The height (H) of Gulliver was less than 6 feet, as described in Gulliver’s Travels:

“…a strange creature [Gulliver] to be seen…, not so big as a splacnuck (an animal in that country very finely shaped, about six feet long,) and in every part of the body resembling a human creature…” (Chapter II)

Galofré-Vilà et al. surveyed heights across the last 2000 years in England using femurs of skeletal remains [2]. According to this report, in the eighteenth century when Gulliver undertook the adventure, the height of males was 1.71 m on average.

Swift adopted the base of 12 in imagining these fictitious peoples, as seen below:

“[His Majesty’s mathematicians] Having taken the height of my body by the help of quadrant and finding it to exceed theirs in the proportion of twelve to one…” (Chapter III)

For Lilliputians, their size was 1/12 that of Gulliver, as stated in the text cited above. For the Brobdingnagians, their size can be deduced to be 12 times that of Gulliver, based on the following indirect statement:

“…a hailstone is near eighteen hundred times as large as one in Europe.” (Chapter V)

Supposing Gulliver is 1.71 m in height, the average for English males in the eighteenth century, the H of the Lilliputians and the Brobdingnagians can be estimated as 0.143 and 20.52 m, respectively (Table 1).

Table 1 Physiological parameters of Lilliputians, Gulliver and Brobdingnagians Full size table

Swift calculated weight (W) on the assumption that it is proportional to the cube of H. To the best of our knowledge, however, this is unlikely. As shown in Eq. 1, W is proportional to the square of H, not the cube of H. This principle was established in 1869 by Quetelet, a Belgian statistician, after a physical survey of tens of thousands of soldiers [3]. Based on this, the body mass index (BMI), which is defined by W/H2, was proposed and is now widely used as an index of obesity. It is also known, however, that Quetelet’s law is not applicable to outliers of H, including children, unless modifying the exponent of H.

In the present study, Quetelet’s law is applied to estimate W of tiny and gigantic creatures with extremely short and tall H, respectively, on the assumption that their body structures are geometrically similar to Gulliver as stated in the original text shown below, although nobody had looked at their real stature.

“…a strange creature [Gulliver] … in every part of the body resembling a human creature [Lilliputians]…” (Chapter II)

“…His Majesty’s mathematicians concluded from the similarity of their bodies, that mine must contain at least 1724 of theirs…” (Chapter III)

Assuming that each group has a BMI of 23, W for the Lilliputians, Gulliver and the Brobdingnagians will be 0.47, 67.3 and 9685 kg, respectively (Table 1). The sizes of the Lilliputians and the Brobdingnagians are close to those of rats and large dinosaurs, respectively.