Pyramid Volume Calculator
Compute the volume of a right or oblique pyramid from a rectangular base and perpendicular height.
How the result changes
Only base length changes; all other inputs stay at your current values. The line illustrates the formula across the shown range. This is not a forecast of real-world outcomes.
About this calculation
Pyramid Volume Calculator: Compute the volume of a right or oblique pyramid from a rectangular base and perpendicular height. Enter base length, base width, perpendicular height; the reported quantities are pyramid volume (m³), base area (m²). The equations and examples below show how those inputs lead to the result and where the model's assumptions matter.
Formula
volume = base length × base width × perpendicular height / 3
Worked example
With Base length: 6 m, Base width: 4 m, Perpendicular height: 9 m, pyramid volume is 72 m³.
Method and inputs
Calculate the rectangular base area as length times width. Multiply that area by the perpendicular distance from the base plane to the apex, then divide by three. The one-third factor holds for any pyramid with that base area and altitude.
Worked example
A base 6 meters by 4 meters has area 24 square meters. With perpendicular height 9 meters, the pyramid volume is 24 × 9 / 3 = 72 cubic meters.
A pyramid with base 6 by 4 meters and altitude 9 meters has volume 72 cubic meters regardless of whether its apex sits over the center or to one side. Shifting the apex changes sloping faces and surface area, but not base area or perpendicular height.
How to read the result
The volume occupies one third of the prism with the same base and height. The second output gives base area to help verify the first multiplication. Cubic meters describe space, not material mass or surface area.
If a structure is a truncated pyramid, the full-pyramid equation overstates its volume. One approach is to subtract the smaller missing tip from an imagined full pyramid, using similar dimensions. Do not use the present output directly as a material purchase quantity when the shape is hollow.
Assumptions and checks
The base must be rectangular and the height must be perpendicular to it. A sloping edge from apex to a base corner is not the altitude. For an irregular base, measure its area separately and use area times height divided by three.
Using a slant height overestimates volume. Another frequent mistake is forgetting the division by three and reporting the bounding prism volume. Keep all three lengths in meters if the output is to be interpreted in cubic meters.
Common questions
What does the pyramid volume calculator calculate?
It calculates enclosed volume from rectangular base dimensions and the perpendicular altitude, and also reports the base area used in the calculation.
When should I recalculate or check another method?
Recalculate if the measured height is an edge or face distance rather than the perpendicular altitude. Surveyed or manufactured objects may need separate corrections for hollows, truncation and irregular surfaces.
Inputs
- Base length (m)
- Base width (m)
- Perpendicular height (m)