Trapezoidal Prism Volume Calculator

a and b are the two parallel sides of the trapezoid cross-section. In a gutter, a is the top opening width and b is the bottom width (or vice versa). It does not matter which side you label a or b; the average (a+b)/2 is the same either way.

Measure the gutter cross-section: top width (a), bottom width (b), and depth (h). Multiply the trapezoid area by the gutter length (L). Example: top 12 cm, bottom 8 cm, depth 10 cm, length 3 meters: V = (12+8)/2 x 10 x 300 = 30,000 cm^3 = 30 liters capacity.

Measure the wall cross-section (top thickness a, bottom thickness b, wall height h) and wall length L. Volume in cubic feet or meters gives the concrete needed. Example: top 8 inches, bottom 16 inches, height 48 inches, length 20 feet: V = (8+16)/2 x 48 x 240 = 138,240 cubic inches = 80 cubic feet = 2.96 cubic yards.

When a = b, the trapezoid becomes a rectangle and the formula simplifies to V = a x h x L. This is identical to the rectangular prism volume formula. The trapezoidal formula is a generalization that works for both equal and unequal parallel sides.

The height h is always the perpendicular distance between the two parallel sides, not the slant side length. If you know the slant side and the difference in base lengths, you can calculate h using the Pythagorean theorem: h = sqrt(slant^2 - ((a-b)/2)^2).

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