Quick answer
A triangular pyramid's volume is V = ⅓ × (½ × base × triangle height) × pyramid height. A triangle with base 6 and height 4 and a pyramid height of 5 gives a volume of 20.
Enter the triangle base and height and the pyramid height. The calculator returns the volume.
Related tools: Pyramid Volume Calculator: Volume of a pyramid from its base area and height (rectangular base). Triangular Prism Volume Calculator: Volume of a triangular prism. Cylinder Volume Calculator: Volume of a cylinder.
How to use the Triangular Pyramid Volume Calculator
- Enter triangle base (above 0).
- Enter triangle height (above 0).
- Enter pyramid height (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Triangle base | A number | > 0 |
| Triangle height | A number | > 0 |
| Pyramid height | A number | > 0 |
Formula and method
Formula
V = (1/3) × (½ b t) × h
IEEE-754 double precision; shown to at most 6 decimal places.
Base triangle area times pyramid height divided by 3.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Triangle base = 6; Triangle height = 4; Pyramid height = 5.
| Result | Value |
|---|---|
| Volume | 20 |
Example 2
Inputs: Triangle base = 3; Triangle height = 2; Pyramid height = 3.
| Result | Value |
|---|---|
| Volume | 3 |
The first line is the headline result (volume). IEEE-754 double precision; shown to at most 6 decimal places.
The arithmetic
Base area = ½ × 6 × 4 = 12. Volume = ⅓ × 12 × 5 = 20. As with every pyramid, the volume is one third of the prism with the same base and height (60).
Tetrahedron
A regular tetrahedron is a special case. The pyramid height is the perpendicular distance from the apex to the base plane, not a slanted edge. Values must be positive.
How the result changes with triangle base
Holding every other input at the first worked example, this table changes only triangle base. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Triangle base | Volume |
|---|---|
| 3 | 10 |
| 6 | 20 |
| 12 | 40 |
| 24 | 80 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Triangle base: entering "0" shows "Triangle base must be greater than 0." beside that field and no result.
Choosing between the Triangular Pyramid 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 |
|---|---|---|
| [Pyramid Volume Calculator](/math/pyramid-volume-calculator/) | base length, base 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 triangle base to confirm this.
Frequently asked questions
What is a tetrahedron?
A pyramid with four triangular faces.
Why one third?
Three such pyramids fill a prism.
Is height the slant height?
No. Use the vertical height from the apex to the base plane, not the slanted edge.
What does the Triangular Pyramid Volume Calculator calculate?
Volume of a pyramid with a triangular base. It returns Volume.
What formula does the Triangular Pyramid Volume Calculator use?
V = (1/3) × (½ b t) × h. Base triangle area times pyramid height divided by 3.
What do I need to enter in the triangular Pyramid Volume Calculator?
You enter Triangle base, Triangle height and Pyramid 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 triangular Pyramid Volume result?
With triangle base 6, triangle height 4 and pyramid height 5, the volume is 20.
Related calculators
- Pyramid Volume Calculator — Volume of a pyramid from its base area and height (rectangular base).
- 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.