Rectangular Prism Volume Calculator
From length, width, and height, get the volume, the surface area, and the space diagonal — the three numbers that describe any box.
Three dimensions, three answers
Enter length, width, and height and the calculator returns the volume (l×w×h), the surface area (2(lw+lh+wh)), and the space diagonal (√(l²+w²+h²)) at once.
Keep units consistent
The dimensions are unit-agnostic — your answers come back in the same unit (squared for the surface area, cubed for the volume), so don't mix centimetres with inches.
What is a rectangular prism volume calculator?
Box dimensions in, full box out
A rectangular prism — a box or cuboid — is a solid with six rectangular faces. This calculator turns its three measurements (length, width, and height) into the three numbers that describe the whole shape: its volume, its surface area, and its space diagonal. Each is fixed once you know the three sides, which makes this the tool you need for shipping boxes, rooms, water tanks, aquariums, and any geometry homework where a box shows up.
Enter the length, width, and height in any length unit to get the volume, surface area, and space diagonal instantly.
Three short formulas, all built from the length (l), width (w), and height (h).
volume = l × w × hThe volume is simply the three sides multiplied together (l × w × h). The surface area adds up all six faces — there are three pairs of identical rectangles — giving 2 × (lw + lh + wh). The space diagonal, the line from one corner straight through to the opposite corner, comes from a 3-D Pythagoras: √(l² + w² + h²). Because volume multiplies all three sides, it grows much faster than the surface area as the box gets bigger.
Suppose you have a box with a length of 4, a width of 3, and a height of 2.
Volume
4 × 3 × 2 = 24 cubic units — the space inside the box.
Surface area
2 × (4×3 + 4×2 + 3×2) = 2 × (12 + 8 + 6) = 52 square units — the material to wrap it.
Space diagonal
√(4² + 3² + 2²) = √29 = 5.385165 — the longest straight object that fits inside.
The three outputs answer three different everyday questions. The volume (24 for a 4 × 3 × 2 box) is the capacity — how much it holds; if you measure in decimetres, cubic decimetres are litres, so it tells you how much water a tank or aquarium takes. The surface area (52) is how much material you need to wrap, line, or paint the outside — six faces in total. The space diagonal (about 5.385165) is the longest straight object that can fit corner to corner, which answers the practical question "will this pole fit in the box?". A cube is the special case where all three sides are equal, so a 2 × 2 × 2 box gives a volume of 8, a surface area of 24, and a diagonal of about 3.464102. The key insight is that volume scales with all three dimensions at once, so doubling every side multiplies the capacity eightfold while the surface area only quadruples.
The formulas are exact, but a couple of practical points are worth keeping in mind.
Right-angled boxes and consistent units
These formulas describe a perfect rectangular prism with right angles at every corner. Real objects — a box with rounded edges, a tank with wall thickness, a room with sloped ceilings — will differ a little from the computed value. The dimensions are also unit-agnostic, so the answers are only meaningful if you keep one unit throughout: lengths in centimetres give a volume in cubic centimetres and a surface area in square centimetres, never a mix.