Calculator Inputs
Example Data Table
| Base Type | Dimensions | Base Area | Height | Volume |
|---|---|---|---|---|
| Square | Side = 6 m | 36 m² | 10 m | 120 m³ |
| Rectangle | Length = 8 m, Width = 5 m | 40 m² | 9 m | 120 m³ |
| Triangle | Base = 7 m, Triangle Height = 4 m | 14 m² | 12 m | 56 m³ |
| Regular Polygon | 5 sides, side = 3 m | 15.4843 m² | 11 m | 56.7758 m³ |
| Known Base Area | Base Area = 40 m² | 40 m² | 15 m | 200 m³ |
Formula Used
The core pyramid volume formula is:
V = (1 / 3) × B × h
Where:
- V = pyramid volume
- B = base area
- h = perpendicular height
Base area formulas used by this calculator:
- Square base: B = a²
- Rectangular base: B = l × w
- Triangular base: B = (1 / 2) × b × ht
- Regular polygon base: B = (Perimeter × Apothem) / 2
- Known base area: use the entered value directly
For square, rectangle, and regular polygon options, the page also estimates lateral area and total surface area when enough dimensions are available.
How to Use This Calculator
- Select the base shape that matches your pyramid.
- Enter the vertical height of the pyramid.
- Fill in the required base dimensions for that shape.
- Choose the unit label you want displayed.
- Click Calculate Volume.
- Review the result card shown above the form.
- Use the chart to understand how volume changes with height.
- Export the values with the CSV or PDF buttons.
Frequently Asked Questions
1. What is the formula for pyramid volume?
Use one third of the base area multiplied by the vertical height. The formula is V = (1/3) × base area × height.
2. Why does the calculator ask for vertical height?
Pyramid volume depends on perpendicular height, not slanted edge distance. Using slant height alone would produce an incorrect volume value.
3. Can I calculate volume from a square base?
Yes. Enter the square side length and the vertical height. The calculator finds base area first, then applies the pyramid volume formula.
4. Does this work for a rectangular pyramid?
Yes. Choose the rectangular base option, enter length, width, and vertical height, and the tool will compute base area and volume.
5. What if I already know the base area?
Choose the known base area option. Then enter the base area directly with the vertical height to calculate volume faster.
6. What does the graph show?
The graph plots volume against height while keeping the current base area fixed. It helps visualize the linear effect of height on volume.
7. Are surface area values always shown?
No. Surface area needs enough geometric detail. It appears for square, rectangular, and regular polygon bases when the needed values can be derived.
8. Can I export my result?
Yes. After calculation, use the CSV button for spreadsheet-friendly output or the PDF button for a clean printable summary.