Pyramid Calculator

Calculate the volume and surface area of a right rectangular pyramid

Your result will appear here.

About the Pyramid Calculator

A pyramid tapers from a polygonal base to a single apex. Its volume is one third of the product of base area and perpendicular height, regardless of the specific polygon used for the base.

Surface area also depends on the sloping triangular faces, so slant height and base geometry matter when estimating exterior covering.

How to Use the Pyramid Calculator

  1. Choose the base shape supported by the calculator.
  2. Enter the base dimensions.
  3. Enter the perpendicular height for volume.
  4. Calculate volume and, when needed, use the correct slant dimensions for surface area.

How the Calculation Works

Pyramid volume is V = (1/3)Bh, where B is base area and h is perpendicular height from the base plane to the apex.

Surface area is base area plus the areas of the triangular side faces. For regular pyramids, those faces can often be expressed using base perimeter and slant height.

Worked example

Pyramid Calculator Worked Example

Square pyramid with 6×6 base and height 9

Base area B=6×6=36. Volume=(1/3)×36×9=108 cubic units.

Result guide

Understanding Your Pyramid Calculator Result

Volume depends on the base area and the perpendicular height, while surface area depends on the shape and slant geometry of the side faces. Keeping those measurements separate is essential when a real model gives you several different heights.

Before you rely on the answer

Assumptions and Limitations

  • The apex and base geometry match the selected pyramid type.
  • Perpendicular height is used for volume.
  • Surface-area calculations use the correct slant dimensions.

Practical tip

Using This Result in Practice

Draw the perpendicular height inside the pyramid and the slant height on a face. Keeping those two lines visually separate prevents a common formula error. For a non-regular pyramid, calculate each triangular face separately instead of assuming one slant height applies to every side.

Related calculations

Useful Calculations to Continue With

If the pyramid is part of a broader solid-geometry comparison, use the Surface Area Calculator for other shapes.

If you need to calculate one triangular side face separately, use the Triangle Calculator.

Common questions

Pyramid Calculator FAQ

Why is pyramid volume one third of base area times height?

A pyramid occupies one third the volume of a prism with the same base area and perpendicular height.

Is slant height used in pyramid volume?

No. Volume uses perpendicular height.

How is pyramid surface area found?

Add the base area to the areas of all triangular side faces.