Volume of a Trapezoidal Prism Calculator

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A trapezoidal prism is a solid with a trapezoid as its constant cross-section, extended along a straight length — think of a highway embankment, a drainage channel, or a retaining wall's cross-section extended along its run. Its volume, like that of any prism, is its cross-sectional area multiplied by the prism's length, which makes this shape common in civil engineering and earthworks calculations (estimating soil or concrete volume for embankments, canals, and foundation footings whose cross-section tapers from a wider top or bottom).

How it works

Enter the trapezoid's two parallel sides (a and b) and its height (the perpendicular distance between those two parallel sides), plus the prism's length. The calculator first finds the trapezoid's cross-sectional area using the standard trapezoid area formula, (a+b)/2 × h, then multiplies that area by the prism length to get the total volume — exactly the same "cross-sectional area × length" logic used for any prism.

Enter trapezoid parallel side a.
Enter trapezoid parallel side b.
Enter trapezoid height.
Enter prism length.
Click Calculate to see your results.

Examples

Sides 4 and 6, trapezoid height 3, prism length 10

Trapezoid area = (4+6)/2 × 3 = 5 × 3 = 15. Volume = 15 × 10 = 150.

Sides 8 and 12, trapezoid height 5, prism length 20

Trapezoid area = (8+12)/2 × 5 = 10 × 5 = 50. Volume = 50 × 20 = 1000.

Common mistakes to avoid

Confusing the trapezoid's height (the perpendicular distance between the parallel sides) with the prism's length (the extension distance).
Forgetting to divide by 2 in the trapezoid area formula (computing (a+b)×h instead of (a+b)/2×h).
Assuming the cross-section must taper along the prism's length — a true trapezoidal prism keeps the same trapezoid shape all the way through.

Frequently asked questions

Enter the same value for both parallel sides — the trapezoid area formula reduces automatically to base × height, exactly matching a plain rectangular cross-section.

The trapezoid height is the perpendicular distance between its two parallel sides, defining the cross-section's shape; the prism length is how far that same cross-section is extended in the third dimension to create the solid.

No — the trapezoid area formula, (a+b)/2 × h, is symmetric in a and b, so swapping which side is labeled which gives exactly the same area and volume.

That would make it a frustum-like shape rather than a true prism, and this simple cross-section × length formula would no longer apply directly — you'd need to account for how the trapezoid changes shape along the length.

The area formula (a+b)/2 × h describes only the flat 2D cross-section; multiplying that area by the prism's length is what extends the calculation into three dimensions to get an actual volume.

The volume exactly doubles, since volume is directly proportional to length once the cross-sectional area is fixed.

Free Volume of a Trapezoidal Prism Calculator