Quick answer
A rectangular pyramid's volume is V = ⅓ × length × width × height. A 6 × 4 base with a height of 9 has a volume of 72.
Enter the base length, width and height. The calculator returns the volume.
Related tools: Triangular Pyramid Volume Calculator: Volume of a pyramid with a triangular base. Cylinder Volume Calculator: Volume of a cylinder. Sphere Volume Calculator: Volume and surface area of a sphere.
How to use the Pyramid Volume Calculator
- Enter base length (above 0).
- Enter base width (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 length | A number | > 0 |
| Base width | A number | > 0 |
| Height | A number | > 0 |
Formula and method
Formula
V = (1/3) × l × w × h
IEEE-754 double precision; shown to at most 6 decimal places.
A third of the base area times the height.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Base length = 6; Base width = 4; Height = 9.
| Result | Value |
|---|---|
| Volume | 72 |
Example 2
Inputs: Base length = 3; Base width = 3; Height = 3.
| Result | Value |
|---|---|
| Volume | 9 |
The first line is the headline result (volume). IEEE-754 double precision; shown to at most 6 decimal places.
A third of the prism
The pyramid is exactly one third of the prism with the same base and height: 6 × 4 × 9 = 216, and a third is 72. The Great Pyramid of Giza, with a 230 m base and 139 m height, has a volume of about 2.4 million m³.
Height
Use the vertical height from the apex to the base, not the slant height. The calculator handles rectangular bases only; for other bases use ⅓ × base area × height.
How the result changes with base length
Holding every other input at the first worked example, this table changes only base length. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Base length | Volume |
|---|---|
| 3 | 36 |
| 6 | 72 |
| 12 | 144 |
| 24 | 288 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Height: entering "-1" shows "Height must be greater than 0." beside that field and no result.
Choosing between the 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 |
|---|---|---|
| [Triangular Pyramid Volume Calculator](/math/triangular-pyramid-volume/) | triangle base, triangle height and pyramid height | 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 |
| [Cone Volume Calculator](/math/cone-volume-calculator/) | radius and height | 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
- Rectangular base
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 height to confirm this.
Frequently asked questions
What is the volume of a square pyramid with base 10 and height 6?
A square pyramid with base 10 and height 6 has volume ⅓ × 10 × 10 × 6 = 200.
Is the slant height used?
No, only vertical height.
How do I find surface area?
Add the base and four triangular faces.
What does the Pyramid Volume Calculator calculate?
Volume of a pyramid from its base area and height (rectangular base). It returns Volume.
What formula does the Pyramid Volume Calculator use?
V = (1/3) × l × w × h. A third of the base area times the height.
What do I need to enter in the pyramid Volume Calculator?
You enter Base length, Base width and Height.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Rectangular base.
What is an example of a pyramid Volume result?
With base length 6, base width 4 and height 9, the volume is 72.
Related calculators
- Triangular Pyramid Volume Calculator — Volume of a pyramid with a triangular base.
- 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.
- Cube Volume Calculator — Volume, surface area and diagonal of a cube.
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.