# Gross tonnage

Gross tonnage is calculated by measuring a ship's volume (from keel to funnel, to the outside of the hull framing) and applying a mathematical formula.

Gross tonnage (often abbreviated as GT, G.T. or gt) is a unitless index related to a ship's overall internal volume. Gross tonnage is different from gross register tonnage.[1] Neither gross tonnage nor gross register tonnage is a measure of the ship's displacement (mass) and should not be confused with terms such as deadweight tonnage or displacement.

Gross tonnage, along with net tonnage, was defined by The International Convention on Tonnage Measurement of Ships, 1969, adopted by the International Maritime Organization in 1969, and came into force on July 18, 1982. These two measurements replaced gross register tonnage (GRT) and net register tonnage (NRT). Gross tonnage is calculated based on "the moulded volume of all enclosed spaces of the ship" and is used to determine things such as a ship's manning regulations, safety rules, registration fees, and port dues, whereas the older gross register tonnage is a measure of the volume of certain enclosed spaces.

## History

The International Convention on Tonnage Measurement of Ships, 1969 was adopted by IMO in 1969.[2] The Convention mandated a transition from the former measurements of gross register tonnage (grt) and net register tonnage (nrt) to gross tonnage (GT) and net tonnage (NT).[2] It was the first successful attempt to introduce a universal tonnage measurement system.[2]

Various methods were previously used to calculate merchant ship tonnage, but they differed significantly and one single international system was needed.[2] Previous methods traced back to George Moorsom of Great Britain's Board of Trade who devised one such method in 1854.[2]

The tonnage determination rules apply to all ships built on or after July 18, 1982.[2] Ships built before that date were given 12 years to migrate from their existing gross register tonnage (GRT) to use of GT and NT.[2] The phase-in period was provided to allow ships time to adjust economically, since tonnage is the basis for satisfying manning regulations and safety rules.[2] Tonnage is also the basis for calculating registration fees and port dues.[2] One of the Convention's goals was to ensure that the new calculated tonnages "did not differ too greatly" from the traditional gross and net register tonnages.[2]

Both GT and NT are obtained by measuring ship's volume and then applying a mathematical formula.[2] Gross tonnage is based on "the moulded volume of all enclosed spaces of the ship" whereas net tonnage is based on "the moulded volume of all cargo spaces of the ship".[2] In addition, a ship's net tonnage is constrained to be no less than 30% of her gross tonnage.[2]

## Calculation

The gross tonnage calculation is defined in Regulation 3 of Annex 1 of The International Convention on Tonnage Measurement of Ships, 1969. It is based on two variables, and ultimately a one-to-one function of ship volume:

• V, the ship's total volume in cubic meters (m3), and
• K, a multiplier based on the ship volume.

The value of the multiplier K varies in accordance with a ship's total volume (in cubic metres) and is applied as a kind of reduction factor in determining the gross tonnage value - which does not have a unit such as cubic metres or tons. For smaller ships, K is smaller, for larger ships, K is larger. K ranges from 0.22 to 0.32 and is calculated with a formula which uses the common or base-10 logarithm:

$K = 0.2 + 0.02 \times \log_{10}(V)\,$

Once V and K are known, gross tonnage is calculated using the formula, whereby GT is a function of V:

$GT = K \times V\,$

which by substitution is $GT = V\times(0.02\times\log_{10}(V)+0.2)$.

As an example, we can calculate the gross tonnage of a ship with 10,000 m3 total volume.

$K = 0.2 + 0.02 \times \log_{10}(V)\,$
$= 0.2 + 0.02 \times \log_{10}(10,000)\,$
$= 0.2 + 0.02 \times 4\,$
$= 0.2 + 0.08\,$
$= 0.28\,$

Then the gross tonnage is calculated:

$GT = K \times V\,$
$= 0.28 \times 10,000\,$
$= 2,800\,$

The inverse, on the other hand, is not as simple. Newton's method may be used for obtaining an approximation to a ship's volume given its gross tonnage. The exact formula is:

$V = \frac{50 \times \ln 10 \times GT}{W(500,000,000,000 \times \ln 10 \times GT)}$

where ln is the natural logarithm and W is the Lambert W function.