Case 1
- Hexagon side
- 4
- Prism length
- 10
415.692194
Open with these valuesHexagonal Prism Volume Calculator
415.692194units³
Result: 415.692194 units³A regular hexagon of side a covers 3√3/2 × a², about 2.598 × a². Multiply that by the length and you have the volume: a hex bar of side 4 and length 10 holds 240√3, roughly 415.7 cubic units. Enter the side, not the width across the flats — that one is √3 times longer.
The numbers at a glance
Held fixed: Hexagon side 4.000.
| Prism length | Result |
|---|---|
| 2.500 | 103.923048 |
| 5.000 | 207.846097 |
| 7.500 | 311.769145 |
| 10.000Your value | 415.692194 |
| 12.500 | 519.615242 |
| 15.000 | 623.538291 |
| 17.500 | 727.461339 |
| 20.000 | 831.384388 |
Worked examples
Case 2
- Hexagon side
- 1
- Prism length
- 1
2.598076
Open with these valuesCase 3
- Hexagon side
- 2
- Prism length
- 5
51.961524
Open with these valuesHow it's calculated
V = (3√3 ÷ 2) × a² × L
- StepMeasure one edge of the hexagon, not the width across the flats.
- StepMeasure the length from one hexagonal end to the other, same unit.
- ResultRead the volume in the cube of the unit you entered.
Reference table
| Side, length | Exact | Volume |
|---|---|---|
| 0.5, 3 | 9√3 ÷ 8 | 1.948557 |
| 1, 1 | 3√3 ÷ 2 | 2.598076 |
| 2, 5 | 30√3 | 51.961524 |
| 3, 8 | 108√3 | 187.061487 |
| 4, 10 | 240√3 | 415.692194 |
Questions
How do I calculate the volume of a hexagonal prism?
Find the area of the hexagonal end — (3√3/2) × a², about 2.598 × a² — then multiply by the prism length. For a side of 4 and a length of 10 that is 41.569219 × 10 = 415.692194 cubic units.
Do I enter the side or the width across the flats?
The side, meaning one of the six equal edges. The width across the flats is √3 times the side and the width across the corners is exactly twice it, so divide by 1.732051 or by 2 before entering.
Why is the hexagon area (3√3/2) × a²?
A regular hexagon is six equilateral triangles meeting at the centre. Each has area (√3/4) × a², and six of them give (3√3/2) × a². That cross-section is the same at every slice along the prism.
Does this work for an irregular hexagon?
No. The formula assumes a regular hexagon — all six sides equal, every angle 120° — swept straight along the length. A tapered or twisted bar needs a different calculation.
Which units does the answer use?
Whatever you entered, cubed. Side and length in centimetres give cubic centimetres, in inches cubic inches. Both inputs must use the same unit.
Sources and last check
Information, not professional advice.