One Measurement Unlocks Everything About a Cube
A cube is the simplest 3D shape: six identical square faces, twelve equal edges, eight vertices. Because every edge is the same length, one measurement — a single side — determines the volume, the surface area, and both diagonals.
This volume of a cube calculator takes that side length and returns V = a³ plus the bonuses most calculators skip: surface area (6a²), face diagonal (a√2), space diagonal (a√3) and base area — each with the working shown, in your choice of units.
V = a³ · surface area · diagonals
Please enter a positive side length.
A cube has 6 identical square faces, 12 equal edges and 8 vertices. Doubling the side multiplies the volume by 8 and the surface area by 4.
How to Use the Volume of a Cube Calculator
- Measure one edge of the cube (any edge — they are all equal).
- Enter the side length and pick your unit (cm, m, mm, in, ft).
- Click Calculate Volume.
- Read the results: volume front and center, with surface area and both diagonals below, plus step-by-step working.
Cube Formulas
Surface area: SA = 6a² (six square faces)
Face diagonal: d = a√2 | Space diagonal: D = a√3
Base area: a²
Worked example: side a = 5 cm. Volume = 5³ = 125 cm³. Surface area = 6 × 25 = 150 cm². Face diagonal = 5√2 ≈ 7.07 cm; space diagonal = 5√3 ≈ 8.66 cm.
Quick Reference: Cubes 1–10
| Side (a) | Volume (a³) | Surface area (6a²) |
|---|---|---|
| 1 | 1 | 6 |
| 2 | 8 | 24 |
| 3 | 27 | 54 |
| 4 | 64 | 96 |
| 5 | 125 | 150 |
| 6 | 216 | 216 |
| 7 | 343 | 294 |
| 8 | 512 | 384 |
| 9 | 729 | 486 |
| 10 | 1,000 | 600 |
Working Backwards: Find the Side From the Volume
Sometimes you know the capacity and need the size. Reverse the formula with the cube root: a = ∛V. A volume of 27 cm³ gives a = ∛27 = 3 cm. A 1-litre cube (1,000 cm³) has 10 cm sides, and a 125-litre storage cube works out to ∛125,000 = 50 cm per side
Real-World Uses for Cube Volume
Students meet cubes in geometry class — volume, surface area and diagonals are exam staples. Movers and shippers estimate box volumes for packing and freight. DIYers calculate concrete, soil or storage volumes for cube-shaped containers. 3D designers sanity-check bounding boxes.
Scaling tip: double the side and the volume grows 8× (2³) while surface area grows only 4× (2²) — why big containers hold so much more than they look.
Frequently Asked Questions
What is the formula for the volume of a cube?
V = a³, where a is the side length. Multiply the side by itself three times: a × a × a.
How do you find the surface area of a cube?
A cube has 6 identical square faces, each of area a², so surface area = 6a².
What is the space diagonal of a cube?
The space diagonal runs from one corner to the opposite corner through the center: D = a√3. The face diagonal (across one square face) is d = a√2.
How is the volume of a cube different from a rectangular box?
A cube is the special case where length = width = height = a, so V = a³. A general box uses V = l × w × h.
What are the units of cube volume?
Cubic units matching your side: cm → cm³, m → m³, inches → in³. Surface area uses square units.
If I double the side of a cube, what happens to the volume?
Volume multiplies by 8 (2³) and surface area by 4 (2²). This cube-square scaling is why larger objects have relatively less surface per unit volume.
How do I find the side length of a cube from its volume?
Take the cube root: a = ∛V. For V = 27 the side is 3; for V = 1,000 the side is 10. On a basic calculator, raise the volume to the power 1/3.
Final Thoughts
The cube rewards simplicity: measure once, know everything. Whether it is homework, a shipping box or a concrete form, one side length plus V = a³ is all you need — and now you have the surface area and diagonals for free.
Volume Handled? Explore More Geometry
Pair it with our percentage calculator for fill-rates and our cubic yard calculator for bulk materials.