Volume of a Trapezoidal Prism Calculator
Get the volume of any trapezoidal prism — a ditch, trough, ramp, or footing with a trapezoid cross-section. Enter the two parallel sides, the height between them, and the prism length in inches, feet, centimeters, or meters.
Example: with Parallel side a (top) 6 · Parallel side b (bottom) 4 · Height between them (h) 3 · Prism length (L) 10 · Unit feet → Volume: 150 ft³.
- Cross-section area (a+b)/2 × h15 ft²
- Holds (liquid)≈ 1,122.1 gal (4,247.5 L)
Computed by the calculator below using its default values. Change any input to see your own numbers.
V = trapezoid area × length = (a+b)/2 × h × L. Averaging the two parallel sides is what makes the trapezoid work.
Cross-section times length
Every prism obeys the same rule: volume equals the area of its constant cross-section times its length. For a trapezoidal prism the cross-section is a trapezoid, whose area is the average of the two parallel sides times the height between them: (a + b)/2 × h. A ditch 6 ft wide at the top, 4 ft at the bottom, and 3 ft deep has a 15 ft² cross-section, so 10 ft of it holds 150 ft³.
The average-the-parallel-sides trick is why this shape shows up in earthwork. Excavated trenches are dug with sloped walls for stability, so they are trapezoids by design, and contractors bid the spoil volume in cubic yards — divide cubic feet by 27. Water troughs, canals, wheelchair ramps, and concrete curb sections all yield to the same three numbers plus a length.
How it’s calculated
V = (a + b)/2 × h × L, where a and b are the parallel sides of the trapezoid, h is the perpendicular distance between them, and L is the prism length. Liquid conversions use exact factors: 1 gal = 231 in³, 1 ft³ = 7.480519 gal = 28.316847 L, 1 m³ = 1,000 L = 264.172 gal, 1 cm³ = 1 mL.
h must be the perpendicular height between the parallel sides, not the sloped wall length, and the cross-section must be constant along the full length.
Common trapezoidal prisms
| Object | Trapezoid (a, b, h) | Length | Volume |
|---|---|---|---|
| Drainage ditch | 4 ft, 2 ft, 1.5 ft deep | 100 ft | 450 ft³ ≈ 16.7 yd³ |
| Feed trough | 24 in, 18 in, 12 in deep | 96 in | 24,192 in³ ≈ 104.7 gal |
| Irrigation canal | 6 ft, 4 ft, 3 ft deep | 1,000 ft | 15,000 ft³ ≈ 555.6 yd³ |
| Concrete ramp | 0.5 m, 0.3 m, 0.2 m | 1.2 m | 0.096 m³ = 96 L |
Computed with V = (a+b)/2 × h × L; yd³ = ft³ ÷ 27, gallons at 231 in³/gal.
Common mistakes
- Using the sloped side wall as h — the formula needs the straight-line perpendicular height between the two parallel sides.
- Averaging the wrong pair: average the two parallel sides (top and bottom widths), never a width with the height.
- Mixing units, like widths in inches and length in feet; convert everything to one unit before multiplying.
- Forgetting the ÷2 — (a+b) × h × L doubles the true volume.
Frequently asked questions
What is the volume of a trapezoidal prism?
V = (a + b)/2 × h × L: average the two parallel sides, multiply by the height between them to get the cross-section area, then multiply by the prism length. All in one unit.
Which measurement is the height?
The perpendicular distance between the two parallel sides of the trapezoid — for a ditch, the vertical depth. It is not the sloped wall length, which is always longer.
How do I get cubic yards for excavation?
Compute the volume in cubic feet, then divide by 27. The 100-ft ditch example (450 ft³) is about 16.7 yd³ of spoil — what a hauler will actually quote on.
Does it matter which parallel side I call a or b?
No. Addition is symmetric, so top-then-bottom or bottom-then-top gives the identical average and volume. Just be sure both are the parallel pair.
What if my channel tapers along its length?
Then the cross-section is not constant and this formula alone is not enough. Compute the area at each end and use the average-end-area method: V ≈ (A1 + A2)/2 × L.