Everyday utility

Rectangular Prism Calculator

Enter length, width, and height to calculate volume, total surface area, and space diagonal of a rectangular prism (cuboid). Use the same unit for all three dimensions.

Last reviewed May 19, 2026 by ToolSpilo Editorial Team.

Review method: Reviewed against standard rectangular prism formulas and 3D Pythagorean theorem derivation.

Calculator tool

How this calculator works

Use the explanation to understand the formula, assumptions, and practical limits behind the calculator result.

What a Rectangular Prism Is

A rectangular prism (also called a cuboid or box) is a 3D solid with six rectangular faces where opposite faces are identical. Boxes, bricks, rooms, and shipping containers are rectangular prisms. A cube is a special rectangular prism where all three dimensions are equal.

Formulas

Let ll be the length, ww the width, and hh the height.

MeasurementFormula
VolumeV=l×w×hV = l \times w \times h
Surface areaA=2(lw+lh+wh)A = 2(lw + lh + wh)
Space diagonald=l2+w2+h2d = \sqrt{l^2 + w^2 + h^2}

Worked Example

For a box 8 m long, 5 m wide, 3 m high:

V=8×5×3=120 m3V = 8 \times 5 \times 3 = 120\text{ m}^3
A=2(8×5+8×3+5×3)=2(40+24+15)=2×79=158 m2A = 2(8\times5 + 8\times3 + 5\times3) = 2(40 + 24 + 15) = 2 \times 79 = 158\text{ m}^2
d=64+25+9=98≈9.90 md = \sqrt{64 + 25 + 9} = \sqrt{98} \approx 9.90\text{ m}

The Space Diagonal

The space diagonal is the longest straight line inside the prism, running from one corner to the opposite corner through the interior. It is derived from the Pythagorean theorem applied twice — once across a face, then again in 3D.

Practical Uses

Rectangular prism calculations are used for shipping (box volume, weight limits), concrete (pouring slabs or footings), aquariums, room interior volume, storage containers, and material estimates.

Frequently asked questions

How is the surface area formula derived?

A rectangular prism has three pairs of opposite faces. Each pair contributes: lwlw (top and bottom), lhlh (front and back), and whwh (left and right). Multiplying each by 2 gives:

A=2(lw+lh+wh)A = 2(lw + lh + wh)

For an 8×5×3 box: 2(40+24+15)=158 m22(40 + 24 + 15) = 158\text{ m}^2.

What is the space diagonal of a rectangular prism?

The space diagonal connects opposite corners passing through the center of the box. Apply the Pythagorean theorem first to a face diagonal, then again in the third dimension:

d=l2+w2+h2d = \sqrt{l^2 + w^2 + h^2}

For a 3×4×12 box, d=9+16+144=169=13d = \sqrt{9 + 16 + 144} = \sqrt{169} = 13. This is the longest object that can fit inside the box.

How does a rectangular prism differ from a cube?

A cube is a special rectangular prism where all three dimensions (ll, ww, hh) are equal. A standard rectangular prism can have different values for each dimension. The volume and surface area formulas work for both; for a cube they simplify to V=s3V = s^3 and A=6s2A = 6s^2.

How do I calculate the volume of a room in cubic meters?

Measure the floor length and width and the ceiling height in meters, then multiply: V=l×w×hV = l \times w \times h. For a 5 m × 4 m room with a 2.5 m ceiling: V=5×4×2.5=50 m3V = 5 \times 4 \times 2.5 = 50\text{ m}^3. This tells you the air volume for HVAC sizing or the material volume for filling.