Tank Volume Calculator (Vertical, Horizontal, Dished Ends)

How is tank volume calculated?

The shell of a cylindrical tank holds its cross section times its length: V = π / 4 × D² × L. With metres in, cubic metres come out, and multiplying by a thousand gives litres. A rectangular tank is simply the product of its three sides.

Where the ends are not flat, the head volumes are added. Each 2:1 ellipsoidal head holds π × D³ / 24 and each hemispherical head π × D³ / 12. A torispherical head depends on its crown and knuckle radii, and the calculator works its volume out from the geometry. A cone bottom holds π / 12 × D² × cone height.

Volume from level in a horizontal tank

In a horizontal cylinder the liquid section is a circular segment. Its area is A = R² × acos((R − h) / R) − (R − h) × √(2Rh − h²), and multiplying by the length gives the filled volume. That is why level and volume are not proportional in a horizontal tank: at a quarter of the height the tank is only 19.5 percent full. The calculator also handles partly filled dished ends and produces a level and volume table.

Example

A flat ended horizontal tank with a 2 metre bore and 5 metre length holds 15.71 cubic metres, or 15 708 litres. With liquid 0.5 metres deep the wetted section is 0.614 square metres and the filled volume 3.07 cubic metres. Fitting 2:1 ellipsoidal heads to the same tank raises the total to 17.80 cubic metres.

Limits

Use inside dimensions. Internals such as agitators and coils are not deducted. The tank is assumed level, and a sloped tank shifts the table. For custody transfer a calibration table must be produced by an authorised body.