Case 1
- Octagon side
- 4
- Prism length
- 10
772.548340
Open with these valuesOctagonal Prism Volume Calculator
772.548340units³
Result: 772.548340 units³A regular octagon of side a covers 2(1 + √2) × a², about 4.828 × a² — nearly five squares of the side. Multiply by the length for the volume: side 4, length 10 gives 320(1 + √2), about 772.5 cubic units. Enter one edge, not the width across the flats.
The numbers at a glance
Held fixed: Octagon side 4.000.
| Prism length | Result |
|---|---|
| 2.500 | 193.137085 |
| 5.000 | 386.274170 |
| 7.500 | 579.411255 |
| 10.000Your value | 772.548340 |
| 12.500 | 965.685425 |
| 15.000 | 1,158.822510 |
| 17.500 | 1,351.959595 |
| 20.000 | 1,545.096680 |
Worked examples
Case 2
- Octagon side
- 1
- Prism length
- 1
4.828427
Open with these valuesCase 3
- Octagon side
- 5
- Prism length
- 10
1,207.106781
Open with these valuesHow it's calculated
V = 2(1 + √2) × a² × L
- StepMeasure one of the eight equal edges of the octagon.
- StepMeasure the length between the two octagonal ends, same unit.
- ResultRead the volume in the cube of the unit you entered.
Reference table
| Side, length | Exact | Volume |
|---|---|---|
| 0.5, 3 | 3(1 + √2) ÷ 2 | 3.621320 |
| 1, 1 | 2(1 + √2) | 4.828427 |
| 2, 6 | 48(1 + √2) | 115.882251 |
| 4, 10 | 320(1 + √2) | 772.548340 |
| 5, 10 | 500(1 + √2) | 1207.106781 |
Questions
How do I calculate the volume of an octagonal prism?
Find the area of the octagonal end, 2(1 + √2) × a², then multiply by the prism length. The area factor is about 4.828427, so a side of 4 and a length of 10 give 77.254834 × 10 = 772.548340 cubic units.
What is the area of a regular octagon?
A regular octagon with side a has area 2(1 + √2) × a², about 4.828427 × a². For a side of 4 that is 77.254834 square units, and that cross-section stays the same all the way along the prism.
Do I enter the side or the width across the flats?
The side, meaning one of the eight equal edges. The width across the flats is (1 + √2) times the side, about 2.414 times, so divide by that before entering.
Why does the volume equal the cross-section times the length?
A prism is its cross-section swept along a straight line, so its volume is always cross-section area times length. That holds for any prism — octagonal, hexagonal or rectangular. Doubling the length doubles the volume while the cross-section stays put.
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.