Math calculators

Cube Calculator

Updated Aug 29, 2026 By Jehan Wadia
Rate Formulas

Cube Inputs

Accepts positive/negative integers, decimals and E‑notation (e.g. 1.5e3). Maximum 20 characters.
Areas are shown in this unit squared, volumes in this unit cubed.

Results

Cube of the side length
4³ = 64 cm³
4³ = 4 × 4 × 4 = 64 cm³
Side Length
a
4 cm
Cube (a³)
a × a × a
64 cm³
Volume
V = a³
64 cm³
Surface Area
S = 6a²
96 cm²
Face Diagonal
d = a√2
5.65685 cm
Space Diagonal
D = a√3
6.9282 cm
Total Edge Length
L = 12a
48 cm
Cube Root (∛a)
side of a cube whose volume is 4 cm³
1.5874 cm

Step-by-Step Solution

Cube Diagram

How Volume & Surface Area Grow With Side Length

Scaling Comparison

Scale Side Volume Surface Area Space Diagonal

Introduction

A cube is a box shape with 6 equal square faces. Every edge is the same length. That one length, called the side (a), tells you everything else about the cube.

This cube calculator does the math for you. Type in the side length and it finds the volume (a³), the surface area (6a²), the face diagonal (a√2), the space diagonal (a√3), and the total edge length (12a). You can also work backward: enter the volume and the calculator finds the side length using the cube root (a = ∛V).

You can enter numbers in mm, cm, m, km, inches, feet, or yards, and show your answers in any of those units. Volume can also be entered in liters, milliliters, or US gallons. Decimals and E-notation like 1.5e3 both work.

Every answer comes with a step-by-step solution, so you can see how each formula works. A diagram, a chart, and a scaling table show how volume and surface area grow when the side length grows. This makes the tool useful for homework, shipping boxes, concrete blocks, tanks, and any job where you need cube volume fast.

How to use our Cube Calculator

Type in one number — the side length of a cube or its volume — and the calculator gives you the volume, surface area, face diagonal, space diagonal, total edge length, and a step-by-step solution.

Pick a mode tab: Choose "Side Length → Properties" if you know how long one edge is. Choose "Volume → Side Length" if you know the volume and want to find the edge using the cube root.

Side length: Type the length of one edge of the cube. You can use whole numbers, decimals, or E-notation like 1.5e3. Then pick the unit next to the box: mm, cm, m, km, in, ft, or yd.

Volume: In the second tab, type the volume of the cube. Pick its unit from the list: mm³, cm³, m³, km³, in³, ft³, yd³, liters, mL, or US gallons. Volume must be zero or more.

Show results in: Pick the unit you want your answers in. Lengths use this unit, areas use it squared, and volumes use it cubed. The calculator converts for you, but you can also use our unit converter calculator or volume conversion calculator for other jobs.

Calculate: Click this button to get your cube results, the step-by-step math, the diagram, the growth chart, and the scaling table.

Reset: Click this to clear your work and start over with the default cube.

What Is a Cube?

A cube is a 3D shape with 6 square faces, 12 edges, and 8 corners. Every edge is the same length. That one length is called the side, written as a. Because all sides match, you only need one number to find everything else about a cube. If your box is not a perfect cube, use the general volume calculator instead.

Cube Formulas

These are the main formulas used for a cube with side length a:

  • Volume: V = a × a × a = a³
  • Surface area: S = 6a² (six equal square faces — see the surface area calculator for other shapes)
  • Face diagonal: d = a√2 (corner to corner across one flat face, from the Pythagorean theorem)
  • Space diagonal: D = a√3 (corner to the opposite corner, through the middle)
  • Total edge length: L = 12a
  • Side from volume: a = ∛V (the cube root)

Cubing a Number vs. the Cube Root

To cube a number means to multiply it by itself three times. For example, 4³ = 4 × 4 × 4 = 64. You can raise numbers to any power with the exponent calculator. The cube root does the opposite. It asks: what number times itself three times gives this answer? So ∛64 = 4. If you know the volume of a cube, the cube root gives you the side length. For other roots, try the square root calculator or the general root calculator.

Why Volume Grows So Fast

When you double the side of a cube, the volume does not double. It gets 8 times bigger, because 2³ = 8. The surface area gets 4 times bigger, because 2² = 4. Triple the side and the volume jumps 27 times. This is why a big box holds much more than it looks, and why small changes in side length change volume a lot. To measure that jump as a percent, use the percentage increase calculator.

Units Matter

Length uses plain units like cm, m, in, or ft. Area uses squared units like cm². Volume uses cubed units like cm³. Volume can also be shown in liters or gallons — see the liters to gallons calculator. Note that 1 cm³ equals 1 mL, and 1,000 cm³ equals 1 liter. Always keep your units the same before you do the math; the cm to inches calculator and feet to meters calculator can help you line them up.

Where Cubes Show Up

Cubes are used to measure shipping boxes, storage bins, fish tanks, concrete blocks, sugar cubes, dice, and Rubik's Cubes. Builders use cube volume to order material, often in cubic yards or cubic feet. Shippers use it to figure out how much fits in a truck — see the CBM calculator and volumetric weight calculator. Students use it to learn powers, roots, and 3D geometry alongside tools like the sphere volume calculator, cylinder volume calculator, and cone volume calculator.

Quick Example

A cube has a side of 5 cm.

  • Volume = 5³ = 125 cm³
  • Surface area = 6 × 5² = 150 cm²
  • Face diagonal = 5 × 1.414 ≈ 7.07 cm
  • Space diagonal = 5 × 1.732 ≈ 8.66 cm
  • Total edge length = 12 × 5 = 60 cm

Formulas used

Cube of the side length (volume)
V = a^3 = a \times a \times a
Side length from volume (cube root)
a = \sqrt[3]{V}
Surface area
S = 6a^2
Face diagonal
d_f = a\sqrt{2}
Space diagonal
d_s = a\sqrt{3}
Total edge length
L = 12a
Unit conversion of side length
a_{out} = a_{in} \times \frac{f_{in}}{f_{out}}

Frequently asked questions

Can I enter a negative side length?

Yes. The calculator will still cube it, so (−4)³ = −64. But a real cube cannot have a negative size. That is why volume, surface area, and the diagonals are worked out from the positive value, |a|. A yellow note tells you when this happens.

What does the Cube Root box show when I enter a side length?

It shows ∛a — the cube root of the number you typed. If you enter 4, it shows about 1.5874. That is the side of a cube whose volume would be 4. It is a bonus answer, not part of your cube's size.

How do I find the side length if I only know the volume?

Click the Volume → Side Length tab, type the volume, and pick its unit. The calculator takes the cube root for you. Example: a volume of 64 cm³ gives a side of 4 cm.

Why is the space diagonal longer than the face diagonal?

The face diagonal only crosses one flat square face. The space diagonal goes from one corner all the way through the middle to the far corner. Since √3 (about 1.732) is bigger than √2 (about 1.414), the space diagonal is always longer.

Can I enter the volume in gallons and get the side in inches?

Yes. Pick gallons in the volume list, then pick inches in the Show results in box. The calculator converts everything for you. It works with any mix of units in the lists.

What is E-notation and how do I type it?

E-notation is a short way to write very big or very small numbers. Type 1.5e3 for 1,500 or 2e-4 for 0.0002. Both the side length box and the volume box accept it.

Why does my answer show only about 6 digits?

Results are rounded to 6 significant digits so they stay easy to read. Very large or very small answers switch to scientific notation, like 1.2 × 1013. The math behind the scenes uses the full value.

Can this calculator work out a box that is not a cube?

No. A cube must have all 12 edges the same length. If your box has a different length, width, and height, use a general volume or box calculator instead.

How do I turn cm³ into liters or gallons?

Use these simple facts:

  • 1 cm³ = 1 mL
  • 1,000 cm³ = 1 liter
  • 1 liter ≈ 0.264 US gallons

You can also type the volume in liters or gallons in the reverse tab and let the tool convert.

What does the orange dashed line on the chart mean?

It marks your cube's side length on the graph. The blue line shows volume growing and the green line shows surface area growing. You can see how fast volume climbs compared to surface area.

What is the scaling table for?

It shows your cube at 0.5×, 1×, 1.5×, 2×, and 3× its side length. Your cube is the highlighted row. It is a fast way to see how volume and surface area change when you resize a cube.

Can I find the side length from the surface area?

Not directly in this tool, but the math is easy. Divide the surface area by 6 to get one face, then take the square root. Example: 96 cm² ÷ 6 = 16, and √16 = 4 cm. Then type 4 into the side length box.

Why did my numbers change when I switched the results unit?

The cube stays the same size, but the unit changed. A 4 cm cube is also 40 mm, and its volume goes from 64 cm³ to 64,000 mm³. Bigger units give smaller numbers, and smaller units give bigger numbers.

Can I use fractions like 1/2?

No. Change the fraction to a decimal first. Type 0.5 instead of 1/2, or 2.25 instead of 2 1/4.

Why does the calculator say my number is too large?

Cubing grows fast, so huge inputs make numbers a computer cannot handle. Try a smaller number, or pick a larger unit like km or m instead of mm.

Why can't I enter a negative volume?

Volume is the space inside a shape, so it can never be less than zero. In math, ∛−8 = −2, but that answer has no meaning for a real box or tank.

Do the results update as I type?

Yes. The tool updates a moment after you stop typing. You can also press Enter or click Calculate to see the answers and any error messages right away.

How many corners, edges, and faces does a cube have?

A cube has 8 corners, 12 edges, and 6 square faces. Every face is the same size and every edge is the same length.

Is a cube the best shape for holding volume?

No. A sphere holds the most volume for the least surface area. But a cube is the best box shape, so it wastes less material and stacks well, which is why boxes and crates are often close to cubes.

What is a good real-life use for the space diagonal?

It tells you the longest straight item that fits inside the cube. If a cube box has 30 cm sides, the space diagonal is about 51.96 cm, so a 50 cm rod fits corner to corner but a 55 cm rod does not.