Trail climbs and descents: what is gradient?

Everyone knows the road signs showing the percentage gradient of a dangerous descent or a mountain pass climb. Cyclists are particularly tuned in to this data, especially on climbs, because the gradient is a reliable indicator of difficulty. In trail running, it is a crucial factor: it slows your progress and determines when you switch from running to walking, as well as when you use poles. More and more GPS watches display this information, helping you manage your effort more effectively. Despite the importance of gradient, many people do not know how it is calculated and, above all, confuse a percentage gradient with an angle in degrees.

How do you calculate the percentage gradient between two points?

You need two pieces of data:

• The horizontal distance between points A and B;

• The difference in elevation between points A and B.

On road signs, gradients are expressed as percentages. The formula is:

Percentage gradient = (difference in elevation between A and B / total distance between A and B) x 100

For example, the Grand Serre vertical kilometre in Isère is considered one of the steepest VKs in the world, with 1,000 m of elevation gain over 1.8 km. The gradient is calculated as follows:

(1000 / 1800) x 100 = 55.5

The average gradient of the Grand Serre VK is therefore 55.5%, which means that for every 100 metres travelled horizontally, you gain 55.5 metres of elevation. Or, put another way, you climb 55.5 centimetres for every metre travelled. In other words, it is seriously steep!

What is the difference between a percentage gradient and degrees?

Although percentages are the most common way to describe a gradient, you will sometimes see degrees used instead. The two are very different. If maths was never your strong suit, hold on tight: we are about to revisit a few trigonometry concepts from your school days!

Gradient in degrees = tangent of the elevation angle expressed in degrees x 100

A quick diagram will help make the calculation easier to understand.

Point B is the bottom of the slope you need to climb, for example the start of the Grand Serre VK. Point A is the top of the climb, in other words the finish of the VK at the mountain summit.

The value L represents the distance you need to cover between the start and finish of the race, namely 1.8 km. The value h is the positive elevation gain you need to climb between points B and A, namely 1,000 m.

The value ⍺ represents the angle formed by the slope relative to a horizontal plane. To calculate it, you first need to determine the value l, the horizontal distance between B and A.

If you know the gradient percentage, you can determine its angle in radians using the arctangent function. Yes, it gets a little complicated:

Gradient expressed in degrees = arctan (elevation gain / horizontal distance)

Lost already? Don’t worry, you do not need an advanced maths degree to understand the essentials.

• A gradient can be expressed as a percentage or in degrees.

• A 55% gradient is not the same as a 55-degree gradient. Remember your geometry lessons: a 90-degree angle is a right angle, so a 90-degree gradient is a vertical line. To climb it, you will need to swap your trail shoes for a harness and rope!

• Online converters can convert a gradient from a percentage to degrees.

• Degrees are not commonly used to express a gradient, but if you come across them or discuss a climb, do not confuse percentages with degrees! The simplest approach? Talk about climbs and descents only in percentages. You will avoid mistakes and everyone will understand you!