Rectangular Prism Calculator
Enter length, width, and height to get a box’s volume, surface area, and space diagonal.
4 × 3 × 2
A rectangular prism (box) with length l, width w, and height h has volume V = l × w × h, surface area SA = 2(lw + lh + wh), and space diagonal d = √(l² + w² + h²). For a 4 × 3 × 2 box, V = 24, SA = 52, and d ≈ 5.39.
What a rectangular prism is
A rectangular prism — often just called a box or cuboid — is a solid with six rectangular faces meeting at right angles. Its three dimensions are the length, width, and height. Because every face is a rectangle and every corner is square, the volume, surface area, and diagonal all follow directly from those three numbers.
volume, surface area, and space diagonal from the three side lengths
Worked example
Take a box with l = 4, w = 3, and h = 2:
- 1 Multiply the three sides for volume. V = l × w × h = 4 × 3 × 2 = 24 cubic units.
- 2 Add the three distinct face areas. lw + lh + wh = (4×3) + (4×2) + (3×2) = 12 + 8 + 6 = 26.
- 3 Double it for the surface area. SA = 2 × 26 = 52 square units — a box has two copies of each face.
- 4 Take the root of the squared sides for the diagonal. d = √(4² + 3² + 2²) = √(16 + 9 + 4) = √29 ≈ 5.39 units, the longest straight line inside the box.
Volume, surface area, and diagonal of a few boxes
A cube is the special case l = w = h, so all three sides are equal.
| l × w × h | Volume (lwh) | Surface area | Space diagonal |
|---|---|---|---|
| 4 × 3 × 2 | 24 | 52 | ≈ 5.39 |
| 5 × 5 × 5 (cube) | 125 | 150 | ≈ 8.66 |
| 10 × 4 × 3 | 120 | 164 | ≈ 11.18 |
| 2 × 2 × 8 | 32 | 72 | ≈ 8.49 |
| 1 × 1 × 1 (unit cube) | 1 | 6 | ≈ 1.73 |
Reading the results
Watch the units. Volume is in cubic units (units³), surface area in square units (units²), and the diagonal in the same linear units as the sides. Mixing units — say centimetres for length and metres for height — is the most common mistake; convert everything first.
The space diagonal is the longest segment that fits inside the box, running corner to corner through its interior. It is a 3-D extension of the Pythagorean theorem: √(l² + w² + h²). A cube is simply the case where l = w = h, which is why its diagonal reduces to s√3.