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How to Calculate Cylinder Volume

A cylinder is a geometric solid bounded by two parallel congruent circular bases and a curved surface formed by parallel segments connecting corresponding points of the bases.

The Governing Geometric Formulas

1. Volume (V): V = π × r² × h Where π ≈ 3.14159, r is the base radius, and h is the vertical height.

2. Base Area (A_b): A_b = π × r²

3. Lateral Surface Area (A_L): A_L = 2 × π × r × h

4. Total Surface Area (A_total): A_total = 2 × π × r² + 2 × π × r × h = 2 × π × r × (r + h)

Cylinder volume – calculation example

Let’s calculate the capacity of a hot water storage tank with an interior diameter of 24 inches (radius 12 inches) and height of 60 inches:

1. Enter the radius: radius = 12 inches.
2. Enter the height: height = 60 inches.
3. Find base area: base area = 452.39 sq inches.
4. The calculation results are available for you: volume = 27,143.4 cubic inches (117.5 US Gallons / 444.8 Liters).
5. Total surface area: surface area = 5,428.7 sq inches (37.7 sq ft).

💡 Cavalieri’s principle states that an oblique (tilted) cylinder of the same perpendicular height has the exact same internal volume as a vertical cylinder.