Pyramid Calculator
Base, height, volume and surface in one view.
Your numbers
Your results
Volume
Volume
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Slant height (along length faces)
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Slant height (along width faces)
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Lateral surface area
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Total surface area
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Pyramid Calculator by TheCalcTools
How the Pyramid Calculator works
Enter the rectangular base and the vertical height from the base to the apex.
Volume is one third of base area times height.
Each pair of triangular faces has its own slant height, from the Pythagorean theorem.
The formula
V = ⅓ × l × w × hSlant (length faces) = √(h² + (w/2)²)
Worked example
Using the default values shown in the calculator:
| Base length | 6 |
|---|---|
| Base width | 4 |
| Height | 9 |
- V = ⅓ × 6 × 4 × 9 = 72.000.
- Slant heights 9.220 and 9.487; total surface area 117.265.
Result:
| Volume | 72.000 |
|---|---|
| Slant height (along length faces) | 9.220 |
| Slant height (along width faces) | 9.487 |
| Lateral surface area | 93.265 |
| Total surface area | 117.265 |
Frequently asked questions
Why is the volume one third?
Three congruent pyramids fit inside a prism of equal base and height, so a pyramid holds one third of the prism’s volume.
Is the apex above the centre?
The calculator assumes a right pyramid with the apex directly above the centre of the base.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.