Triangular Prism Calculator
Calculate volume from a triangular end face and the length of a prism.
How the result changes
Only triangle base 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
Triangular Prism Calculator: Calculate volume from a triangular end face and the length of a prism. Enter triangle base, triangle altitude, prism length; the reported quantities are prism volume (m³), triangle end area (m²). The equations and examples below show how those inputs lead to the result and where the model's assumptions matter.
Formula
volume = triangle base × triangle altitude × prism length / 2
Worked example
With Triangle base: 6 m, Triangle altitude: 4 m, Prism length: 10 m, prism volume is 120 m³.
Method and inputs
Find the triangular end area as one half times its base times perpendicular altitude. Multiply this constant cross-sectional area by the prism length. This applies to a prism whose parallel end faces are congruent triangles.
Worked example
A triangular end with base 6 meters and altitude 4 meters has area 12 square meters. If the prism extends 10 meters, it encloses 120 cubic meters.
Doubling the prism length while keeping its triangular end unchanged doubles volume. Doubling both base and altitude of the triangular end multiplies end area, and therefore volume, by four. These scaling checks can reveal a misplaced one-half factor.
How to read the result
The area output describes one triangular end, while the volume output includes the full extrusion length. Surface area would also need the three side lengths of the triangle, which are not all specified here.
For a roof-shaped space, the triangular end area may be easy to survey from span and rise. The volume then assumes that exact triangle continues along the whole building. Dormers, sloped ends and internal voids must be handled separately.
Assumptions and checks
The triangle altitude must be perpendicular to its chosen base. The prism is assumed to keep the same cross section along its length, so tapered wedges need a different model.
Using a sloping triangle side as the altitude changes the end area. Omitting the one-half factor doubles volume. The prism length is the distance between parallel triangular faces, not the length of a sloping edge.
Common questions
What does the triangular prism calculator calculate?
It reports the triangle end area and the enclosed prism volume, based on base, perpendicular triangle altitude and prism length.
When should I recalculate or check another method?
Recalculate when a measured dimension changes or when the object tapers. If the goal is material mass, multiply a verified volume by density after checking that hollow spaces have been removed.
Inputs
- Triangle base (m)
- Triangle altitude (m)
- Prism length (m)