Degrees? Percentages?
 

I'm confused about the connection between degrees of slope and percentages of slope. I want to be real clear up front: I've looked at the detailed sciento-mathematical descriptions on the internet, and they don't give me what I want. I don't want another definition of how each is figured. That won't help.

What I want is to be able to translate--approximately, and in very broad strokes--percentages to degrees, or degrees to percentages as I'm riding and looking at maps and tour guides. As an example of what I'm looking for: I know that a 5 degree slope is going to be hard for me; but what's its equivalent in %s? Yes, the answer to that question will help me, but what I really need ... I need to have a rule of thumb to work with. Anybody willing to give me information that will get me 80% of the way to an accurate translation of degrees to percentages and vice-versa?

I don't know that you'll find an easy way you can do this in your head. It's definitely too complicated for me.:foo:https://sciencing.com/convert-percen...s-8093249.html I wonder if it's often necessary to do this. It might be easier to just get used to dealing with both measurements. Sort of like when we talk about bike sizes in inches or cm. Most folks know their size either way w/o actually doing a conversion. Hope this makes sense. Edit- If you use something like RWGPS you'll have consistent measurements.

basically rise over run for grade or percent. The other is simply a degree as in angular measurement from the horizontal.

A 100% grade will be a 45° slope.

Roofers gotchu covered (at least for a certain range)!
https://cimg1.ibsrv.net/gimg/bikefor...1710f8dede.jpg

Here's another one that includes lower pitches.
https://cimg3.ibsrv.net/gimg/bikefor...b684218456.jpg

It's complicated
https://cimg0.ibsrv.net/gimg/bikefor...2b6297bdb8.jpg

Best follow what's known as Eddy's Rule,
modified for reality in consumer societies.
Ride up grades before buying upgrades.

OK, thanks. That helps. But a couple of questions--
 

1. Are those Canadian degrees? Aren't they 10% bigger than American degrees? (Sorry sorry sorry.)
2. So if 45% is (according to this diagram) 12/12m, which is 100%, then I can I extrapolate arithmatically to 6/12 would be 50% and 22.5 degrees? Which is important at the lesser angles, the ones we typically encounter riding, i.e. 2/24 = 15% more or less or 9.2 degrees? Or is there some trigonometric factor that varies it from the strictly arithmatic?

If I remember high school trigonometry, the tangent of the angle of the grade is the percentage grade. For example, the tangent of 45 degrees is 1 (or 100%).

Decide on the range of slopes you actually expect to encounter, then make yourself a couple of tables covering that range:

• one table showing percent grade to degrees
• one table showing degrees to percent grade

After a while, you may develop a better intuitive feel for the unit with which you were originally unfamiliar.

No, you cannot directly extrapolate. As the charts show 6/12 is 26.5° which is larger than the 22.5° you've calculated.
As shelbyfv noted there is no easy way you can do this in your head. Best to use one of the calculators provided. OR, don't worry about it and just climb.

You could use an online calculator and plug in values for typical gradients that we encounter as cyclists.
https://www.calcunation.com/calculat...to-percent.php

1 degree = 1.8%
2 degrees = 3.5%
3 degrees = 5.2%
4 degrees = 7.0%
5 degrees = 8.8%
6 degrees = 10.5%
7 degrees = 12.3%
8 degrees = 14.1%
9 degrees = 15.8%
10 degrees = 17.6%

I'm curious as to what kind of maps/routes you're looking at that are using degrees instead of slope %?

Is the analysis for the purpose of general knowledge about the grades/percentages you ride? - or to measure and document the grades on given routes?

If the latter, PLEASE, come ride with me for a month - with an end goal of creating a detailed set of cycling maps Distances and elevations are readily available, but to include all the gradients and flats in those climbs is more important to many than the elevation change. Or is that already on cycling maps/apps?

There used to be a great cycling map of the Santa Cruz Mts.
What a great app! Better than GPS.

I'd love to. I love the PNW.

Why I was asking
 

MSU: Thanks, this is perfect. Just exactly what I needed.

I see that people curious about what I'm doing with the data and where I see it. I'm working on strengthening my riding (and I'm a map nut, too), so I'm conscious of the grades I'm riding, always trying to bump up my threshhold.

In the process, I have discovered that cyclists and SOME maps talk about %s. But vehicles and signage and OTHER maps tend to use degrees. When I have used my pickup truck to scout routes, the truck records slopes in degrees. Because of the track, I now can more or less recognize a 3 degree slope from a 5 degree slope. But when I look at a cyclist's notes, they use percentages. But these are very, very different: a 5 degree slope is killer (for me) and a 5 percent slope is just hard. Eventually, I'll develop a gut instinct, but I'm a data-to-gut person, not a gut-to-data.

You have all given me just exactly what I need. Thank you.

Please show an example of a road sign indicating slope in degrees.

For while you ride math in your head:

25% = 14 degrees. (Very near exact!)
10% < 6 degrees (5.71)

0.56 % per degree Edit: I got these mis-labeled!
1.78 degrees per %

The plot between percent and degrees is nearly a straight line between 0 and 30 degrees.

Edit: this is trig. Past 30 degrees and the conversion becomes less and less linear. (Down to 0.45 degrees per % at 45 degrees and 0.35 degrees per % at 60 degrees. Good thing is that we don't spend a lot of time riding at those angles.

Might've put that backwards. Anyway, though, my truck measures slope in degrees, which is what started this whole thing.
https://cimg4.ibsrv.net/gimg/bikefor...f0dc13bfc4.png
https://cimg9.ibsrv.net/gimg/bikefor...46bc7628fd.png

kick it in the 52/11 with a 10 mph or higher headwind to simulate the climb.

Rise/ Run = % Slope

When I saw this question, this is exactly what I thought about, roofing. I used to do roofing in the summer as a teenager, suck job, but it taught me this stuff.

What Iride said. Everybody way overestimates the number of degrees in a hill slope. 10% is a pretty serious hill when you are riding up it but it's only 4.5 degrees.

I used to have a carpenter buddy who'd say he didn't understand math, but flawlessly calculated construction dimensions. He's shrug and say it was just numbers.