Vertical Cylinder Volume
A vertical cylinder stands upright with its circular base on the ground. This is the most common orientation for water tanks, silos, drums, and drinking glasses. Volume is simply V = πr²h, and partial fill is just as simple: V = πr² × fill height.
Vertical Cylinder Volume
Vertical Cylinder Formula
For a vertical cylinder with radius r and height h:
Total volume: V = πr²h Partial fill at depth d: V_partial = πr²d Percentage filled: (d / h) × 100%
This is the simplest case — the fill level is directly proportional to the volume. Double the liquid height, double the volume. This linear relationship is why vertical tanks are preferred when you need to gauge fill levels accurately.
Example: A rain barrel with diameter 60 cm and height 90 cm. V = π × 900 × 90 = 254,469 cm³ = 254.5 litres.
Advantages of Vertical Cylinders
Vertical cylinders take up less floor space for a given volume — height is free, but floor area costs money. A tall, narrow tank holds the same volume as a short, wide one but occupies a smaller footprint.
Gauging is simpler. A dipstick reading is directly proportional to fill volume. A mark at half the height means exactly half full.
Gravity-fed systems work naturally with vertical tanks. The water pressure at the outlet depends on the liquid height above it, so taller tanks provide more pressure.
Common Vertical Cylinder Sizes
Standard 55-gallon drum: diameter 57 cm, height 85 cm, holds 208 litres. Rain barrel: diameter 60 cm, height 90 cm, holds about 254 litres. Home water heater: diameter 46 cm, height 120 cm, holds about 200 litres. Grain silo: diameter 5 m, height 15 m, holds about 294,524 litres.
These are all vertical cylinders. The formula V = πr²h applies to each one — the only difference is scale.