Calculate a pyramid volume
Choose one base method. Enter all length values in the selected unit.
Formula used
The universal pyramid formula is V = B × h ÷ 3.
V is volume. B is the base area. h is the perpendicular height.
B = length × width
B = side²
B = ½ × base × triangle height
B = n × side² ÷ [4 × tan(π ÷ n)]
When slant height is known, use h = √(slant height² − base apothem²).
How to use this calculator
- Select the base shape that matches your pyramid.
- Choose direct height or slant-height conversion.
- Select one length unit for every input.
- Enter the base dimensions or a known base area.
- Enter the vertical height, or slant height and apothem.
- Press Calculate Volume to show results above the form.
- Download CSV or PDF after checking the displayed values.
Example data table
| Base type | Base measurements | Vertical height | Base area | Volume |
|---|---|---|---|---|
| Rectangular | 6 m × 4 m | 9 m | 24 m² | 72 m³ |
| Square | 8 m side | 15 m | 64 m² | 320 m³ |
| Triangular | 10 m × 7 m | 12 m | 35 m² | 140 m³ |
| Regular hexagon | 6 sides, 5 m each | 10 m | 64.952 m² | 216.506 m³ |
| Custom area | 48 m² supplied | 9 m | 48 m² | 144 m³ |
Understanding pyramid volume
Why volume matters
Pyramids appear in school geometry, architecture, packaging, landscaping, and model building. Their volume tells you how much space exists inside a solid shape. This matters when estimating material, storage, excavation, or container capacity. A pyramid narrows from a flat base to one apex. That shape creates a volume smaller than a prism with matching base area and height.
Find the base area first
The key measurement is the base area. A rectangular pyramid uses length times width. A square pyramid uses the side length squared. A triangular pyramid uses one half times its base and perpendicular triangle height. Regular polygon pyramids use the number of sides and side length. When the base is irregular, calculate its area separately and enter the custom result.
Use the perpendicular height
Next, find the perpendicular height. This is the straight distance from the base plane to the apex. It is not normally the sloping edge. Using slant height by mistake produces an oversized answer. Some designs provide slant height and base apothem instead. The calculator can derive the perpendicular height with the Pythagorean theorem. The slant height must exceed the apothem.
Apply the one-third rule
After finding base area and perpendicular height, multiply them together. Divide that product by three. The result uses cubic units. Centimetres produce cubic centimetres. Metres produce cubic metres. Inches produce cubic inches. Keep every length measurement in one chosen unit before calculating. This prevents silent conversion errors.
Check and save your result
The calculator also offers useful checks. It shows the base area and derived vertical height. It converts the final result into cubic metres, litres, and cubic feet. These comparisons help with plans that mix drawing units and supply units. Save a CSV file for worksheets, quotes, or project notes. Save a PDF summary when a printable record is needed.
For reliable estimates, measure twice and record the measurement source. Use internal dimensions for capacity. Use external dimensions for material envelopes. Round only after the final calculation. Use enough decimal places for small parts. Use practical rounding for construction orders. A volume result is an estimate when dimensions are estimated. Confirm unusual shapes with drawings or professional specifications.
Compare the result with an equivalent prism. The pyramid should hold exactly one third of that prism. This simple check quickly reveals most formula mistakes. Label exported files securely with units, date, and project reference for later review.
Frequently asked questions
1. What is the volume formula for every pyramid?
Use V = B × h ÷ 3. B is the base area. h is the perpendicular height from the base plane to the apex.
2. Can I calculate a square pyramid?
Yes. Choose Square base, enter one side length, then enter the vertical height. The calculator squares the side before applying the pyramid formula.
3. Does slant height equal vertical height?
Usually no. Slant height follows a face. Vertical height goes straight from the apex to the base plane. Use the vertical measurement for volume.
4. How does the slant-height option work?
It uses h = √(slant height² − base apothem²). The slant height must be longer than the base apothem for a real vertical height.
5. What is a base apothem?
For a regular polygon, it is the distance from the base center to the midpoint of one side. It is perpendicular to that side.
6. Can I use an irregular base?
Yes. Find the base area separately, choose Custom base area, and enter that area. Then provide the perpendicular pyramid height.
7. Why are my result units cubed?
Volume measures three-dimensional space. Length uses linear units, area uses square units, and volume uses cubic units such as m³ or cm³.
8. Can I mix centimetres and metres?
Convert every input to one unit first. Mixing units without conversion creates incorrect base areas and volumes. The calculator assumes all entered lengths share one unit.
9. How are litres calculated?
The calculator converts the result to cubic metres, then multiplies by 1,000. One cubic metre equals 1,000 litres.
10. Is this useful for material estimates?
Yes, for geometric estimates. Add waste, compaction, thickness, or supplier requirements separately. Real projects may need professional drawings and specifications.
11. What should I export after calculation?
Export the CSV for spreadsheets or the PDF for printing. Both include key measurements, formulas, and converted volume values from the displayed result.