Rectangular Prism Formulas (Volume, Surface Area)

A rectangular prism (cuboid) is a box with six rectangular faces. Its volume is V = l·w·h; its surface area is SA = 2(lw + lh + wh); and its space diagonal is √(l² + w² + h²).

Rectangular Prism formulas

Volume: $V = l w h$
Surface area: $SA = 2(lw + lh + wh)$
Space diagonal: $d = \sqrt{l^2 + w^2 + h^2}$

where l, w, h = length, width, height, V = volume, SA = surface area

Volume

V = l w h

Worked example

A 6 × 4 × 3 box has volume 72 cubic units.

V = l w h = 6\cdot 4\cdot 3 = 72

Surface area

SA = 2(lw + lh + wh)

Worked example

Its surface area is 108 square units.

SA = 2(lw + lh + wh) = 2(24 + 18 + 12) = 108

Space diagonal

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

Interactive rectangular prism explorer

Drag a slider (or type a value, or use the arrow keys) and watch the diagram, the results, and the full step-by-step substitution update live.

Length l

Width w

Height h

Volume V 72units³

Surface area SA 108units²

Space diagonal d 7.81units

Step-by-step substitution

V = l · w · h = 6 · 4 · 3 = 72
SA = 2(lw + lh + wh) = 2(24 + 18 + 12) = 108
diagonal = √(l²+w²+h²) = 7.81

Classroom use: rectangular prism formulas

Who it's for: Grades 6–9 · Middle-school students applying V = lwh and computing surface area from nets.

Learning objectives

After using this page, students will be able to:

Compute volume of a rectangular prism from three dimensions.
Compute surface area as the sum of three pairs of congruent faces.
Solve for a missing dimension given the volume.

Suggested classroom activity

Hold volume constant at 24 and ask for every whole-number prism that achieves it, checking each in the explorer. Students find that surface area varies widely while volume does not — the packaging-design question in miniature.

Standards alignment

Aligned to the Common Core State Standards for Mathematics. Codes are given exactly as published so they can be matched against state crosswalks.
Code	Standard
`6.G.A.2`	Find volumes of right rectangular prisms; apply V = lwh and V = Bh.
`6.G.A.4`	Represent 3-D figures using nets and use the nets to find surface area.
`7.G.B.6`	Solve real-world problems involving area, volume, and surface area of 2-D and 3-D objects.

Free to use and adapt in class under the terms on our license page — no account, no sign-up, no ads. Content last reviewed August 2026.

Related & next steps

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Frequently asked questions

What is the volume of a rectangular prism?

The volume of a rectangular prism is V = l·w·h, length times width times height. A 6 × 4 × 3 prism has volume 72 cubic units.

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