Partially Filled Horizontal Tank Volume Calculator

Horizontal Tank Volume Formula Explained

The liquid volume in a partially filled horizontal cylinder is the circular segment area times the shell length:

V = [r^2 x acos((r - h)/r) - (r - h) x sqrt(2 x r x h - h^2)] x L

Where r = tank radius (m), h = liquid fill height (m), L = straight shell length (m). The result is in m3; multiply by 1000 for liters.

Example: a 3 m diameter (r = 1.5 m) x 6 m tank filled to h = 1 m: segment area = 1.5^2 x acos(0.5/1.5) - 0.5 x sqrt(2 x 1.5 x 1 - 1) = 1.228 m2, volume = 1.228 x 6 = 7.37 m3 = 7,370 L.

Fill Height vs Volume Reference

For a horizontal cylinder, volume is NOT linear with fill height:

| Fill Height (h/r) | % of Total Volume |

|---|---|

| 10% | 5.2% |

| 25% | 19.5% |

| 50% (h = r) | 50.0% |

| 75% | 80.5% |

| 90% | 94.8% |

At 30% height you have only ~25% volume; at 70% height you already have ~75%. This nonlinearity is why dipstick charts are needed for accurate inventory — a linear gauge would be wrong by up to 10% of tank volume.

Worked Example: Dipstick Calibration

A 3 m diameter x 6 m horizontal tank (total capacity 42,412 L) needs a dipstick chart. At h = 1 m:

V = 7.37 m3 = 7,370 L (17.4% of capacity)

At h = 1.5 m (half full): V = 21,206 L (exactly 50%). At h = 2.5 m: V = 35,042 L (82.6%). Generate a table at 0.1 m increments for the operator's dipstick. For tanks with dished heads, add the head volume and calibrate against a strapping table.