Climbs – cyclist’s biggest challenge. Every cyclist like to boast about how steep a climb he conquered. The steeper the climb, the more pride. But do you know how to calculate the climb gradient?
The climb gradient is calculated as the elevation gain per 100-meter traveled distance. The term rise over run is often used. For example, if you gain 8 meters of elevation in 100 meters, the climb gradient is 8%.
Modern bike computers and even smart watches are already able to track gradients but are often inaccurate. It’s, therefore, good to know how to calculate gradient using a simple formula, in which many make a key mistake. Keep reading so you won’t be one of them.
How do I calculate the climb gradient?
At the start of every climb, there is a road sign showing the climb gradient. Unfortunately, they don’t tell the inexperienced cyclist much. We are used to gradients being measured in degrees. So why express them in percentages?
Expressing the gradient in percentages simplifies the calculation. It’s much easier for the average person to calculate the gradient in percentages than degrees. And once you know what a certain percentage brings, road signs become quite useful.
A gradient is calculated as the elevation gain per 100-meter (or 100 feet) traveled distance. You just remove the meters (or feet) from elevation gain and add a percentage sign. Viola, you just calculated a climb gradient.
Don’t make a crucial mistake
Life would be quite ideal if everything were as simple as it looks at first sight. But unfortunately, it isn’t.
If we want to measure the climb gradient, the distance we have traveled does not help us very much. To calculate the gradient, we need the aerial distance of the climb. The road from the start to the top of a climb is usually winding and consequently longer. Therefore, we cannot use it in our calculation.
Matt de Neef has explained this perfectly in his blog. Below is a summary of his explanation.
If we look at the climb as a right-angled triangle, then we need the data of both triangle legs (a and b) to calculate the gradient. As cyclists, we are riding on a hypotenuse (c).
Fortunately, the school system has taught us the Pythagorean theorem (a²+b²=c²), which allows us to calculate the run (a) from the data of the other two sides.
So, in our case, we subtract the square of the rise (b) from the square of the hypotenuse (c), which is our “real” length of the climb.
The mathematical notation would look like this:
Once we have a², we just need to square the number to get the run (a) we need.
If we take the example of a 10 km climb where we ascend 500 meters, our calculation would look like this:
a²=100,000,000 – 250,000
The elevation gain is then divided by the calculated distance and multiplied by 100. This gives the percentage gradient.
(500/9,987) * 100 = 5,0 %
You can see that the calculated distance (9,987 meters) is quite close to the ridden length of the climb (10,000 meters). The difference in the gradient calculated by the simple formula and the correct formula presented above is extremely small (5% vs. 5.006%).
In cycling, therefore, the convention is to use the rise-over-run formula, and you’ll get a reasonably reliable indication of the gradient of the climb.
Downsides of the gradient calculation
Unfortunately, this type of calculation has some drawbacks.
Firstly, the calculated gradient is, in fact, the average gradient. This means that it does not consider all the characteristics of the climb.
As cyclists, we know that a climb where the gradient constantly fluctuates from steep to gentle is much more difficult to ride than a climb with an even gradient. So a climb may have some extremely steep sections, but the average gradient will be much lower due to the flatter parts. The average gradient alone, therefore, does not give us the full picture of the climb.
The second problem is the data itself. The elevation gain data is often incorrect or has quite large variations (up to several tens of meters). As a consequence, the calculation of the gradient may be incorrect.
How steep does a certain gradient feel?
The gradient percentage is an objective figure, but each cyclist perceives it in their own way. A well-prepared athlete won’t even break a sweat on the flatter climbs, while a beginner will already find it hard to breathe.
Despite the differences in gradient perception, cyclists agree on what is and is not a steep gradient. When a road reaches a 10% gradient, no one claims that it is not steep. Everyone suffers there.
Below is an example of what a given gradient feels like to a cyclist, with an example of a climb with such an average gradient.
Commonly known as “false flat.” A gradient that is not demanding and feels almost like a flat road, but at the same time still drains some energy over a longer distance. This kind of gradient usually leads to steeper parts of the climb.
Example: Col de la Savine (France)
A gradient that does not pose a major challenge to any serious cyclist but still takes its toll after a few kilometers. This kind of gradient already gives you the feeling of climbing.
Example: Col de la Croix-de-Fer (France)
A difficult gradient that starts to tire your legs quickly. Experienced riders will successfully overcome it but will be tired at the top, while some less experienced riders may find it too challenging.
Example: Col de Telegraphe (France)
An extremely difficult gradient that can only be overcome by well-prepared cyclists. Legs get tired quickly and gears run out even faster. Only suitable for extremely fit riders.
Example: Alto de l’Angliru (Spain)
Difficult, very difficult. World-class cyclists can handle this gradient for a few meters, but longer distances seem unbeatable. A steep gradient also makes the descent very difficult.
Example: Bihan Pass (Saudi Arabia)
Hell on Earth. Much too difficult for amateur riders. Even some pros would have problems. A gradient that forces you to get off the bike.
Example: Pozza San Glisente (Italy)
How are climbs categorized?
In professional races, you can see the categorization of each climb by looking at the course profile. It falls into one of five categories (from easiest to hardest) – Category 4, Category 3, Category 2, Category 1, and HC.
What does this mean?
Each climb is assigned a category according to its difficulty. Most of the hardest climbs know which category they fall into, while the new climbs need to be categorized using a simple formula.
Thierry Gouvenou, who is in charge of planning the Tour de France route, revealed to Rouleur that they assign a point value to the climb. This is obtained by multiplying the length of the climb (in km) by the square of the average gradient.
Climb length x (average gradient)² = climb difficulty
Depending on the value obtained, the climb is assigned to one of five categories:
Up to 75 points – Category 4
75-150 points – Category 3
151-300 points – Category 2
301-600 points – Category 1
601+ points – Hors Catégorie
For amateur cyclists like myself, the categorization of the climbs on Strava is more interesting.
I regret to tell you that the categorization is not the same as in the Tour de France. If, for example, you climb the Col du Telegraphe, which belongs to the HC category on Strava, you have conquered a climb classified as “only” Category 1 on the Tour de France.
Strava also considers the climb’s length and average gradient in its calculation. Their formula multiplies the length of the climb (in meters) by the average gradient.
Climb length x average gradient = climb difficulty
The minimum gradient of the climb to be categorized is 3%.
Depending on the score, the climbs are classified into the following categories:
8,000+ points – Category 4
16,000+ points – Category 3
32,000+ points – Category 2
64,000+ points – Category 1
80,000+ points – Hors Catégorie
The steepest climbs in the world
For a long time, I thought that professional cyclists in races like the Tour de France, the Giro d’Italia and La Vuelta a España were tackling the steepest climbs in the world. Even when I talked to other cyclists and they shared the same opinion.
Then I started looking into it and found out I was wrong. Professional cyclists indeed tackle steep and challenging climbs, but they are far from being among the toughest climbs in the world.
Some time ago, I made a list of the 20 hardest climbs in the world. Not one of them has ever been included in a professional race. The reason is quite simple. They are too hard to allow normal racing.
Take a look at the list of the world’s hardest climbs, and perhaps you’ll find a new challenge for yourself.