Volume of a Pyramid Formula
Geometry Formulas: Area, Volume, Perimeter
What is the formula for the volume of a pyramid?
Answer
Volume of a pyramid
V = (1/3) · a · b · h
Here a is the side (or base), b is the second side, h is the height, perpendicular to the base. The result comes out in cubic units.
Where the formula comes from
V = (1/3) · a · b · h
The same one third as the cone, and for the same reason: three pyramids of equal base and equal height fill the prism built on that base. Swap the rectangular base for a circle and this formula becomes the cone’s.
Worked examples
Let a = 6, b = 6, h = 9. Then the volume of a pyramid = 108 cubic units.
Let a = 4, b = 5.5, h = 3. Then the volume of a pyramid = 22 cubic units.
The common mistake
Using the edge of a face as the height. The height runs from the apex straight down to the base plane; the sloping edge and the slant height of a face are both longer, and all three are different numbers.
Other quantities: Pyramid
Found an error in the calculation or the information?
Related Calculations
See Also
- Square Footage Calculator - Width × length in feet to square feet
- Square Feet to Square Meters (Sq Ft to Sq M) - Convert Square Feet to Square Meters
- Square Meters to Square Feet (Sq M to Sq Ft) - Convert Square Meters to Square Feet
- Gravel Calculator - Area to cubic yards, tons and coverage
- Topsoil Calculator - Cubic yards, weight and coverage for any area
- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
Share This Calculation
Print
<a href="https://calculat.io/en/geometry/shape-formula/volume--pyramid">Volume of a Pyramid Formula - Calculatio</a>Facebook
Twitter
Telegram
WhatsApp
Viber
Email
Values from the Formula (b = 6, h = 9)
| If a = | Volume |
|---|---|
| 1 | 18 cubic units |
| 2 | 36 cubic units |
| 3 | 54 cubic units |
| 4 | 72 cubic units |
| 5 | 90 cubic units |
| 10 | 180 cubic units |
Geometry Formulas: Area, Volume, Perimeter
These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the volume of a pyramid? (The answer is: V = (1/3) · a · b · h). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter