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Math • Pyramid Volume Calculator

Pyramid Volume Calculator

Calculate the volume and surface area of a square-based pyramid from its base side length and height.

Volume (V = ⅓ × base × h)
108.000
Total Surface Area
149.842
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Calculation Guide & Reference

Square Pyramid Volume & Surface Area Mathematics

Pyramid volume calculator computes the volume and surface area of a square-based pyramid from its base side length and height.

Standardized Mathematical Formula
V = (1/3) × Base Area × Height

A pyramid's volume is exactly one-third of a prism sharing the same base and height — the same 1/3 relationship that connects a cone to its equivalent cylinder.

Variables:
Base:Side length of the square base
Height:Perpendicular height from base center to apex
How It Works (Step-by-Step)
  • 1Enter the base side length and the height (apex above the base center).
  • 2View the volume and total surface area (base plus four triangular faces).
Real-World Numerical Example
A Pyramid with a 6-Unit Base and 9-Unit Height

A square-based pyramid has a base side length of 6 units and a height of 9 units.

•Base area: 6² = 36 square units.
•Volume: (1/3) × 36 × 9 = 108 cubic units.
•Slant height: √((6/2)² + 9²) = √90 ≈ 9.49.
•Surface area: 36 + (2 × 6 × 9.49) ≈ 149.84 square units.
Result: The pyramid has a volume of 108 cubic units and a total surface area of approximately 149.84 square units.
Calculation Best Practices & Tips
Examine the discriminant (b² - 4ac) before solving quadratics to instantly know if roots are real, distinct, repeated, or complex.
In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

V = (1/3) × Base Area × Height — one-third of the base area multiplied by the perpendicular height, regardless of the base shape.

The 1/3 × base area × height formula works for any pyramid regardless of base shape — only the base area calculation changes (a triangle's area formula instead of a square's).

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