Ullage · IMDG 4.2.1.9

Liquid expansion and ullage calculator

Leave the ullage cushion the IMDG rule demands, before the tank ships.

Fill a tank to the brim and the cargo expands as it warms in transit. Without the ullage cushion the tank goes hydraulically full, the relief valve lifts or the shell deforms, and the booking is rejected at the gate. The binding rule is IMDG Code 4.2.1.9, referenced to 50 degrees Celsius.

Type the tank capacity, the SDS Section 9 density and expansion coefficient, and the fill and transit temperatures.

Last updated 2026-05-09. Math runs in your browser, no data leaves your computer.

Pick the closest cargo to prefill density, alpha, and hazard class, then override any field from your SDS.

Density at the filling temperature, from SDS Section 9. This converts the safe fill volume into the cargo mass you book.

The expansion coefficient from the SDS. The more a cargo expands, the more ullage the rule reserves, so this drives the fill cap.

Toxic or corrosive cargo loads to the tighter 95% rule; everything else to 97%. Match this to the cargo's IMDG classification, not a guess.

The tank's rated volume from the data plate. T11 is usually 24,000 L.

The cargo temperature at the gantry when you load. A hot fill leaves less room to expand, so the cap drops.

The IMDG reference, 50 deg C by default. Leave it unless the carrier specifies a different figure for the trade lane.

General guidance only. Verify against the cited primary sources before you commit to a shipment, declaration, or contract.

Ullage and the IMDG fill rule in chemical-trade context

Liquids expand when warm. A 24,000 L ISO tank loaded brimful at 25 degrees Celsius cannot stay brimful at 50 degrees in a Red Sea crossing; the cargo expands by alpha times the temperature delta times the volume, and that excess has to go somewhere. If the tank has ullage (an air cushion at the top), the cushion compresses; the tank shell stays intact. If the tank has no ullage, the cargo presses on the roof, the relief valve lifts (or worse, the shell deforms), and the cargo is lost.

IMDG Code Chapter 4.2 codifies the rule. The Chapter 4.2.1.9 fill-degree formula (verify the current sub-section numbering at imo.org for the IMDG Amdt in force) says that for non-toxic non-corrosive liquid dangerous goods in portable tanks, the degree of filling at the filling temperature must not exceed 97 percent divided by (1 plus alpha times (tr minus tf)). The tighter 95 percent variant applies to toxic or corrosive liquids; the tighter cushion accounts for the consequences of release. The reference temperature tr is 50 degrees Celsius unless the carrier specifies otherwise; tf is the temperature at the time of filling.

For a methanol cargo (UN 1230, alpha 0.00120, toxic / corrosive class) loading at 25 degrees Celsius, the maximum fill volume in a 24,000 L T11 is 95 / (1 + 0.00120 times 25) = 95 / 1.030 = 92.23 percent of capacity, which is 22,135 L of methanol at 25 degrees. At 50 degrees this 22,135 L expands to 22,799 L, leaving 1,201 L (5 percent) ullage. Loading any more would burn the cushion.

For a citric acid 50% cargo (non-toxic non-corrosive, alpha 0.00043) at 25 degrees, the same tank can hold 97 / (1 + 0.00043 times 25) = 96.0 percent or 23,041 L. The cushion at 50 degrees is 736 L, just within IMDG. The denser, less expansive cargo earns a higher fill.

A worked example

You load methanol (UN 1230, alpha 0.00120, corrosive class) into a 24,000 L T11 at 25 deg C and the depot offers to top it to 96% to maximise the parcel. On paper that is 23,040 L of product.

It can't. Methanol is a high-expansion cargo on the tighter 95% rule, so the cap is 95 / (1 + 0.00120 x 25) = 92.23%, or 22,135 L. The depot's 96% fill leaves no ullage at 50 deg C, the relief valve lifts mid-voyage, and the tank is rejected at the gate. The cushion is the rule, not a courtesy.

Load to 22,135 L instead. At 50 deg C that expands to 22,799 L, leaving 1,201 L of ullage, exactly the cushion the rule reserves. The parcel is 900 L smaller on paper and ships without a relief-valve event.

Working off a lab density rather than the loading-temperature figure? The density at temperature calculator corrects it first at /tools/chemicals/density-at-temperature-calculator.

Want the full tank fill run across all four binding limits, not just ullage? The ISO tank loading calculator does it at /tools/iso-tank-loading.

Frequently asked

What is "ullage"?

The empty space at the top of a tank, between the liquid surface and the tank roof. Ullage is the cushion that absorbs liquid expansion as the cargo warms in transit. Zero ullage at the reference temperature is a hard fail; the tank pressurises, the relief valve lifts, and at worst the shell ruptures.

What is the IMDG 4.2.1.9 fill rule?

Portable tanks (T11, T14, T20, etc) must be loaded so that at the reference temperature (default 50 degrees Celsius), the cargo plus its expansion does not exceed the maximum degree of filling. The general formula under IMDG Code Chapter 4.2.1.9 (verify current sub-section numbering at https://www.imo.org/ for the IMDG Amdt in force at your shipment date): degree of filling equals 97 percent divided by (1 plus alpha times (tr minus tf)) for non-toxic non-corrosive cargo; 95 percent for toxic or corrosive cargo. Alpha is the cargo thermal expansion coefficient; tr is reference 50 deg C; tf is filling temperature.

When is the rule binding?

On every IMDG-regulated tank shipment of liquid dangerous goods, including methanol (UN 1230), sulphuric acid (UN 1830), caustic soda solution (UN 1824), hydrochloric acid (UN 1789), toluene (UN 1294), and most other commodity-chemical liquids. The depot computes the fill volume at loading temperature and stamps the loading docket; if the loaded volume exceeds the calculated maximum, the tank is rejected.

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