Posts Notes Resume

False Peaks

03 May 2023

Whether you’re a casual hiker or 8000 m peak mountaineer, you probably know of “false peaks” - the dreaded end of your ascent that, upon reaching it, turns out to only be an illusion of perspective hiding how much ascent you have to go until the real summit. I’ve been hiking a lot lately, and wanted to visualize the effect to see how big (or small) it is and what drives it.

For instance, say you’re 1.8 m tall and hiking up a 20 degree slope. You’re 100 m from what looks like the top, but it’s a false peak. The real peak is actually 600 m away along the same slope angle. How high do you think the real peak can be and not be visible behind the false peak 600 m away?

The false peak 100 m away on a pretty mild 20 deg slope hides a 4.8x climb! Here’s the same visualization1 with all the dials exposed for you to play around with:

Having it visualized like this brings some thoughts to mind. First, there’s not much to it! I know this particular visualization ignores a lot of the realities of mountains (e.g. no mountain I know of has a single perfect slope up to its peak), but still when drawn like this there’s no real mystery to the idea of false peaks.

But that doesn’t mean this isn’t useful. For instance, from this it’s clear that your height doesn’t have much effect on how bad a false peak can be until you’re steps from the peak. And, related, how bad a false peak can be has nothing to do with how far from the false peak you are. This is the kicker of false peaks (and why they can be so mentally brutal) - you don’t know until you’re at the top of the false peak! You can see both of these by adjusting the “Your Height (cm)” and “Distance To False Peak (m)” values. Adjusting the “Distance To False Peak (m)” between 500 m, 250 m, 100 m, 50 m, and 10 m shows that until you’re < 100 m from the false peak, the amount of hidden climb to the real peak is close to constant. And similarly, until you’re < 100 m from the false peak your height doesn’t have much effect.

What does matter is the slope of the false peak (because that determines your sight line angle), and how far away the real peak is from the false peak. In the case of mountains that get steeper as you ascend (common for the higher peaks), your “slope of the false peak” is just the line connecting where you are on the climb to the real peak. The slope of this will get steeper as you ascend, and so it is commonly the case that you may be able to see your real peak at the start but then, as you progress, will not be able to. This can fool you!

And since the hidden climb just scales linearly (given a constant false peak slope) with the distance from false peak to real peak, the situation is worst when you’re at the false peaks farthest away from your real peak. Brutal!


  1. You can see the code here, although I warn that this was an excuse for me to start learning HTML canvases. So, keep that in mind as you look through it (aka: it is likely I am missing a lot of best practices).