Pyramid Frustum Calculator

What Is a Pyramid Frustum Calculator?

A pyramid frustum is what remains when the top of a square pyramid is sliced off parallel to its base — like the shape of the ancient Mesoamerican step pyramids or a lampshade with a square profile. This calculator finds the volume, lateral surface area, and total surface area from the two base side lengths and the vertical height.

How to Use This Pyramid Frustum Calculator

1. Measure the bottom (larger) square side a and the top (smaller) square side b.
2. Measure the vertical height h between the two square faces.
3. Enter a, b, and h into the fields above and click Calculate.

Formula

• Slant Height = √(h² + ((a − b)/2)²)
• Volume = (h/3) × (a² + ab + b²)
• Lateral Surface Area = 2(a + b) × slant
• Total Surface Area = Lateral + a² + b²

Worked Example

A frustum-shaped planter has a bottom side of 40 cm, a top side of 25 cm, and stands 20 cm tall. Slant = √(20² + 7.5²) ≈ 21.36 cm. Volume = (20/3)(1600+1000+625) ≈ 21,500 cm³. Lateral Surface Area = 2(65)(21.36) ≈ 2,777 cm².