Trapezoidal Prism Volume Calculator - Volume, Area, and Capacity

The trapezoidal prism volume calculator finds the three-dimensional space inside a prism whose two end faces are trapezoids. Use it whenever a channel, beam, duct, or trough has a trapezoid cross section and a measurable length, and you need volume, surface area, or capacity in gallons and liters.

• • Channel and trough volume: Estimate how much water, gravel, or grain a trapezoidal channel or feed trough will hold between two parallel ends.
• • Beam and stock material: Check the volume of a cut beam, ramp, or wedge-shaped stock piece that has trapezoidal cross sections along its length.
• • Trench and excavation estimates: Approximate the volume of a trapezoidal trench or ditch where the bottom width and the top width differ because of slope.
• • Duct and tank capacity: Calculate the capacity of a custom duct, hopper, or tank whose cross section is a trapezoid rather than a rectangle or circle.

The trapezoid face has two parallel sides and a perpendicular height. The prism length is measured between the two trapezoid faces, so the shape is fully described by four linear measurements and a single unit.

Volume answers how much material fills the shape. Surface area answers how much material wraps or coats the outside. The calculator shows both because the same four measurements drive the lateral faces, the end faces, and the inside volume.

For a 3D solid with a circular base that tapers to a single point, Cone Volume Calculator gives the volume from a base radius and a height, which is a different but related case to the trapezoidal prism.

The calculator applies the standard prism volume formula, where the cross section is a trapezoid. The trapezoid area is half the sum of the two parallel sides times the perpendicular height, and the prism volume is that area times the prism length.

• a: Length of the first parallel side of the trapezoid face.
• b: Length of the second parallel side of the trapezoid face.
• h: Perpendicular height of the trapezoid face, measured at a right angle to both parallel sides.
• L: Prism length between the two trapezoid faces.

The lateral surface area uses the trapezoid perimeter times the prism length. The legs of an isoceles trapezoid have length sqrt(((a - b) / 2)^2 + h^2), and the total surface area adds the two trapezoid end faces back on top of the lateral area.

The same formula works when b equals a (rectangular cross section), when b equals 0 (triangular cross section), and when the user has only one or two of the parallel sides. The calculator reports a validation message if any input is zero or negative so the result never hides a bad measurement.

According to Wolfram MathWorld, the volume of a right prism is the area of its base cross section multiplied by the prism length.

According to Wolfram MathWorld, the area of a trapezoid is half the sum of the two parallel sides multiplied by the perpendicular height between them.

For a circular cross section extruded along a length, Cylinder Volume Calculator follows the same base-area-times-length pattern as the trapezoidal prism.

Four measurements describe the shape, and the order of operations matters. The two parallel sides feed the trapezoid area, the height controls the cross section, and the length multiplies the cross section into a 3D volume.

When the two parallel sides are equal, the trapezoid becomes a rectangle. The trapezoid area is then a times h, and the calculator still works because the same formula simplifies to a rectangular prism volume.

The legs of the trapezoid are only needed for surface area. Volume never requires them, which is why a single trapezoid height measurement is enough to find how much the prism holds.

When the cross section has more than four sides, Polygon Area Calculator extends the area step beyond a trapezoid.

Measure the trapezoid face, decide on a linear unit, and read the volume, surface area, and capacity from the results panel.

1. 1 Enter parallel sides a and b: Measure the two parallel sides of the trapezoid face and type the values in the same unit.
2. 2 Enter trapezoid height h: Measure the perpendicular height between the parallel sides, not the slanted leg.
3. 3 Enter prism length L: Measure the length of the prism between the two trapezoid end faces.
4. 4 Pick the linear unit: Use the unit selector so all four inputs use the same linear unit (cm, m, in, or ft).
5. 5 Read the results: The results panel shows volume, trapezoid area, lateral and total surface area, and capacity in gallons and liters.

For a small planter with a=30 cm, b=20 cm, h=18 cm, and L=60 cm, the calculator shows 27,000 cm^3 of soil capacity, 27 L, and about 7.13 US gallons.

Before you multiply by the prism length, Area Calculator can verify the trapezoid area step on its own with a, b, and h.

The most useful result is the consistent four-number summary: trapezoid area, volume, lateral surface area, and total surface area. The capacity conversion then bridges that summary to common tank and packaging units.

• • One formula, four outputs: Get trapezoid area, prism volume, lateral surface area, and total surface area from the same four measurements without re-entering data.
• • Unit-aware capacity: Convert cubic centimeters, meters, inches, or feet into US gallons and liters so tank and packaging estimates line up with real containers.
• • Edge case handling: Detect zero or negative inputs and surface a validation note so the result does not silently mix bad measurements with real ones.
• • Geometry cross check: Compare the trapezoidal prism with other prisms and solids in the same category to confirm that the cross section and length assumptions are consistent.
• • Trapezoid variants: Treat equal parallel sides as a rectangular prism and one parallel side as zero as a triangular prism without switching tools.

Volume is most useful when the cross section is correctly described. If the parallel sides are not really parallel, or the height was measured along the slanted leg, the result will not match a real container.

The capacity numbers round to two decimal places, which is enough precision for most containers and small channel estimates. Use the cubic-unit output for any calculation that needs more significant figures.

The formula is simple, but the four measurements are judgments. The strongest drivers are the size of the parallel sides, the perpendicular height, and the prism length.

• • The calculator assumes a right prism with parallel trapezoid faces. An oblique prism or a twisted shape is not described by the four measurements here.
• • The lateral and total surface area assume an isoceles trapezoid, where the two legs are equal. Right or scalene trapezoids give a different leg length and a different surface area.
• • Capacity conversions use NIST standard values for liters and US gallons, but the result is a liquid volume equivalent rather than a measurement of dry material weight.

When the same shape is reused across multiple projects, keep the same input order and the same unit. That makes the output easy to compare with a previous run without re-measuring the cross section.

For non-isoceles trapezoids where the legs are not equal, the lateral surface area shown here is a close approximation, not an exact value. The volume is still exact for any trapezoid with a perpendicular height h.

According to Omni Calculator trapezoidal prism volume page, the trapezoidal prism volume is half the sum of the two parallel sides times the trapezoid height times the prism length.

When the shape is not a prism or the cross section is not a trapezoid, Volume Calculator covers rectangles, cylinders, spheres, and other common solids in one place.