14-12-2021 | Frank Jansen

**A question in our mailbox. "A friend is mine of into off-piste skiing and always talks about gradients in degrees, say 30 degrees. However, percentages are more common for cyclists. Why this difference and how do you convert from one to the other?"**

Skiers do indeed use degrees to indicate how steep a slope is. The number of degrees is calculated from the horizontal axis, or X-axis.

A slope percentage can be calculated in two ways. The original way is to look at how much the road rises (a) over a certain horizontally measured distance (b). However, most profile websites (such as Cyclingcols and Climbfinder) use the climbed distance (c) instead of the horizontal distance, so that a (fictitious) climb that goes straight up is 100% steep instead of infinite. Incidentally, for roads up to 40% it makes very little difference which of these two formulas you use. For very extreme climbs, the difference becomes greater.

Different values are used for that distance (B or C). For example, most elevation profiles use one kilometre or 500 metres. But your bike computer uses a much smaller value, sometimes only 5 or 10 metres. That is why you can sometimes see extremely high values (sometimes as much as 30%) on your screen when you are climbing, while the average for that kilometre is many times lower. This often leads to nice conversations over drinks: how steep was the Mortirolo really? It all depends on the distance you measure. In addition, a bicycle computer with its barometric altimeter always lags behind reality. If you're entering the steep part of Col de la Redoute at 40km/hour, you will see the dreaded 20% on your screen much later.

In road construction, percentages are common because they are clearer than degrees. This is because a percentage rises faster than the number of degrees. Using the original way of calculating percentages, an angle of 45 degrees means a slope of 100%. By using percentages, small differences are much easier to make clear. If the slope is more than 45 degrees, there is not much point in measuring in percentages anymore, because the number quickly becomes larger and larger. The percentage of a 90-degree slope is even infinite.

Conversion is not even that simple, if you want to know the exact calculation you can read it here. The figure below (source: Wikipedia) clearly shows the relationships between the numbers.

The picture also makes it immediately clear how steep ski slopes actually are compared to climbs. The simplest slope is (in most Alpine countries) the blue one. This is usually a maximum of 20 degrees, which is more than 30%! Anyone who has ridden up the Col de la Loze and ride a bit along the blue piste knows how tough it is, so it is not surprising.

Red slopes can be up to 30 degrees, or 50%*! And then there are black runs that can be up to 35 degrees, or 55%*. By the way, off piste skiers go even steeper, up to 60 degrees. That is more than 80%*! Even for Pogacar that's simply too much.

*Thanks to Rogier van Rijn and Michiel van Lonkhuyzen.*

* we have used the modified formula that takes a vertical line as 100% (as described earlier).