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Pyramid Calculator: Volume, Slant Height, Surface Area

This free pyramid calculator finds the volume, slant height, edge length, lateral area and total surface area of a square pyramid from its base side and its height.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

A pyramid has a flat base and triangular sides that meet at a point. Roofs, tents, monuments and glass shapes are pyramids.

Enter the base side and the height.

How to Use This Tool

  1. Enter the value or values asked for in the boxes.
  2. Choose the unit label if there is a choice.
  3. Press Calculate.
  4. Read every result in the table and copy what you need.

How the Calculation Works

Volume = ⅓a²h. Slant height l = √(h² + (a ÷ 2)²). Each face has area ½ a l, so the lateral area is 2al. The total surface area adds the base a². The edge e = √(h² + a² ÷ 2).

Worked Example

A pyramid with a base of 6 and a height of 4 has a slant height of 5, a volume of 48, a lateral area of 60, a total surface area of 96 and an edge of 5.831.

Common Uses

  • Roofs and tents.
  • Monuments and models.
  • Packaging design.
  • Homework.

Tips and Common Mistakes

  • The height is straight up, not along the slope.
  • Use one unit throughout.
  • The Great Pyramid is a square pyramid.
  • Measure carefully: a small error in a length is squared in an area and cubed in a volume, so a 5 percent error in a side can become a 10 percent error in the area or a 15 percent error in the volume.
  • Round only at the end. If you copy a result into another calculation, copy the full number from the tool rather than a rounded one, so small errors do not build up.

Next, you may need the cone calculator, cube and box calculator, cylinder calculator, regular polygon calculator.

Everything runs in your browser. Nothing you type is uploaded, stored or sent to any outside service.

Frequently Asked Questions

Volume = ⅓ × base area × height. For a square base of side a, V = ⅓a²h.
The height of one triangular face, measured along its middle. It is √(h² + (a ÷ 2)²).
The sloping edge from a corner of the base to the tip, √(h² + a² ÷ 2).
The volume rule works for any base, but this tool handles a square base.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.