A prism with a trapezoid cross-section — common for canals, trenches, and sloped retaining walls.
How it works
The trapezoid cross-section’s area (the average of the two parallel bases, times the height) is multiplied by the prism’s length to get the total volume.
What this does not include
This does not include other prism shapes — for a triangular cross-section, use this site’s triangular prism calculator instead.
How to use this calculator
- Enter both trapezoid bases, the trapezoid height, and the prism length.
A worked example
A trapezoidal prism with parallel sides 4 and 6, height 3, length 10: volume = ((4+6)/2 × 3) × 10 = 150.
Parallel sides both 2 (a rectangular cross-section), height 5, length 4: volume = 40.
What the variables mean
| Variable | Meaning |
|---|---|
| Base 1, Base 2 | The trapezoidal cross-section’s two parallel sides |
| Height | Height of the trapezoidal cross-section |
| Length | How far the cross-section is extruded |
Edge cases worth knowing
This is the trapezoid area formula extruded into a third dimension — the same (base1+base2)/2 × height calculation this site’s trapezoid area calculator performs, multiplied by the prism’s length.
Equal base lengths turn the cross-section into a rectangle, and the formula still holds, reducing naturally to length × width × height.
Frequently asked questions
What’s a real-world example of a trapezoidal prism?
An irrigation canal or drainage ditch, which typically has a wider top and narrower bottom, forming a trapezoid cross-section extended along its length.
What happens if both bases are equal?
The trapezoid becomes a rectangle, and this calculator correctly reduces to the standard rectangular-prism volume formula.
Is the trapezoid height the same as the prism length?
No — the trapezoid height is the cross-section’s own height (perpendicular between the two parallel bases), while the prism length is how far that cross-section extends.
