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