Kong: Skull Island

The Movie

Kong: Skull Island is a 2017 monster film rebooting the King Kong franchise. A team of Vietnam war-era soldiers and scientists travel to an uncharted island and encounter Kong and a number of huge scary monsters. Kong is particularly huge in this movie, but his size has varied widely between the different movies.

You can view the trailer for the movie here:

Math Scenario 1: How Big is King Kong?

There are lots of movies starring King Kong, starting with the 1933 classic movie which started it all.

Kong’s size varies a lot – both between different movies, but also even within one movie! In the original movie Kong appeared to vary in size from around 5.5 metres to 18 metres tall in some scenes.

This series of 3 animations shows the size of Kong as he was depicted in various movies, with comparison to some other famous movie monsters and real life creatures, and the Empire State Building that Kong climbs in several of the films’ climaxes.

 

 

A large gorilla might measure about 1.8 metres tall when standing up, and weigh around 160 kg – so a similar height to an adult male human, but around double the weight.

One way we can estimate the weight of King Kong in his various movies is to use the cube scaling law.

This law says that if an object increases in size uniformly, then its volume will increase with the cube (third power) of the increase in one of the dimensions.

If we assume that Kong represents a uniformly scaled-up normal gorilla and has the same density, we can estimate how heavy the various versions of Kong are.

King Kong 2005

Kong is about 7.6 metres tall in this movie:

Dimension increase = kong height / normal height

Dimension increase = 7.6 / 1.8

Dimension increase = 4.222

We can use this scaling factor cubed to work out the estimated weight of Kong:

Kong weight = (height increase factor)^3 * gorilla weight

Kong weight = (4.222)^3 * 160

Kong weight = 12.04 tonnes

King Kong 1976 / 1933

Kong’s size varies a lot within these movies, but one of the common sizes is about 12 metres tall.

Dimension increase = kong height / normal height

Dimension increase = 12 / 1.8

Dimension increase = 6.667

We can use this scaling factor cubed to work out the estimated weight of Kong:

Kong weight = (height increase factor)^3 * gorilla weight

Kong weight = (6.667)^3 * 160

Kong weight = 47.41 tonnes

Kong: Skull Island (2017)

This is the biggest Kong has ever been on film so far, at around 32 metres tall:

Dimension increase = kong height / normal height

Dimension increase = 32 / 1.8

Dimension increase = 17.78

We can use this scaling factor cubed to work out the estimated weight of Kong:

Kong weight = (height increase factor)^3 * gorilla weight

Kong weight = (17.78)^3 * 160

Kong weight = 899.3 tonnes

Real-Life Example: Estimating Dinosaur Size

Dinosaurs have always captivated the public’s imagination, no doubt in part due to their immense size.

Estimating the dimensions – length, height – of dinosaurs has always been a challenge, in part because it’s rare to find complete skeletons. Many of the most interesting (for example largest) dinosaurs are only known from a small fraction of the bones making up their entire skeleton. There’s a great article on the topic here.

Estimating the length of dinosaurs is often done from key bones like the femur.

Initial estimates of weights of larger dinosaurs have sometimes been calculated by using laws like the cube scaling law used to estimate Kong’s weight here. There are several complicating factors that limit how effective this approach can be:

  • Densities of animals don’t necessarily stay constant as they get bigger. For example, elephant bones have lots of air cavities in them to keep weight down.
  • The cube law only holds if all dimensions of the animal scale up uniformly. If a sauropod dinosaur gets longer and taller but not much “fatter”, then its volume and weight likely won’t scale in a cubic way.