A triangular prism shows up anywhere a shape is extruded from a triangular cross-section — roof trusses, tent shapes, wedge-cut materials, and countless textbook problems. Because the cross-section never changes along the prism's length, both its volume and surface area reduce to two simple formulas built on the base triangle's area and perimeter.
How the Triangular Prism Calculator works
The calculator first finds the base triangle's area and perimeter, then applies two prism formulas. If you supply the base and height, area is the familiar ½ × base × height. If you supply three side lengths instead, the calculator uses Heron's formula — computing the semi-perimeter s = (a+b+c)/2, then area = √(s(s−a)(s−b)(s−c)) — after first confirming the three sides actually form a valid triangle (each side must be shorter than the sum of the other two). Once the base area and perimeter are known, volume is base area × prism length, and surface area is 2 × base area (the two triangular ends) + perimeter × length (the three rectangular sides).
Inputs and what they mean
Base & Height mode assumes an isosceles base triangle for the perimeter calculation, since only the base and perpendicular height are known — the two remaining sides are treated as equal slant sides computed from the base and height via the Pythagorean theorem. This only affects the surface-area perimeter term; volume (base area × length) is exact either way. Three Sides mode is exact for both volume and surface area, since all three side lengths are known directly. The prism length is a separate input from the base triangle's own base and height — don't confuse the two when reading a diagram.
Limits and edge cases
This calculator assumes a right prism — the two triangular ends are directly opposite each other, connected by rectangular (not parallelogram) side faces. An oblique prism, where the ends are offset at an angle, has the same volume formula (base area × length, measured perpendicular to the base) but a different surface-area calculation since the side faces become parallelograms rather than rectangles. In Three Sides mode, if the entered lengths fail the triangle inequality (one side longer than the sum of the other two), the calculator flags the input as invalid rather than returning a nonsensical negative-under-the-square-root result.