How to use the Trapezoid Calculator
- Identify the two parallel sides — these are the ones that never meet.
- Enter each parallel side length as a and b.
- Measure the perpendicular distance between them and enter it as the height.
- Read the area.
- The median is the average of the parallel sides and equals the width at half height.
How the calculation works
A trapezoid's area is its average width multiplied by its height. Averaging the two parallel sides gives the median — the width exactly halfway up — and because the sides taper linearly, that median width is a true representative of the whole shape. Multiplying it by the height gives the area exactly, with no approximation involved.
The height must be measured perpendicular to the parallel sides, not along a sloping edge. On sloped ground or an angled wall this is the measurement most often taken wrongly, and because the error scales the entire result linearly, a 10% error in height is a 10% error in area or volume.
This formula is the reason the trapezoid rule of numerical integration works, and it is also the workhorse of earthworks. Cut-and-fill volumes are computed by taking trapezoidal cross-sections at regular chainages and averaging consecutive areas along the run — the same logic applied twice, once across the section and once along the length.
A = ((a + b) / 2) × h; median = (a + b) / 2Source: Standard planar geometry; end-area volume method per AASHTO earthwork computation practice.
Worked example
A drainage swale has a 2.4 m top width, a 0.8 m base and a 0.6 m depth. What is the cross-sectional area?
- Parallel sides: a = 2.4 m (top), b = 0.8 m (base).
- Median: (2.4 + 0.8) / 2 = 1.6 m.
- Area: 1.6 × 0.6 = 0.96 m².
- Over a 40 m run: 0.96 × 40 = 38.4 m³ of excavation.
0.96 m² per cross-section, giving 38.4 m³ of spoil over the 40 m length.
Frequently asked questions
Does it matter which parallel side I call a?+
No. The formula averages them, so swapping a and b gives the identical answer.
What if no sides are parallel?+
Then it is not a trapezoid. Split the shape into triangles and use Heron's formula on each.
Is a parallelogram a special case?+
Yes — when both parallel sides are equal, the average is that length and the formula reduces to base times height.
Why is the median useful on its own?+
It is the effective average width, which is what you multiply by length for volumes and by depth for flow area.
Last reviewed August 31, 2026. We review this page whenever the underlying formula, tax year, published rate or standard changes.