Bike Forums > How do you calculate %gradient of a hill?
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 08-18-11, 12:07 PM #1 teachme Senior Member Thread Starter     Join Date: May 2011 Location: Nederland, Texas Bikes: 2011 Specialized Sectuer, 1988 Bianchi Posts: 1,441 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) How do you calculate %gradient of a hill? I've been reading on various threads about climbing hills of 2% gradient or 4% gradient,etc... What exactly does this mean? And can one calculate the %gradient of a hill one has just climbed?
 08-18-11, 12:09 PM #2 gregf83  Senior Member   Join Date: Jun 2008 Location: Vancouver, BC Bikes: Posts: 8,114 Mentioned: 3 Post(s) Tagged: 0 Thread(s) Quoted: 530 Post(s) rise/run. Measure the elevation change and divide by the distance traveled. For example, if you climb a hill that has a change in elevation of 500 ft and it is 5000 ft long the gradient would be 500/5000 = 10%.
 08-18-11, 12:15 PM #3 teachme Senior Member Thread Starter     Join Date: May 2011 Location: Nederland, Texas Bikes: 2011 Specialized Sectuer, 1988 Bianchi Posts: 1,441 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) Oh! The definition of slope. Thanks for clearing that up!
08-18-11, 01:00 PM   #4
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That will give you the average of a slope. But I don't know of many hills that are consistently at one angle. On a 10% slope you will find parts that are steeper and some that are less.

Many moons ago I climbed Ventoux. 13 miles at an average of 7.67%---EASY.

But that did not account for the Km at 12% that followed the 2 Km at 10%.- nor the final stretch at 10%. And to be honest- The downhill bit in the middle (Or so it felt) when it slackened off to 5%
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08-18-11, 02:09 PM   #5
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Quote:
 Originally Posted by gregf83 rise/run. Measure the elevation change and divide by the distance traveled. For example, if you climb a hill that has a change in elevation of 500 ft and it is 5000 ft long the gradient would be 500/5000 = 10%.
Actually it would be the elevation change divided by the square root of the distance traveled squared minus the elevation change squared.

08-18-11, 02:11 PM   #6
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 Originally Posted by BluesDawg Actually it would be the elevation change divided by the square root of the distance traveled squared minus the elevation change squared.
Huh?

08-18-11, 02:20 PM   #7
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 Originally Posted by teachme Huh?
Just when you thought it was beginning to make sense. Personally, I have given up on trying to understand.

 08-18-11, 02:22 PM #8 BluesDawg just keep riding     Join Date: Feb 2005 Location: Milledgeville, Georgia Bikes: 2018 All-City Cosmic Stallion, 2017 Niner Jet 9 Alloy, 2015 Specialized AWOL Comp frameset (custom build), 2015 Zukas custom road, 2003 KHS Milano Tandem, 1986 Nishiki Cadence rigid MTB, 1980ish Fuji S-12S Posts: 13,401 Mentioned: 6 Post(s) Tagged: 0 Thread(s) Quoted: 100 Post(s) Slope is rise over run. The run is the horizontal distance, not the distance along the slope, which is the hypotenuse of the triangle formed by the rise and the run. The hypotenuse squared is equal to the sum of the squares of the other two sides of a right triangle. Or something like that.
08-18-11, 02:52 PM   #9
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 Originally Posted by gregf83 rise/run. Measure the elevation change and divide by the distance traveled. For example, if you climb a hill that has a change in elevation of 500 ft and it is 5000 ft long the gradient would be 500/5000 = 10%.
Not quite, it's a little more complex then that, if the elevation change is 500' and the distance you travelled is 5000' you have two sides of a triangle, but you need the third side, to do the calculation, so our old friend from school Pythagoras, you have side A & C, but you need A & B if a²+b²=c² then c²-a²=b² so 5000²=25,000,000 and 500² is 250,000 then b should be square root of 24,750,000 or 4,974.937185533 / 500 would be a 9.9% slope, not a 10% slope. The steeper the climb of course, the bigger the difference. Few hills are the same slope all the way up, so the best you can get is the average.

08-18-11, 02:59 PM   #10
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 Originally Posted by Wogster Not quite, it's a little more complex then that,
Give me a break. My answer provides more accuracy than what's available from any bike altimeter. Besides if you use a GPS to measure the distance traveled it will give you the run assuming the earth is flat.

 08-18-11, 04:10 PM #11 NOS88 Senior Member     Join Date: Mar 2006 Location: Montgomery County, Pennsylvania Bikes: Posts: 6,490 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) I use my GPS unit...... I guess maybe I shouldn't.... __________________ A conclusion is the place where you got tired of thinking. - S. Wright Favorite rides in the stable: Indy Fab CJ Ti - Colnago MXL - S-Works Roubaix - Habanero Team Issue - Jamis Eclipse carbon/831
 08-18-11, 04:11 PM #12 jdon Senior Member   Join Date: May 2009 Bikes: Posts: 4,239 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) 1-2%- this ain't bad.. 3-4%- okay, this is getting old.. 5-7%- I didn't think this route had a climb.. 8-10%- woah, I have no legs today.. 11-14%- damn, what a grind, glad I went for the compact 15-18%- why? why? why?.. 19% > - what a stupid, stupid sport.. Eff me, I just wanna die... apres ride- Those climbs were awsome! What a great day! That's how I calculate them. Backed up by my Garmin of course.
 08-18-11, 04:50 PM #13 Robert Foster Banned.   Join Date: May 2008 Location: Southern california Bikes: Lapierre CF Sensium 400. Jamis Ventura Sport. Trek 800. Giant Cypress. Posts: 3,498 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) we do know that slope and grade are different?
08-18-11, 05:09 PM   #14
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 Originally Posted by Robert Foster we do know that slope and grade are different?
Inform, don't quiz.

08-18-11, 05:33 PM   #15
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Quote:
 Originally Posted by teachme I've been reading on various threads about climbing hills of 2% gradient or 4% gradient,etc... What exactly does this mean? And can one calculate the %gradient of a hill one has just climbed?
After? I figure mine before the ride so that I know what I'm dealing with. I don't use a Garmin so I use MapMyRidedotcom. I map the ride then press elevation, it will show the grades with %'s.

I've heard you have to use at least a 1/2 mile section or it is too far from accurate. Many argue about accuracy but this way I get an idea of what I'm dealing with.

This is an image taken from the site with my snipping tool. (similar to google maps)

elevation by mrbeanz1, on Flickr

08-18-11, 05:58 PM   #16
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Quote:
 Originally Posted by BluesDawg Inform, don't quiz.
Slope is measured in degrees for road building grade is measured in percent. A 45 degree slope is a 100 percent grade. The formula is based on:

The slope is the Tangent of the angle.

Slope is rise/run, and the % grade is 100 times the slope. So a slope of 1/1 would be a 100% grade, Let us say 100 feet with 100 feet of gain, which is indeed a 45 degree angle.

So if you know the degree of the angle, just enter it into your scientific calculator then hit Tangent. Or use your Iphone in calculator mode and turn it on its side and hit "TAN"

08-18-11, 07:53 PM   #17
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 Originally Posted by jdon 1-2%- this ain't bad.. 3-4%- okay, this is getting old.. 5-7%- I didn't think this route had a climb.. 8-10%- woah, I have no legs today.. 11-14%- damn, what a grind, glad I went for the compact 15-18%- why? why? why?.. 19% > - what a stupid, stupid sport.. Eff me, I just wanna die... apres ride- Those climbs were awsome! What a great day! That's how I calculate them. Backed up by my Garmin of course.
Oh, ok!

08-18-11, 08:03 PM   #18
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 Originally Posted by gregf83 Give me a break. My answer provides more accuracy than what's available from any bike altimeter. Besides if you use a GPS to measure the distance traveled it will give you the run assuming the earth is flat.
All I did was translate what Bluesdawg said, into something someone who hasn't taken algebra in more then 35 years, would understand better.... Don't be so sure about the GPS giving you earth-is-flat distance, for bicycle riding, car driving, jogging or walking, that would be almost completely useless for anything other then figuring the grade of a hill. I never actually worry about the grade, it's more like, have I seen a hill like this one before, and was I successful in climbing it the last time, if so, then I can do it again, if not, I either need to try it or go a different route that isn't as steep. That's easiest on a topo map.

 08-18-11, 08:35 PM #19 BlazingPedals Senior Member     Join Date: Dec 2004 Location: Middle of da Mitten Bikes: Trek 7500, RANS V-Rex, Optima Baron, Velokraft NoCom, M-5 Carbon Highracer, homebuilt recumbent Posts: 9,841 Mentioned: 5 Post(s) Tagged: 0 Thread(s) Quoted: 456 Post(s) if you're measuring a 20% grade and you incorrectly use the distance traveled instead of the horizontal distance, you'll be off by 0.4%. For lesser grades, the inaccuracy is less. My conclusion: it's not exact, but it's close enough fer gov'mint work.
 08-18-11, 08:55 PM #20 JohnDThompson  Old fart     Join Date: Nov 2004 Location: Appleton WI Bikes: Several, mostly not name brands. Posts: 18,102 Mentioned: 41 Post(s) Tagged: 0 Thread(s) Quoted: 712 Post(s) I just look for the sign:
 08-18-11, 09:16 PM #21 TheHen Senior Member   Join Date: Jul 2010 Bikes: Posts: 790 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) For BikeForum.net purposes, use one or more of the formulas or websites given above and add 2-5%, depending on how likely it seems that anyone else knows where the hill in question is.
08-18-11, 09:31 PM   #22
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 Originally Posted by JohnDThompson I just look for the sign:
John, there was a post a couple of years ago of "Pictures of Your Bike with a Percent Grade Sign". It took about two years before I finally got to one of those signs. There are a few hills around here that have the "Steep Hill" sign (otherwise known as the "truck on cheese" sign), but you just won't see that percent grade on a sign around here. And the original poster is in Beaumont, which is flat as a pancake.

Teachme, a couple of other comments. Some of these electronic gizmos show the slope directly, so it's not like people run around measuring rise over run all the time. If you're interested in slope of a bridge, try photographing it from the side, then measuring on the photograph. You can also take a 2' level along, and measure from one end down and divide it out. And if there's 4 different ways to measure the slope of a hill, you're allowed to use whichever one sounds steeper. So on Church Hill, with my 2' level, I couldn't find a place on it anywhere that was over 5%, but the local cyclists are still convinced it's 7-8%.
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08-18-11, 09:37 PM   #23
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 Originally Posted by StephenH John, there was a post a couple of years ago of "Pictures of Your Bike with a Percent Grade Sign". It took about two years before I finally got to one of those signs.
Ok. Full disclosure: that sign was in Grand Tetons National Park on the road to Deadman's Bar on the Snake River.

08-18-11, 09:51 PM   #24
BluesDawg
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 Originally Posted by BlazingPedals if you're measuring a 20% grade and you incorrectly use the distance traveled instead of the horizontal distance, you'll be off by 0.4%. For lesser grades, the inaccuracy is less. My conclusion: it's not exact, but it's close enough fer gov'mint work.
Definitely. I never said it mattered.

Besides, given the wildly varying elevation figures I find for the same routes on different sites and different GPS devices, you could probably round off any calculations to the nearest 5%.

08-18-11, 09:58 PM   #25
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 Originally Posted by Mr. Beanz After? I figure mine before the ride so that I know what I'm dealing with. I don't use a Garmin so I use MapMyRidedotcom. I map the ride then press elevation, it will show the grades with %'s.
I've found mapmyride to be pretty inaccurate with grades. If you go too granular it over estimates grade and if you go too broad it underestimates them, IME.

For example, here's an instance of going too granular. A quarter mile chunk of road I ride all the time. MMR says it hits 20% up near the top. It gets nowhere near that.

http://www.mapmyride.com/routes/fullscreen/40664720/

On the other hand when I have this bit of road as part of a 12 mile ride it takes too big of a stretch of road for the average and the hill comes in under 2%.

Actual grade probably peaks out around 7%. Average for the quarter mile I'd guess around 5%.

Last edited by LesterOfPuppets; 08-18-11 at 10:45 PM.

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