Rooms, shipping boxes, bricks, aquariums and shipping containers are rectangular prisms. Volume tells you capacity, surface area how much material or paint is needed, and the space diagonal the longest pole that fits inside.
How to use the Rectangular Prism Calculator
- Length l
- Width w
- Height h
Results update as you type, and everything is calculated in your browser.
How it works
Enter the three dimensions in any units. Each field has its own unit menu.
Inputs explained
| Field | What to enter |
|---|---|
| Length l | Units: cm, m, mm, in, ft, yd … |
| Width w | Units: cm, m, mm, in, ft, yd … |
| Height h | Units: cm, m, mm, in, ft, yd … |
What each result means
- Volume = [Length l]×[Width w]×[Height h]
- Surface area = 2×([Length l]×[Width w] + [Length l]×[Height h] + [Width w]×[Height h])
- Space diagonal = sqrt([Length l]^2 + [Width w]^2 + [Height h]^2)
- Base diagonal = sqrt([Length l]^2 + [Width w]^2)
- Lateral area (four sides) = 2×[Height h]×([Length l] + [Width w])
- Surface to volume ratio = 2×([Length l]×[Width w] + [Length l]×[Height h] + [Width w]×[Height h])÷([Length l]×[Width w]×[Height h])
Example values
How the main result changes when Length l changes and everything else stays at the example values above:
| Length l (cm) | Volume (cm³) |
|---|---|
| 5 | 120 |
| 7.5 | 180 |
| 10 | 240 |
| 12.5 | 300 |
| 15 | 360 |
| 20 | 480 |
Formula
V = l·w·h, A = 2(lw + lh + wh), d = √(l² + w² + h²)
Worked example
Inputs: Length l: 10 cm; Width w: 6 cm; Height h: 4 cm.
Results: Volume = 240 cm³; Surface area = 248 cm²; Space diagonal = 12.328828 cm; Base diagonal = 11.661904 cm; Lateral area (four sides) = 128 cm²; Surface to volume ratio = 1.033333 cm⁻¹.
Key terms
- Cuboid
- Another name for a rectangular prism.
Frequently asked questions
What is a rectangular prism?
A box whose six faces are rectangles, a cuboid.
How many litres is 50 × 30 × 40 cm?
60,000 cm³ = 60 L.
What is the longest rod that fits in a box?
The space diagonal √(l² + w² + h²).
Is a cube a rectangular prism?
Yes, with all edges equal.