GeometryFormula

Cube Formulas (Volume, Surface Area, Diagonal)

A cube is a solid with six equal square faces. Its volume is V = s³, the side length cubed; its surface area is SA = 6s², six identical faces; and its space diagonal (corner to corner) is s√3.

Cube formulas

  • Volume: V=s3V = s^3
  • Surface area: SA=6s2SA = 6s^2
  • Space diagonal: d=s3d = s\sqrt{3}

where s = edge length, V = volume, SA = surface area

Volume

V=s3V = s^3
Worked example

A cube of side 2 has volume 8 cubic units.

V=s3=23=8V = s^3 = 2^3 = 8

Surface area

SA=6s2SA = 6s^2
Worked example

Its surface area is 24 square units.

SA=6s2=6⋅22=24SA = 6s^2 = 6\cdot 2^2 = 24

Space diagonal

d=s3d = s\sqrt{3}

Interactive cube 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.

s = 4
Volume V 64units³
Surface area SA 96units²
Space diagonal d 6.93units

Step-by-step substitution

  • V = s³ = 4³ = 64
  • SA = 6s² = 6 · 4² = 96
  • space diagonal = s√3 = 4 · 1.7321 = 6.93

Classroom use: cube formulas

Who it's for: Grades 6–9 · Middle-school students beginning volume and surface area, including work with nets.

Learning objectives

After using this page, students will be able to:

  • Compute the volume of a cube using V = s³.
  • Compute surface area using SA = 6s² and connect it to a six-square net.
  • Distinguish cubic units from square units in context.

Suggested classroom activity

Pair the explorer with a physical net. Students fold the net, count six faces, then use the explorer to check surface area and volume for their own chosen side length. The units question — why one answer is cm² and the other cm³ — follows naturally from the folding.

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.
CodeStandard
6.G.A.2Find volumes of right rectangular prisms; apply V = lwh and V = Bh.
6.G.A.4Represent 3-D figures using nets and use the nets to find surface area.
7.G.B.6Solve 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

Rectangular PrismSquareAll volume formulasAll surface-area formulas

Add cube to your formula sheet →

Frequently asked questions

What is the volume formula for a cube?

A cube’s volume is V = s³, the edge length cubed. A cube with side 3 has volume 3³ = 27 cubic units.

What is the surface area of a cube?

A cube has six equal square faces, so its surface area is SA = 6s². A cube of side 5 has surface area 6 × 25 = 150 square units.

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