Enter length, width, and height — get volume, surface area, and diagonal instantly.
Enter length, width, and height to see your results
This cuboid calculator — also known as a rectangular prism calculator or box volume calculator — instantly computes the volume, surface area, and space diagonal of any rectangular box from its length, width, and height. Unlike a cube or sphere, a cuboid has three independent dimensions, so all three measurements must be supplied together; no single known value can determine the other two. Whether you're sizing a shipping box, calculating a room's volume, or estimating aquarium capacity, this free tool multiplies and combines your three dimensions in one step and shows the exact formula used.
A cuboid (rectangular prism, or rectangular box) is a three-dimensional solid with six rectangular faces meeting at right angles, defined by three independent measurements: length (l), width (w), and height (h). From these three values, the volume (V = l×w×h), surface area (S = 2(lw+lh+wh)), and space diagonal (d = √(l²+w²+h²)) all follow directly. This calculator takes all three dimensions as input and computes all three derived properties at once.
This tool is built for students verifying solid geometry homework, shippers and logistics planners calculating box or container volume, contractors estimating room or storage space, aquarium and tank owners computing water capacity, and anyone with a rectangular box's dimensions who needs its volume, surface area, or diagonal without manually working through the formulas by hand.
Rectangular boxes are the most common 3D shape in everyday life — from shipping cartons to rooms to furniture — but computing their volume, surface area, or diagonal by hand becomes error-prone once you're juggling three different dimensions across multiple formulas. This calculator combines all three cuboid properties into a single instant calculation, which is especially useful for shipping cost estimates (based on volume), material estimates (based on surface area), and fit checks (based on diagonal).
Shipping and logistics companies calculate dimensional volume for freight pricing. Contractors and homeowners compute room or storage space volume for HVAC or capacity planning. Aquarium and fish tank owners determine water volume from tank dimensions. Warehouse managers calculate storage box or pallet volume for space planning. Movers and packers check whether long items will fit inside a box using the diagonal measurement.
How length, width, and height combine into volume, surface area, and diagonal
Unlike a cube or sphere, a cuboid has no single "known value" shortcut — length, width, and height must all be supplied to compute volume, surface area, or diagonal.
Because all three formulas are symmetric in l, w, and h, swapping which dimension you call "length" versus "width" or "height" never changes the results.
Length, width, height, and diagonal are linear measurements; surface area is squared; volume is cubed — all of the same base unit.
From entering three dimensions to reading all three results
Type in the cuboid's length in the first input field.
Type in the cuboid's width in the second input field.
Type in the cuboid's height in the third input field.
The calculator multiplies and combines the three dimensions to compute volume, surface area, and diagonal.
Review the volume, surface area, and diagonal shown together in the results panel.
Solving a cuboid with length 5, width 4, and height 3
A shipping box measures 5 meters long, 4 meters wide, and 3 meters tall. What is its volume, the cardboard surface area needed to build it, and the longest straight item that could fit diagonally inside?
Explanation: Unlike a cube or sphere, there's no "reverse-solve" shortcut here — all three dimensions had to be supplied together to compute the volume, surface area, and diagonal, since a cuboid has three genuinely independent measurements rather than one.
What each of the three output values represents and how they relate
| Property | What It Represents | Unit Type |
|---|---|---|
| Volume (V) | Three-dimensional space enclosed inside the cuboid | Cubed (e.g. m³, cm³, in³) |
| Surface Area (S) | Combined area of all six rectangular faces | Squared (e.g. m², cm², in²) |
| Diagonal (d) | Straight-line distance from corner to opposite corner | Linear (same unit as l, w, h) |
Reading the results together: the three values describe the same box from different angles — surface area describes the material needed to build or wrap it, volume describes the space it can hold, and the diagonal describes the longest straight line that fits inside it.
Typical ranges: all three inputs and outputs must be positive; there is no theoretical upper bound, and if all three dimensions are equal, the cuboid becomes a cube and these formulas simplify to the cube versions automatically.
Manual verification: multiply your three dimensions directly for volume, sum the three face-area pairs and double the total for surface area, and square-root the sum of the three squared dimensions for diagonal — a quick way to confirm the calculator's math by hand.
Where computing volume, surface area, and diagonal from three dimensions is genuinely useful
Check volume, surface area, and diagonal problems for rectangular prisms step by step.
Calculate dimensional volume for shipping cost and freight cargo estimates.
Determine a room's air volume for HVAC sizing or storage capacity planning.
Compute water volume from a rectangular tank's length, width, and height.
Estimate how much cargo volume a rectangular shipping container can hold.
Calculate individual brick or block volume for material quantity estimates.
Check whether furniture dimensions and diagonal will fit through a doorway.
Estimate cardboard or wrapping material needed for a rectangular box's surface area.
Compute the volume of a rectangular concrete slab, footing, or foundation.
Use the diagonal to check whether a long item will fit diagonally inside a moving box.
Calculate rack or cabinet volume for equipment and airflow planning.
Estimate water capacity for a rectangular pool, cistern, or holding tank.
What this cuboid calculator does well, and where it doesn't apply
How these related terms and shapes compare
| Term | Independent Dimensions | Volume Formula | Example (5×4×3) |
|---|---|---|---|
| Cuboid | 3 (l, w, h can all differ) | l × w × h | 60 |
| Rectangular Prism | 3 (same shape, different name) | l × w × h | 60 |
| Cube | 1 (l = w = h = s) | s³ | s=4 → 64 |
Summary: This cuboid calculator (also called a rectangular prism calculator or box volume calculator) gives you an instant, free way to compute a rectangular box's volume, surface area, and diagonal from its length, width, and height, with the formula shown. Pair it with related tools like the Cube Calculator and Volume Calculator for a fuller picture of solid geometry.
Common questions about cuboid measurements
Trusted educational references to go deeper on cuboids and solid geometry
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