Case 1
- Base edge
- 6
- Vertical height
- 10
120.000000
Open with these valuesPyramid Volume Calculator
Change any value to update the result.
120.000000units³
Pyramid volume: 120.000000 units³Examples
A third of the box it stands in: base area times height, divided by three. This assumes a square base — for a rectangular one, use length × width in place of the edge squared. Enter the vertical height, not the slanted face.
The numbers at a glance
Held fixed: Base edge 6.000.
| Vertical height | Pyramid volume |
|---|---|
| 2.500 | 30.000000 |
| 5.000 | 60.000000 |
| 7.500 | 90.000000 |
| 10.000Your value | 120.000000 |
| 12.500 | 150.000000 |
| 15.000 | 180.000000 |
| 17.500 | 210.000000 |
| 20.000 | 240.000000 |
Worked examples
Case 2
- Base edge
- 3
- Vertical height
- 4
12.000000
Open with these valuesCase 3
- Base edge
- 10
- Vertical height
- 10
333.333333
Open with these valuesHow it's calculated
V = s² × h ÷ 3
- StepMeasure one edge of the square base.Base edge=6
- StepMeasure the height straight up from the centre to the apex.Vertical height=10
- ResultRead the volume in the cube of the unit you entered.120.000000units³
What this number means
Work out the base area first
For a square base that is the edge squared: an edge of 6 makes 36. Multiply by the height and divide by three — 36 × 10 ÷ 3 is 120 cubic units.
The height stands perpendicular on the base
It runs from the centre of the base straight up to the apex. The sloping face is longer and belongs to the surface-area formula.
A third of the box it stands in
The prism over the same base with the same height holds 360 for the default edge 6 and height 10. The pyramid holds 120, exactly a third of it.
Commonly misread
MisconceptionThe base edge is 6, so the base area is 6.
CorrectionThe base area is the edge squared, 36. Only then comes the height, and the division by three.
MisconceptionI entered the length of the sloping face as the height.
CorrectionUse the vertical height from the centre of the base to the tip. The face is longer, so the volume comes out too large.
MisconceptionMy base is a rectangle, so this formula does not apply.
CorrectionUse length × width as the base area and divide by three as before. The one third holds for any flat base at all.
Reference table
| Base edge, height | Base area | Volume |
|---|---|---|
| 2, 6 | 4 | 8.000000 |
| 3, 4 | 9 | 12.000000 |
| 5, 9 | 25 | 75.000000 |
| 6, 10 | 36 | 120.000000 |
| 10, 10 | 100 | 333.333333 |
Questions
How do you calculate the volume of a pyramid?
Multiply the base area by the height and divide by three. A base edge of 6 with height 10 gives 120 cubic units.
Why a third?
Three pyramids of the same base and height fill the prism that stands on that base — the same relationship a cone has to its cylinder.
My base is a rectangle, not a square.
Then use length times width as the base area and divide by three as before. The one-third holds for any flat base at all.
Do I use the slant height?
No, the vertical height from the centre of the base to the tip. The slanted face is longer and belongs to the surface-area formula.