# XKCD: Dimension Analysis

January 13, 2010 Leave a comment

Just a verification that the units work and also evaluating the value:

**Energy**: This is measured in Joules, which are:

**Pressure at the Earth’s core**: This is a pressure, and so measured in Pascals. Pascals are in fact Newtons per Metre squared, or:

**Gas Mileage: **This is the amount of distance it goes per amount of petrol in the car. Therefore it is metres per cubic metres, or:

**Distance:** Distance is just metres.

Therefore the units of the equation are:

Which is of course dimensionless. Now what about the actual values?

**Planck Energy: **Wikipedia puts it at 1.956×10^{9} J

**Earth Core Pressure**: Wikipedia puts it at between 330×10^{9} Pa and 360×10^{9} Pa

**Prius Mileage: **The American Fuel Economy website puts it at about 50 miles per gallon. Google can covert this to 21×10^{6} m^{-2}

**Minimum Width of The English Channel**: Answers.com says, via it’s Columbia Encyclopedia source, that 34×10^{3}^{ }m is the minimum width.

Putting all this into the equation gets a value of around 3.6. Which is certainly near enough!