How to use this right triangular prism calculator
- Measure the three sides of one triangular end and enter them in any order.
- Enter the perpendicular distance between the matching triangular bases as prism height. Keep every length in one unit.
- Select Calculate to see volume, total surface area, triangle area and base perimeter.
- Any edit clears the old result. Copy summarizes a confirmed result; Clear empties all measurements.
Heron’s formula and right-prism formulas
The three base sides must form a non-degenerate triangle. The calculator checks that every pair adds to more than the remaining side.
With semiperimeter q = (a+b+c)/2, Heron’s formula gives base area A = √(q(q−a)(q−b)(q−c)).
A right prism has rectangular side faces perpendicular to its bases. Their combined area is perimeter times prism height, so V = AH and S = 2A + (a+b+c)H.
q = (a+b+c)/2 · A = √(q(q−a)(q−b)(q−c)) · V = AH · S = 2A + (a+b+c)H
Worked examples
3–4–5 base and height 10 cm
Heron’s formula gives a 6 cm² base. Volume is 60 cm³ and total surface area is 2×6 + 12×10 = 132 cm².
Equilateral base side 6 m, height 8 m
The base area is 9√3 ≈ 15.59 m². Volume is about 124.71 m³ and total surface area about 175.18 m².
Limits and input notes
- This is a right prism, meaning the connecting edges are perpendicular to the triangular bases. An oblique prism needs different surface calculations.
- All four inputs must be positive decimals in the same unit.
- A triangle with sides such as 1, 2 and 3 is degenerate and is rejected.
- Rounding is for display only; measurement uncertainty and material allowances are not included.
Frequently asked questions
Does “right” mean the base triangle is right-angled?
No. Here it means a right prism. The base can be any valid triangle; the prism height is perpendicular to it.
Why enter all three triangle sides?
They allow the base area to be found with Heron’s formula without asking for a triangle altitude.
Does total surface area include both ends?
Yes. It includes both triangular bases and all three rectangular faces.
Can the side order change the answer?
No. The three sides may be entered in any order.