space diagonal all follow from those three numbers, in whatever unit the edges were measured.

How to use this calculator.

1. 01Measure the three edges that meet at one corner and enter them as length, width and height. The order makes no difference to any of the results.
2. 02Use the same unit for all three edges. The volume comes out in that unit cubed and the surface area in that unit squared, so centimetres give cm³ and cm².
3. 03For capacity, measure the inside of the container rather than the outside, because no wall thickness is subtracted.
4. 04To check whether a long item fits, compare its length with the space diagonal; if it is shorter and reasonably thin, it can lie corner to corner.

The formula.

Volume V = l × w × h. Surface area SA = 2(lw + lh + wh): the three products are the areas of the three different faces, and each face has an identical partner opposite it. The space diagonal d = √(l² + w² + h²) comes from Pythagoras applied twice — first across the base to get √(l² + w²), then from that base diagonal up to the far top corner. The three results respond differently to scale. Doubling every edge multiplies the volume by 8, the surface area by 4 and the diagonal by 2, which is why a large tank needs less surface per litre than a small one of the same proportions. For a fixed volume, the cube has the smallest surface area of any rectangular box. Each edge must be greater than zero and no more than 1,000,000 units.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, Rice University. Precalculus 2e, 2021. Trigonometry and analytic geometry chapters. Retrieved 2026-08-06.
2. [2]OpenStax, Rice University. College Algebra 2e, 2021. Algebra and function chapters. Retrieved 2026-08-06.
3. [3]NIST/SEMATECH. e-Handbook of Statistical Methods, 2012. Chapter 1.3 and Chapter 4. Retrieved 2026-08-06.