Square Pyramid Volume Calculator
Calculate the volume, surface area, and other dimensions of a square pyramid using its base length and height.
Pyramid Volume and Surface Area Calculator
Calculate the volume and surface area of a regular pyramid with our easy-to-use calculator. Learn about pyramid formulas, real-world applications, and explore interactive examples.
A regular pyramid is a three-dimensional shape with a polygonal base and triangular faces that meet at a point called the apex. Our pyramid calculator helps you determine both the volume and surface area using the base length and height. Essential for architecture, engineering, and mathematical studies.
Formula
Volume = (1/3)Bh
Surface Area = B + (1/2)Pl
Where:
- B:area of the base
- h:height of the pyramid (perpendicular to base)
- P:perimeter of the base
- l:slant height (length of edge from base to apex)
How to Calculate Pyramid Volume
To calculate the volume of a pyramid, multiply the base area by the height and divide by three...
Understanding Surface Area
The total surface area includes the base area plus the sum of all triangular faces...
Real-World Applications
Pyramids are found in ancient architecture, modern buildings, and packaging designs...
Frequently Asked Questions
Why is the volume one-third of the base area times height?
This relationship was proven by ancient mathematicians. A pyramid has exactly one-third the volume of a prism with the same base and height.
What is slant height?
Slant height is the distance from the apex to any point on the base edge, measured along the face of the pyramid. It can be calculated using the Pythagorean theorem.
How does base shape affect calculations?
While the volume formula remains the same, the base area and perimeter calculations change depending on whether the pyramid has a square, triangular, or other polygonal base.