Triangular Prism Volume CalculatorFree online math calculator — instant results, no sign-up
Calculate a prism's volume from its triangular base.
Sign in to save results and favorites.
About the Triangular Prism Volume Calculator
The Triangular Prism Volume Calculator finds the volume of a prism using its triangle base, triangle altitude, and prism length. It calculates the triangular cross-sectional area, then multiplies that area by the prism length. With the default inputs of 4, 3, and 10, the volume is 60 cubic units.
- Triangle base
- The length of the chosen side of the triangular base, entered in the same linear unit as the other dimensions.
- Triangle altitude
- The perpendicular distance from the opposite vertex to the line containing the chosen triangle base, entered in the same linear unit as the other dimensions.
- Prism length
- The perpendicular distance between the two parallel triangular faces, entered in the same linear unit as the triangle dimensions.
Formula and method
V = (b × h / 2) × L; with the default inputs, V = (4 × 3 / 2) × 10 = 60.
- VVolume of the triangular prism, in cubic units.
- bTriangle base length, in linear units.
- hTriangle altitude perpendicular to the chosen base, in linear units.
- LPerpendicular distance between the triangular faces, in linear units.
Multiply the triangle base by its perpendicular altitude and divide by 2 to find the triangular area. Multiply that area by the prism length to find the volume. For the default inputs, the triangular area is 4 × 3 / 2 = 6 square units, and the volume is 6 × 10 = 60 cubic units.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Triangle base4
- Triangle altitude3
- Prism length10
Results
- Result60
How to use the Triangular Prism Volume Calculator
- 1Choose a common length unit for all three measurements and convert any measurements that use different units.
- 2Enter the Triangle base; the default value is 4.
- 3Enter the Triangle altitude perpendicular to that base; the default value is 3.
- 4Enter the Prism length between the triangular faces; the default value is 10.
- 5Read the calculated result: the default inputs give a volume of 60 cubic units.
Reading your result
The Result row reports the triangular prism's volume. With the default inputs, Result = 60 means the prism occupies 60 cubic units, not 60 square or linear units. If all input dimensions are measured in centimeters, the result is in cubic centimeters; if they are measured in meters, it is in cubic meters.
Limitations
The calculation assumes a prism with congruent, parallel triangular faces and a constant cross-sectional area. The triangle altitude must be perpendicular to the selected triangle base; a sloping triangle side is not generally a valid substitute. For an oblique prism, use the perpendicular distance between the triangular faces rather than a slanted connecting edge. Dimensions must use the same unit and be positive for a nondegenerate prism. Measurement uncertainty carries through to the calculated volume, and the formula does not account for cavities or cutouts.
Common questions
Does the triangular base have to be a right triangle?+
No. The formula works for any triangle when the altitude is perpendicular to the chosen base. For an obtuse triangle, that altitude may meet an extension of the base outside the triangle.
What is the difference between Triangle altitude and Prism length?+
Triangle altitude measures a perpendicular distance within the triangular face. Prism length measures the perpendicular separation between the two triangular faces. The default values are 3 for the triangle altitude and 10 for the prism length.
Why do the default inputs produce 60 rather than 120?+
A triangle's area is half its base times its altitude. The calculator first finds 4 × 3 / 2 = 6 square units, then multiplies by 10 to obtain 60 cubic units.
Can I enter the three triangle side lengths instead?+
Not directly. This calculator requires one triangle side as the base, its corresponding perpendicular altitude, and the prism length. If you know all three triangle sides, first find the triangle's area using Heron's formula, then calculate the required altitude as twice that area divided by your chosen base.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
You might also like
Slope Calculator
Slope, angle and line equation through two points.
Area Calculator
Area of common 2D shapes.
Volume Calculator
Volume of common 3D shapes.
Surface Area Calculator
Surface area of 3D shapes.
Circle Calculator
Radius, diameter, circumference and area.
Triangle Calculator
Solve a triangle from three sides.
Results are estimates for informational purposes and are not financial, medical or legal advice.