Volume of a Triangular Prism Calculator
Find the volume and surface area of any triangular prism. Enter the three sides of the triangular cross-section and the prism length — the calculator uses Heron's formula for the triangle area, then multiplies by the length.
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V = triangular base area × length (Heron's formula for the area)
V = A × l
60 units³- 1
Semi-perimeter
s = (3 + 4 + 5) ÷ 2 = 6 - 2
Heron's product
s(s−a)(s−b)(s−c) = 6 × 3 × 2 × 1 = 36 - 3
Triangle base area
A = √36 = 6Heron's formula gives the triangle area from three side lengths alone. - 4
Volume
A × l = 6 × 10 = 60
How does this calculator work?
Triangular prism volume V = A × l, where A is the triangular cross-section area from Heron's formula: A = √[s(s−a)(s−b)(s−c)], s = (a+b+c)/2, and l is the prism length. Lateral surface area = (a+b+c) × l; total surface area = 2A + lateral. All three sides must satisfy the triangle inequality.
Formula
How this is calculated
A triangular prism has two identical triangular cross-sections at each end and three rectangular lateral faces. Its volume equals the triangular cross-section area multiplied by the prism length: V = A × l. The key step is computing A when only the three side lengths are known — Heron's formula handles this without requiring an angle or height.
Heron's formula: compute the semi-perimeter s = (a + b + c) / 2, then the area A = √[s(s−a)(s−b)(s−c)]. The expression under the square root must be positive, which requires the triangle inequality — the sum of any two sides must exceed the third. Sides like 1, 2, 10 violate this and cannot form a triangle.
The three rectangular lateral faces each have area equal to the corresponding triangle side times the prism length. Total lateral area = perimeter × l = (a + b + c) × l. Total surface area = 2A + lateral area. All inputs must be in the same length unit — the volume is in cubic units and areas in square units of that measure.
Frequently asked questions
If you know the base b and perpendicular height h of the triangle, the area is A = (1/2) × b × h and the volume is V = (1/2) × b × h × l. This calculator uses the three-sides approach via Heron's formula. For the base-and-height variant, enter values so that h matches the altitude of a triangle with the three sides you provide.
The triangle inequality states that the sum of any two sides must be greater than the third. Sides 3, 4, 5 satisfy it and form a right triangle. Sides 1, 2, 10 violate it (1 + 2 < 10) and cannot form any triangle — the calculator returns no result in that case.
Rearrange V = A × l to get l = V ÷ A. Compute the triangle area A using Heron's formula from the three side lengths, then divide the target volume by A to find the required prism length.
Also known as
TG we-Calculate Editorial Team. (2026). Volume of a Triangular Prism Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/volume-of-a-triangular-prism-calculator
TG we-Calculate Editorial Team. "Volume of a Triangular Prism Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/volume-of-a-triangular-prism-calculator.
TG we-Calculate Editorial Team, "Volume of a Triangular Prism Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/volume-of-a-triangular-prism-calculator
@misc{wecalculate_volume_of_a_triangular_prism_calculator, title = {Volume of a Triangular Prism Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/volume-of-a-triangular-prism-calculator}}, year = {2026}, note = {TG we-Calculate} }
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