# Trapezoidal Prism Volume Calculator

URL: https://speedycalculator.com/calculators/math/trapezoidal-prism-volume/
Last updated: 2026-10-30

> The trapezoidal prism volume calculator finds the volume of a prism with a trapezoid cross-section from the two parallel sides, the trapezoid height and the prism length.

## Inputs

- Long base B (cm, m, mm, in, ft, yd, km, mi)
- Short base b (cm, m, mm, in, ft, yd, km, mi)
- Trapezoid height h (cm, m, mm, in, ft, yd, km, mi)
- Length ℓ (cm, m, mm, in, ft, yd, km, mi)

## Results

- Volume
- Cross-section area

## Formula

```
V = (B + b)/2 · h · ℓ
```

## Explanation

Ditches, swales, retaining walls, troughs and many concrete foundations have trapezoidal cross-sections. Their volume tells you how much soil to dig or concrete to order.

### How to use the Trapezoidal Prism Volume Calculator

- **Long base B**
- **Short base b**
- **Trapezoid height h**
- **Length ℓ**

Results update as you type, and everything is calculated in your browser.

### How it works

Enter the long base B, the short base b, the height h of the trapezoid and the length ℓ.

### Inputs explained

FieldWhat to enterLong base BUnits: cm, m, mm, in, ft, yd …Short base bUnits: cm, m, mm, in, ft, yd …Trapezoid height hUnits: cm, m, mm, in, ft, yd …Length ℓUnits: cm, m, mm, in, ft, yd …

### What each result means

- **Volume** = ([Long base B] + [Short base b])÷2×[Trapezoid height h]×[Length ℓ]
- **Cross-section area** = ([Long base B] + [Short base b])÷2×[Trapezoid height h]

### Example values

How the main result changes when **Long base B** changes and everything else stays at the example values above:

Long base B (cm)Volume (cm³)54407.55401064012.574015840201,040

## Worked example

Inputs — Long base B: 10 cm; Short base b: 6 cm; Trapezoid height h: 4 cm; Length ℓ: 20 cm.

Results — **Volume = 640 cm³**; Cross-section area = 32 cm².

## Key terms

- **Cross-section**: The shape you get by slicing the solid.

## FAQ

**How much soil is in a trench 1 m deep, 2 m wide at the top, 1 m at the bottom and 10 m long?**
(2 + 1)/2 × 1 × 10 = 15 m³.

**Does it matter which base is on top?**
No.

**How do I convert m³ to litres?**
Multiply by 1,000 – or change the unit menu.

**Is a trapezoidal prism a frustum?**
No – a frustum tapers in both directions.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Solid geometry](https://mathworld.wolfram.com/SolidGeometry.html)