Quick answer
A prism's volume is V = base area × height. A prism with a base area of 12 and a height of 5 has a volume of 60.
Enter the base area and the prism height. The calculator returns the volume.
Related tools: Rectangular Prism Volume Calculator: Volume of a rectangular prism (box). Triangular Prism Volume Calculator: Volume of a triangular prism. Cylinder Volume Calculator: Volume of a cylinder.
How to use the Prism Volume Calculator
- Enter base area (above 0).
- Enter height (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Base area | A number | > 0 |
| Height | A number | > 0 |
Formula and method
Formula
V = base area × height
IEEE-754 double precision; shown to at most 6 decimal places.
Cross-section area times length.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Base area = 12; Height = 5.
| Result | Value |
|---|---|
| Volume | 60 |
Example 2
Inputs: Base area = 2.5; Height = 4.
| Result | Value |
|---|---|
| Volume | 10 |
The first line is the headline result (volume). IEEE-754 double precision; shown to at most 6 decimal places.
Any prism
The formula works for any base shape: rectangular, triangular or hexagonal. A triangular prism with base 4, triangle height 6 (base area 12) and length 5 gives 60. Use consistent units.
Finding the base area
For a rectangle it's length × width, for a triangle ½ × base × height and for a regular hexagon (3√3/2)s². The height is the distance between the two bases, not a slant edge.
How the result changes with base area
Holding every other input at the first worked example, this table changes only base area. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Base area | Volume |
|---|---|
| 6 | 30 |
| 12 | 60 |
| 24 | 120 |
| 48 | 240 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Base area: entering "0" shows "Base area must be greater than 0." beside that field and no result.
Choosing between the Prism Volume Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Rectangular Prism Volume Calculator](/math/rectangular-prism-volume/) | length, width and height | Volume |
| [Triangular Prism Volume Calculator](/math/triangular-prism/) | triangle base, triangle height and prism length | Volume |
| [Cylinder Volume Calculator](/math/cylinder-volume-calculator/) | radius and height | Volume |
| [Sphere Volume Calculator](/math/sphere-volume-calculator/) | radius | Volume |
| [Volume of a Hemisphere Calculator](/math/volume-of-hemisphere/) | radius | Volume |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Positive values
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for base area to confirm this.
Frequently asked questions
What is the volume of a cube as a prism?
A cube is a prism whose base area is side², so its volume is side² × side = side³.
How is a pyramid related?
A pyramid is one third of a prism with the same base and height.
What if the prism is slanted?
Use the perpendicular height.
What does the Prism Volume Calculator calculate?
Volume of any prism from base area and height. It returns Volume.
What formula does the Prism Volume Calculator use?
V = base area × height. Cross-section area times length.
What do I need to enter in the prism Volume Calculator?
You enter Base area and Height.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Positive values.
What is an example of a prism Volume result?
With base area 12 and height 5, the volume is 60.
Related calculators
- Rectangular Prism Volume Calculator — Volume of a rectangular prism (box).
- Triangular Prism Volume Calculator — Volume of a triangular prism.
- Cylinder Volume Calculator — Volume of a cylinder.
- Sphere Volume Calculator — Volume and surface area of a sphere.
- Volume of a Hemisphere Calculator — Volume and surface area of a hemisphere.
- Cone Volume Calculator — Volume, slant height and surface area of a cone.
Sources
- OpenStax, Prealgebra 2e (Rice University): perimeter, area, volume, circumference and the Pythagorean theorem
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.