Builder's Old Measurement

Builder's Old Measurement is the method used in England from approximately 1650 to 1849 for calculating the cargo capacity of a ship. It is a volumetric measurement of cubic capacity. It estimated the tonnage of a ship based on length and maximum beam. It is expressed in "tons burden", and abbreviated "tons bm".
The formula is:
where:

Length is the length, in feet, from the stem to the sternpost;
Beam is the maximum beam, in feet.

The Builder's Old Measurement formula remained in effect until the advent of steam propulsion. Steamships required a different method of estimating tonnage, because the ratio of length to beam was larger and a significant volume of internal space was used for boilers and machinery. In 1849, the Moorsom System was created in the United Kingdom. The Moorsom system calculates the cargo-carrying capacity in cubic feet, another method of volumetric measurement. The capacity in cubic feet is then divided by of capacity per resulting in a tonnage expressed in

History and derivation

King Edward I levied the first tax on the hire of ships in England in 1303 based on tons burthen. Later, King Edward III levied a tax of 3 shillings on each of imported wine, roughly. At that time a was a wine container of 252 wine gallons, approx weighing about, a weight known today as a long ton or imperial ton. In order to estimate the capacity of a ship in terms of for tax purposes, an early formula used in England was:
where:

Length is the length, in feet
Beam is the beam, in feet.
Depth is the depth of the hold, in feet below the main deck.

The numerator yields the ship's volume expressed in cubic feet.
If a is deemed to be equivalent to 100 cubic feet, then the tonnage is simply the number of such 100 cubic feet units of volume.

100 the divisor is unitless, so tonnage would be expressed in 'ft³ of tun'.

In 1678 Thames shipbuilders used a method assuming that a ship's burden would be of its displacement. Since tonnage is calculated by multiplying length × beam × draft × block coefficient, all divided by 35 ft³ per ton of seawater, the resulting formula would be:
where:

Draft is estimated to be half of the beam.
Block coefficient is based on an assumed average of 0.62.
35 ft³ is the volume of one ton of sea water.

Or by solving :
In 1694 a new British law required that tonnage for tax purposes be calculated according to a similar formula:
This formula remained in effect until the Builder's Old Measurement rule was put into use in 1720, and then mandated by Act of Parliament in 1773.

Depth

; Depth to deck
; Depth in hold
; Main deck

American tons burthen

The British took the length measurement from the outside of the stem to the outside of the sternpost, whereas the Americans measured from inside the posts. The British measured breadth from outside the planks, whereas the Americans measured the breadth from inside the planks. Lastly, the British divided by 94, whereas the Americans divided by 95.
The upshot was that American calculations gave a lower number than the British ones. The British measure yields values about 6% greater than the American. For instance, when the British measured the captured, their calculations gave her a burthen of 1533 tons, whereas the American calculations gave the burthen as 1444 tons.
The US system was in use from 1789 until 1864, when a modified version of the Moorsom System was adopted.

France

A similar method was used in France to assess the cargo capacity of ships. This was standardised in 1681 at 1 tonne burthen per 42 French cubic feet. Prior to metrification this unit was called a .