What is the volume of a 3D object?
The volume of a 3D object is the amount of space it occupies. The bigger the volume, the more space the object takes up. One intuitive way to measure volume is to submerge the object in water and measure how much liquid it displaces. Volume is always a positive number — zero or negative volume simply doesn't exist.
How to find the volume of a trapezoidal prism
A trapezoidal prism is a 3D solid whose two parallel cross-sections (bases) are congruent trapezoids, connected by four rectangular faces. To find its volume you only need four measurements:
- b — length of the short parallel base of the trapezoid
- B — length of the long parallel base of the trapezoid
- h — perpendicular height between the two parallel bases of the trapezoid
- ℓ — length of the prism (distance between the two trapezoidal faces)
Trapezoidal prism volume formula
V = ((b + B) / 2) × h × ℓ
The expression (b + B) / 2 × h gives the cross-sectional area of the trapezoid — the area of one trapezoidal face.
Multiplying that area by the prism's length ℓ extends it into three dimensions and yields the volume.
Step-by-step example
Let's use these dimensions:
- Short base b = 5 m
- Long base B = 5 m
- Height h = 3 m
- Length ℓ = 5 m
- Cross-sectional area = (b + B) / 2 × h = (5 + 5) / 2 × 3 = 5 × 3 = 15 m²
- Volume = cross-sectional area × ℓ = 15 × 5 = 75 m³
Measurement systems
This calculator supports two measurement systems:
- Metric — enter dimensions in centimetres (cm); results shown in cm³, m³ and litres (L).
- US / Imperial — enter dimensions in inches (in); results shown in in³, ft³ and US gallons (gal).
FAQs
Can volume be negative?
No. Volume represents physical space, which cannot be negative. All input dimensions must be positive numbers greater than zero.
What is the volume of a trapezoidal prism with all 1 m sides?
V = ((1 + 1) / 2) × 1 × 1 = 1 m³.
What if the two bases are equal?
When b = B the cross-section is a rectangle rather than a trapezoid, and the prism becomes a rectangular prism (cuboid). The formula still works perfectly: V = b × h × ℓ.
What units should I use?
Enter all four dimensions in the same unit (all cm or all inches). The calculator converts the result automatically to larger/smaller units for convenience.