How to find a pyramid's volume
A pyramid's volume is one third of its base area times the height: V = (1/3) × base length × base width × height for a rectangular base. With a 6 × 6 base and height 10, V = (1/3) × 36 × 10 = 120 cubic units.
The same one-third rule covers every pyramid shape: swap in the correct base area and the rest is unchanged, because the taper to a single apex supplies the factor of one third. A cone is a pyramid with a circular base, and the cone volume calculator uses the same one-third rule.
How to use this calculator
Enter the base length, base width, and the height (the straight-up distance from base to apex, not the slant). The result is in cubic units of whatever length unit you used.
Using the slant height by mistake always overstates the volume. If you only know the slant height s and half-width a, recover the true height with Pythagoras: height = √(s² − a²). Keep all three inputs in the same unit. For a rectangular base, get the base area first with the rectangle area calculator.
Why one third
A pyramid fills exactly one third of the prism that shares its base and height. So a pyramid is one third of the matching box — find that box with the rectangular prism volume calculator.
In the worked example the matching box measures 6 × 6 × 10 = 360 cubic units, and a third of that is the 120 the calculator returns — a quick way to check any answer by hand.
Frequently asked questions
- What is the formula for pyramid volume?
- V = (1/3) × base area × height. For a rectangular base, base area = length × width.
- What is the volume of a 6 × 6 pyramid 10 tall?
- 120 cubic units, since (1/3) × 36 × 10 = 120.
- Do I use the slant height or the vertical height?
- The vertical (perpendicular) height from the base to the apex, not the slant height along a face.
- How does this compare to a box?
- A pyramid holds exactly one third of the rectangular prism with the same base and height.
- Does it matter if the apex is off-centre?
- No. An oblique pyramid, whose apex sits off to one side, has exactly the same volume as an upright one with the same base and vertical height. Only the perpendicular height matters, which is why leaning the tip over changes the surface area but not the volume.