A trapezoid volume calculator computes the 3D volume of a trapezoidal prism. Enter the two parallel sides (a, b), the perpendicular height, and the prism length.
A trapezoid is a 2D shape with exactly one pair of parallel sides. Like a triangle, a flat trapezoid has no volume — only area. To calculate "trapezoid volume," extend the trapezoid through a length to create a trapezoidal prism.
Trapezoidal prisms appear in swimming pools with sloped bottoms, drainage ditches, retaining walls, and highway embankments.
V = ½(a + b) × h × L
Where a and b are the two parallel sides, h is the perpendicular height between them, and L is the prism length.
Example: Parallel sides 4 m and 6 m, height 3 m, length 10 m:
V = ½(4+6) × 3 × 10 = 5 × 3 × 10 = 150 m³ = 150,000 L = 39,626 gal.
Shallow end 1 m, deep end 2.5 m, width 6 m, length 12 m: V = ½(1+2.5)×6×12 = 126 m³ = 126,000 L.
Top 1.5 m, bottom 0.5 m, depth 0.8 m, length 50 m: V = ½(1.5+0.5)×0.8×50 = 40 m³.
Top 0.3 m, base 0.6 m, height 2 m, length 15 m: V = ½(0.3+0.6)×2×15 = 13.5 m³ of concrete.
Front 0.3 m, back 0.5 m, width 1.2 m, length 2.4 m: V = ½(0.3+0.5)×1.2×2.4 = 1.152 m³ of soil.
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Answers to common questions about the trapezoid volume calculator.
V = ½(a+b) × h × L where a,b are the parallel sides, h is the perpendicular distance between them, and L is the prism length/depth.
The cross-section is a trapezoid: a = shallow end depth, b = deep end depth, h = pool width, L = pool length. V = ½(shallow+deep) × width × length.
A = ½(a+b) × h. The volume formula is just this area multiplied by the prism length L.
A trapezoid has exactly one pair of parallel sides. A parallelogram has two pairs of parallel sides. A parallelogram's area is simply base × height (no ½ factor needed).
Only if the cross-section has exactly one pair of parallel sides (a trapezoid). For other quadrilaterals, decompose into triangles and sum their volumes.