Triangular Prism Calculator
Find the volume and surface of a right triangular prism from two legs and a height, from three base sides and a height, or the volume alone from a known base area. The formulas are V = Bh, lateral Ph, and total S = 2B + Ph.
Lateral 60 · total S = 72
- The base is a right triangle with legs 3 and 4. The hypotenuse is c = √(a² + b²) = 5.
- Base area B = (1/2)ab = (1/2) × 3 × 4 = 6.
- Volume V = Bh = 6 × 5 = 30. Perimeter P = 12. Lateral = Ph = 60. Total S = 2B + Ph = 72.
Embed Triangular Prism Calculator
Copy this iframe code into a page that permits embeds.
All calculations run locally in your browser. Your entered values are not sent to an external service.
How to Use the Triangular Prism Calculator
From two legs grows a right triangular base. From three sides grows any triangular base (Heron). From a known area B it returns only the volume.
- Choose From right triangle, From three sides, or From B and h.
- Enter non-negative lengths or a non-negative area. Three sides must satisfy the triangle inequality.
- Read the volume. Right-triangle and three-side modes also report the perimeter, the lateral area, and the total surface.
The base triangle alone belongs on the Triangle Area Calculator (½bh, Heron, or SAS). A rectangular box belongs on the Rectangular Prism Calculator (V = LWh). A tent with the same triangular base and height belongs on the Pyramid Calculator (V = (1/3)Bh, one-third of this prism). Converting cubic units belongs on the Volume Converter.
Volume and Surface
A triangular prism is two congruent triangular lids joined by three rectangular walls. Volume is the base area times the perpendicular height, V = Bh — the same prism rule as a box, with a triangle instead of a rectangle. Unfolding the net gives two lids of area B and three walls whose widths are the three sides, so the lateral area is the base perimeter times the height, Ph, and the total is S = 2B + Ph.
A right triangular base uses B = (1/2)ab and hypotenuse c = √(a² + b²). Any three sides use Heron’s formula, the same check as the Triangle Area Calculator: s = (a + b + c) / 2 and B = √[s(s − a)(s − b)(s − c)]. From B and h alone you cannot recover the three sides, so that mode reports volume only. Height is perpendicular. An oblique “leaning” prism still has volume Bh with perpendicular height, but its walls are parallelograms, not rectangles; that case is out of scope.
Triangular Prism Calculator Examples
3-4-5, height 5
B = 6. V = 30. P = 12. Lateral = 60. Total S = 72. The matching triangular pyramid on the Pyramid Calculator (enter B = 6, h = 5) is 10 — one-third of this prism.
Isosceles 5-5-6, height 4
s = 8. B = √[8 × 3 × 3 × 2] = 12, the same area as the Triangle Area Calculator. V = 48. P = 16. Lateral = 64. Total S = 88.
Equilateral side 6, height 4
B = (√3 / 4) × 36 = 9√3 ≈ 15.5884572681. V = 36√3 ≈ 62.3538290725. P = 18. Lateral = 72. Total S = 2B + 72 ≈ 103.176914536.
Base area 6, height 5
V = 30, the same volume as the first example, without naming the sides. Surface stays blank because B does not name the triangle.
Height 0
V = 0. The walls vanish. Total surface is two coincident triangles: 2B = 12. A prism crushed flat is a triangle, not a tank.
Impossible 1, 1, 3
1 + 1 is less than 3. No triangular base exists, so no prism exists. The calculator stops with the triangle inequality.
Three Times the Pyramid
Cavalieri again: a pyramid of the same base and the same perpendicular height is one-third of this prism. The 3-4-5 triangle of height 5 is V = 30 here and V = 10 on the Pyramid Calculator. A rectangular box of the same “fill the base and stack it” idea belongs on the Rectangular Prism Calculator — there the base is a rectangle, so V = LWh instead of Bh.
Do not drop in a 1/3 because the solid “comes to a point.” This page has two parallel triangles. Do not use a slanted wall as the height. And do not treat a box as a triangular prism; a rectangle is a different base.
Common Triangular Prism Mistakes
Using (1/3)Bh for a prism
That is a pyramid, on the Pyramid Calculator. A prism is the full Bh.
Using LWh for a triangular base
That is a rectangular box, on the Rectangular Prism Calculator. Here the base is a triangle, so find B first.
Reporting Ph as the total surface
That is the three walls. Add the two lids 2B, or use 2B + Ph.
Using a slanted wall as the height
Volume wants the perpendicular distance between the two triangular bases. A rectangular face diagonal is longer.
Asking From B and h for a surface area
B is only an area. Lateral area needs the three side lengths. Use the right-triangle or three-sides modes.
Converting liters on this page
V is already in the cube of your input unit. Use the Volume Converter for liters and gallons.
Triangular Prism Calculator FAQs
What is the volume of a triangular prism?
V = Bh. For the 3-4-5 triangle of height 5, B = 6 and V = 30 cubic units.
What is the surface area of a triangular prism?
S = 2B + Ph. The three walls alone are Ph. For 3-4-5 and h = 5 those are 72 and 60.
How do you find the base from three sides?
Heron’s formula, the same as the Triangle Area Calculator. Sides 5, 5, 6 give B = 12.
Is a triangular prism one-third of a pyramid?
No. The pyramid is one-third of this prism. Same 3-4-5 base and height 5: prism 30, pyramid 10.
Does this treat a rectangular box or convert liters?
A box belongs on the Rectangular Prism Calculator. Convert liters on the Volume Converter.
Are my numbers sent to a server?
No. The calculation runs locally in your browser.
Related Calculators
Rectangular Prism CalculatorV = LWh — the same prism rule with a rectangular base.
Pyramid CalculatorV = (1/3)Bh — one-third of this prism, same base and height.
Volume ConverterTurn the cubic units into liters or gallons.
Explore More Geometry Tools
Continue with triangles, boxes, and solid-geometry tools in the SolverCalc collection.
Reviewed by Prof. Dr. Khalil Mudassar (PhD) · Last updated: [mc_modified_date]
Sources
View mathematical references
Disclaimer
This calculator is intended for general educational and practical use. Review important results before relying on them in professional work.