How rectangular prism measurements are calculated
Three perpendicular dimensions describe the whole prism. Volume uses their product, while surface area adds the six rectangular faces.
V = l × w × h; surface area = 2(lw + lh + wh); space diagonal = √(l² + w² + h²)
- Multiply length by width for the base area, then multiply by height for volume.
- Add the three different face areas, lw, lh and wh, then double the sum for all six faces.
- The space diagonal crosses the inside of the prism. Square each dimension, add them and take the square root.
- For a missing dimension, divide the known volume by the product of the other two dimensions.
Worked example: A prism measuring 5 cm by 3 cm by 2 cm has volume 30 cm³. Its surface area is 2 × (15 + 10 + 6) = 62 cm², and its space diagonal is √38 = 6.1644 cm.
Common rectangular prism sizes
| Length | Width | Height | Volume | Surface area | Space diagonal | Litres |
|---|---|---|---|---|---|---|
| 5 cm | 3 cm | 2 cm | 30 cm³ | 62 cm² | 6.1644 cm | 0.03 L |
| 10 cm | 10 cm | 10 cm | 1,000 cm³ | 600 cm² | 17.3205 cm | 1 L |
| 30 cm | 20 cm | 15 cm | 9,000 cm³ | 2,700 cm² | 39.0512 cm | 9 L |
| 60 cm | 40 cm | 40 cm | 96,000 cm³ | 12,800 cm² | 82.4621 cm | 96 L |
| 100 cm | 50 cm | 40 cm | 200,000 cm³ | 22,000 cm² | 118.7434 cm | 200 L |
Swipe the table sideways to see the rest.
Dimensions are in centimetres. Capacity uses the full internal volume.
Things to consider
- Measure length, width and height at right angles to each other.
- For a tank, enter internal dimensions and the water depth to find the water volume.
- Surface area here includes a lid. For an open-top box, subtract length × width.
- A face diagonal lies on one rectangle. The space diagonal runs through the inside.
Frequently asked questions
What is the rectangular prism volume formula?
V = length × width × height. The three measurements must use the same unit. A 5 cm by 3 cm by 2 cm prism has volume 30 cm³.
What is the surface area formula?
Surface area = 2(lw + lh + wh). Each pair of opposite faces has the same area, so double the sum of the three different face areas.
How do I find a missing side from the volume?
Divide volume by the product of the two known sides. For volume 30 cm³, length 5 cm and width 3 cm, height = 30 ÷ (5 × 3) = 2 cm.
What is the space diagonal of a rectangular prism?
It is the straight-line distance between opposite corners through the prism. Its length is √(l² + w² + h²), using the Pythagorean theorem in three dimensions.
Is a cube a rectangular prism?
Yes. A cube is a rectangular prism whose length, width and height are all equal. Other rectangular prisms can have different dimensions.
How many litres does a box or tank hold?
Use its inside dimensions. Multiply volume in m³ by 1,000, or divide volume in cm³ by 1,000, for litres. A 30 cm by 20 cm by 15 cm box holds 9 L when full. For a different tank shape, use the Volume Calculator.
Results are estimates for general information only, not financial, medical or professional advice.