Triangular base area
s = (a + b + c) / 2
A = √[s(s − a)(s − b)(s − c)] using Heron’s formula.
Triangular Prism Calculator — Volume, Surface Area and Length
Enter the Prism Measurements
Triangular Prism Results
Volume (V)—
Total surface area (SA)—
Prism length (L)—
Lateral surface area—
Triangular base area (A)—
Base perimeter (P)—
Base semiperimeter (s)—
Total edge length—
Enter valid measurements to see the formula substitutions.
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Triangular Prism Formulas
For a right triangular prism, let a, b, and c be the sides of either triangular base, A its area, P its perimeter, and L the perpendicular prism length.
Volume
V = AL
Multiply the area of one triangular base by the perpendicular prism length.
Total surface area
SA = 2A + PL
The two triangular bases contribute 2A; the three rectangular faces contribute PL.
Length from volume
L = V / A
Divide the known volume by the triangular base area.
Length from surface area
L = (SA − 2A) / P
The known total area must exceed the combined area of the two bases.
Total edge length
E = 2P + 3L
There are two copies of each base edge and three lateral edges of length L.
Assumptions: This is a right prism: the three lateral edges meet the triangular bases at right angles, so the lateral faces are rectangles. The triangular bases are congruent, and the entered sides satisfy the strict triangle inequality.
How to Use the Triangular Prism Calculator
- Enter all three side lengths of the triangular base.
- Choose whether you know the prism length, volume, or total surface area.
- Enter that known measurement, choose the common length unit and rounding precision, then select Calculate prism.
- Review the unrounded calculation, or copy the summary and download a CSV file.
The selected unit applies to all base sides and the prism length. Area results use the squared unit and volume uses the cubed unit.
Worked Triangular Prism Examples
3–4–5 cm base, 10 cm long
The right-triangle base area is A = 6 cm² and perimeter is P = 12 cm.
V = 6 × 10 = 60 cm³ and SA = 2(6) + 12(10) = 132 cm².
Length from 150 cm³
A 5–5–6 cm triangle has area 12 cm².
L = 150 / 12 = 12.5 cm, giving total surface area 224 cm².
Length from 224 cm²
For the same 5–5–6 cm base, A = 12 cm² and P = 16 cm.
L = (224 − 24) / 16 = 12.5 cm.
Common Triangular Prism Mistakes
Using a triangle side as prism length
The prism length is the perpendicular distance between the two triangular bases, not one of the triangle’s three sides.
Leaving out the rectangular faces
Total surface area includes two triangles plus all three rectangles: 2A + PL.
Using impossible base sides
Each pair of sides must add to more than the remaining side. A 2–3–5 set is flat and has zero area.
Triangular Prism Calculator FAQs
How do you calculate the volume of a triangular prism?
Multiply the triangular base area by the perpendicular prism length: V = AL. When all three base sides are known, find A with Heron’s formula.
How do you calculate the surface area of a triangular prism?
For a right triangular prism, use SA = 2A + PL, where P = a + b + c.
How can I find a triangular prism’s length from its volume?
Divide volume by the triangular base area: L = V / A.
How can I find length from total surface area?
Subtract the two triangular bases and divide by the base perimeter: L = (SA − 2A) / P. The total surface area must be greater than 2A.
Does the triangular base have to be a right triangle?
No. The base may be scalene, isosceles, equilateral, or right. The prism itself is assumed to be right.
Why are my triangle side lengths invalid?
The sum of any two sides must be greater than the third side. Equality would form a flat, zero-area triangle.
Are my measurements uploaded or saved?
No. The calculation runs locally in your browser and does not send or save your measurements.
Calculation Notes and Sources
Last reviewed: July 30, 2026 by the Starlight Tools editorial team.
The formulas follow OpenStax’s treatment of right-prism volume and surface area and its presentation of Heron’s formula. Unrounded values are used throughout; the decimal-place setting changes display only. A scaled form of Heron’s formula reduces overflow and underflow for very large or small valid inputs.
References: OpenStax: Volume and Surface Area and OpenStax: Area and Heron’s Formula.