Pyramid Volume Calculator – Guide & Formulas
Calculate the volume and surface area of regular square and rectangular pyramids with step-by-step math explanations.
Calculate the volume and total surface area of regular square and rectangular pyramids. Enter base parameters and vertical height to solve instantly.
Key Takeaway
Use the free Pyramid Volume Calculator to calculate the volume and surface area of regular square and rectangular pyramids with step-by-step math explanations. Get instant results with step-by-step explanations.
How to Use the Pyramid Volume Calculator
- Select your pyramid base shape: Square or Rectangular.
- Input the base side length(s) and the vertical height.
- Analyze the volume, base area, slant heights, and total surface area.
The Formula
Variable Definitions
- V: Volume of the pyramid
- Abase: Area of the polygon base
- h: Vertical vertical height
Great Pyramid of Giza Sizing
The Great Pyramid of Giza has a square base length of about 230 meters and a height of 146.6 meters. Find its approximate volume.
- Step 1: Set base length a = 230m and height h = 146.6m.
- Step 2: Calculate base area: 230 * 230 = 52,900 sq m.
- Step 3: Apply the formula: (1/3) * 52,900 * 146.6 ≈ 2,585,226 cubic meters.
- Step 4: The volume is approximately 2.58 million cubic meters.
Frequently Asked Questions
Does this calculator support triangular-based pyramids?
This tool is specifically designed for square and rectangular regular pyramids, which are the most common in practical applications.
How is the surface area of a pyramid calculated?
The total surface area is the sum of the base area plus the areas of the triangular side faces. For a regular square pyramid, this equals Base Area + 2 * side * slant height.
How do you find slant height of a pyramid face?
Using the right triangle inside the pyramid, slant height is solved with s = √(height² + (base_width / 2)²).