Cylindrical tank volume calculator

A cylindrical rainwater tank, a diesel drum or a water tank has the shape of a cylinder. Working out how much fits into it is easy. What is more interesting is how much is in it right now: you only need a tape measure to find how high the liquid reaches.

Upright tank

For a tank standing on its base, it is simple. The whole volume is the volume of a cylinder, π · r² · H, where H is the height of the tank and the radius r is half the diameter. The liquid in the tank forms a smaller cylinder with the same base and a height equal to the level h, so there is π · r² · h of it. A level halfway up the height means the tank is half full.

Horizontal tank

When the cylinder lies on its side, the contents no longer grow evenly with the height of the level. At the bottom the tank is narrow and in the middle it is widest, so the first few centimetres of liquid add very little, and the ones around the middle add the most.

Be careful when estimating by eye. When the level in a horizontal tank reaches a quarter of the diameter, the tank is not a quarter full but only about a fifth full.

How it works for a horizontal tank

The cross-section of liquid in a horizontal tank is a circular segment. With radius r and level height h, its area is

$$A=r^2\cdot \arccos \frac{r-h}{r}-(r-h)\cdot \sqrt{2rh-h^2}$$

The volume of liquid is this area multiplied by the length of the tank, L. The angle from the arccosine comes out in radians.