Triangular Prism Volume Calculator
Calculate triangular prism volume using base & height or 3 edge lengths with Heron’s formula. Ideal for ramps, wedges, and roof attics.
Heron's formula computes the exact area of any triangle given solely the lengths of its three perimeter edges.
Multiplying the uniform triangular cross-section along the length produces the total 3D internal volume.
The volume of a triangular prism is calculated by multiplying its triangular face area by its length: V = A_triangle × L. For a triangle with base 4 ft and height 3 ft with prism length 10 ft, volume is 0.5 × 4 × 3 × 10 = 60 cubic feet.
Triangular Prism Volume Calculator Formula
| Variable | Definition | Standard Units |
|---|---|---|
| V | Total volume of the triangular prism | in³, ft³, cm³, or m³ |
| b | Base edge of the triangular cross-section | in, ft, cm, or m |
| h_triangle | Perpendicular height of the base triangle | in, ft, cm, or m |
| L | Length or depth along the prism axis | in, ft, cm, or m |
How to Calculate Triangular Prism Volume
A triangular prism has two identical triangular ends connected by three rectangular sides. Because the cross-section is uniform along its entire length L, the volume is simply the area of the end triangle multiplied by the prism length.
Using Heron's Formula When Triangle Height is Unknown
When measuring triangular roof trusses or land plots, measuring perpendicular height inside the triangle can be difficult. If you know all three sides (a, b, c), compute semi-perimeter s = (a + b + c)/2, then calculate area A = √(s(s - a)(s - b)(s - c)). Multiplying by length gives exact volume.
Common Calculation Mistakes to Avoid
- Confusing the height of the 2D base triangle with the 3D length of the prism
- Entering three sides that violate the triangle inequality theorem (sum of any two must exceed the third)
- Assuming the triangle must be a right-angled triangle
Frequently Asked Questions
What is the formula for the volume of a triangular prism?▼
How do you find volume if you only know the three sides of the triangle?▼
Can a triangular prism be right-angled or equilateral?▼
How do you calculate the volume of a roof attic space?▼
Authoritative Sources & Reference Standards
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811 — National Institute of Standards and Technology (NIST). Verified 2026-10-01.
Official SI unit definitions, conversion factors (Appendix B), and precision standards for cubic meters, liters, and US customary units.
- Common Core State Standards for Mathematics: High School Geometry (Geometric Measurement and Dimension HSG.GMD.A.1–3) — National Governors Association Center for Best Practices & Council of Chief State School Officers. Verified 2026-10-01.
Curricular standards for volume formulas of cylinders, pyramids, cones, and spheres, including Cavalieri’s principle.