How are the categories for climbs decided?

The tour organizers rank them subjectively based on their steepness, length, and also where they occur in the stage (climbs near the finish garner a higher ranking). Another criterion which seldom makes a big difference is road condition. Some people feel that the ratings have been inconsistent over the years, or have been inflated in recent years. In short, there is no scientific way of rating the climbs, it's just a judgement call from the race organizers.

Note, others have indeed tried to quantitatively rank the climbs. You could apply their methodology to climbs near where you live to figure out how a local climb might be ranked at the end of a tour stage.

Another important criteria is where the climb is placed. If you put an otherwise cat 1 climb at the end of a mountain stage with an uphill finish, it becomes an HC climb.

As noted above, part of the ranking of a climb depends on its placement within a stage: usually, the ending climb of a stage gets "bumped up" by a category. You can see that in the plots below, which show climbs as categorized by the organizers of the Tour de France itself for the 2012, 2007, 2005, and 2004 editions of the Tour, and plotted by the length of the climb and its average gradient. If given the length of the climb and gradient, you can calculate the total elevation change for that climb, and the dotted contour lines in each plot show that. Cat 2, 1, and HC climbs are named. For example, in 2004 the Vilard de Lans climb was classified at a Cat 2 climb rather than (evidently) a Cat 3 because it was the end of the stage. Similarly, in 2005 the climb to Pla d'Adet ended the stage, and it appears that its category was also increased from (arguably) Cat 1 to HC.

As an aside, the Madeleine was climbed in both 2004 and 2005 but, as you can see, the length and gradient of the climbs were different in those years. In 2004, the Madeleine was climbed from the southern side; in 2005 and 2012, the approach to the Madeleine was from the north.

For Strava climbs there is an objective categorization that is length in meters times grade in percent, with this categories:

score = length(m) * grade(%)

• Cat 3: score > 16000
• Cat 2: score > 32000
• Cat 1: score > 64000
• Cat HC: score > 80000

For example Alpe d'Huez has a length of 13800m and average gradient of 8.1% (according to Wikipedia), giving a score of 111780, which would place it as a HC climb since its score is way above 80000.

I prefer the cycling lore that it was decided by which gear of a Citroen 2CV you needed to be in to drive up the hill/mountain. For HC climbs you had to go up them in reverse.

Scientific? Not so much. Perceived Gallic? Mais oui!

I was told by Doug Dailey (a club cycling colleague and long ago British champion, British Cycling legend), that the categories were historical, and based on early Citroen capabilities (1920’s ?). If said car could only go up a hill in 1st gear, it was defined as category 1. If it could do it in second, category 2, etc. Sounds plausible and very French. J

@pablete mentioned the Strava Climbs with the formular:

score = distance(m) * grade(%)

This score can be easily boiled down to just the rise in meters because

grade = rise / distance * 100

which means the Strava score is basically this:

score = distance * rise / distance * 100

After simplifying this becomes:

score = rise * 100

Oh! So this is just a very subjective and inaccurate categorization of total rise without any reference point. In my opinion the Strava categorization is completely useless.