Pyramid Volume Calculator
The pyramid volume formula, explained and computed: enter the rectangular base and height for the volume with substitution steps.
How to use this calculator
Enter the length and width of the rectangular base and the vertical height, then press Calculate. The calculator applies V = (1/3) × base area × height and shows each substitution.
How it works
Like the cone, a pyramid holds one-third of the prism with the same base and height. So: find the base area (length × width for a rectangle), multiply by the height, divide by three. The calculator assumes a rectangular base and says so, no hidden assumptions.
Worked example
Example: base 4 × 5, height 6
Step 1, Base area: 4 × 5 = 20.
Step 2, Times height: 20 × 6 = 120.
Step 3, One third: 120 ÷ 3 = 40 cubic units.
Common mistakes
- Forgetting the 1/3: same trap as cones, without it you have computed a box.
- Slant height instead of vertical height: the formula needs the perpendicular height from base to apex.
- Assuming a square base: length and width are separate inputs here; for a square base just enter the same number twice.
When to use it
Pyramids model roof volumes, hoppers, spoil heaps, and of course the Egyptian pyramids. The 1/3 rule generalizes: any pyramid (or cone) is one-third of its prism (or cylinder).
Frequently asked questions
V = (1/3) × base area × height. For a rectangular base that is (1/3) × length × width × height.
Yes, any pyramid is one-third of the prism with the same base and height, whatever the base shape. The base-area part changes; the 1/3 does not.
Height is the perpendicular distance from base to apex; slant height runs down a face. Volume formulas always use the perpendicular height.
Use the same formula with length = width: V = (1/3) × side² × height.