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 Road Cycling “It is by riding a bicycle that you learn the contours of a country best, since you have to sweat up the hills and coast down them. Thus you remember them as they actually are, while in a motor car only a high hill impresses you, and you have no such accurate remembrance of country you have driven through as you gain by riding a bicycle.” -- Ernest Hemingway

 06-26-06, 09:11 AM #1 markwebb The Recycled Cycler Thread Starter     Join Date: Feb 2005 Bikes: Real Steel. Really. Ti is cool, too ! Posts: 2,399 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) How to Calculate % Grade? How do you calculate % grade. As an example, 100 foot rise over 1,320 feet (0.25 miles) = x% grade. How do you calculate it?
 06-26-06, 09:15 AM #2 Alphamoose Senior Member     Join Date: Apr 2003 Location: Cupertino, CA Bikes: Posts: 81 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 1 Post(s) That's 7.5% (100/1320)*100.
 06-26-06, 09:19 AM #3 kyledr Destroyer of Worlds     Join Date: Jun 2006 Bikes: Posts: 446 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 1 Post(s) So this means a 1000 foot rise over 1000 feet is 50% grade and 45 degrees, for instance. So if you want to convert from % to degrees multiply the percent in decimal form (multiply by .01 I think) by 90.
 06-26-06, 09:20 AM #4 TheKillerPenguin Nonsense     Join Date: Sep 2004 Location: Vagabond Bikes: Affirmative Posts: 13,067 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 411 Post(s) How high the climb is in ft divided by the distance climbed in ft. Multiply the answer by 100.
06-26-06, 09:33 AM   #5
KevinF
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Quote:
 Originally Posted by kyledr So this means a 1000 foot rise over 1000 feet is 50% grade and 45 degrees, for instance.
This is where it gets confusing (IMHO). Percent grade calculations are done by the "rise over run" formula (vertical elevation change divided by distance travelled). Typical roads aren't all that steep, so the distance ridden (i.e., the hypotenuse) is essentially the same as the true "run" of the right-triangle being formed by the hill-climb. So you can use the rise / distance-ridden formula to get pretty close to the true grade of the road.

However, in your example of a 1000 foot rise over 1000 feet the hypotenuse and the "true run" are no longer close. The way your statement is worded could mean that you have either a 45 degree angle (if your 1000 feet references the "true run") or you could have a 90 degree angle -- the only way you climb 1000 feet in 1000 feet of riding is if you literally rode straight up.

 06-26-06, 10:14 AM #7 NoRacer Isaias     Join Date: Sep 2005 Location: Essex, MD Bikes: Ridley X-Fire (carbon, white) Posts: 5,182 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 6 Post(s) Percent slope = %m = (rise/run)*100 %m = (100/1320)*100 %m = (.0757)*100 %m = 7.6
09-11-11, 12:13 PM   #8
quickquest88
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Quote:
 Originally Posted by kyledr So this means a 1000 foot rise over 1000 feet is 50% grade and 45 degrees, for instance. So if you want to convert from % to degrees multiply the percent in decimal form (multiply by .01 I think) by 90.
sorry to revive a dead thread, but i just looked this up today after seeing someone on tv clearly misunderstand this.
in this particular example
(rise/run)*100
(1000/1000)*100
(1)*100
100

a 45 degree hill is clearly a 100 grade. as a previous poster mentioned, some people miscalculate this by using sides C and B instead of the proper sides A and B, as refrenced by the pythagorean theorum. a 50% grade is 22.5 degrees.10% grade is 4.5 degrees.

 09-11-11, 12:19 PM #9 ilovecycling Senior Member   Join Date: Dec 2010 Location: RTP, NC Bikes: LOOK 595 & Cannondale CAAD9 Posts: 2,190 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) Buy a Garmin. /Thread
09-11-11, 01:20 PM   #10
canam73
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Quote:
 Originally Posted by Alphamoose That's 7.5% (100/1320)*100.
This (post #2) should have ended the thread. Over 5 years ago.

09-11-11, 06:30 PM   #11
bobbycorno
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Quote:
 Originally Posted by kyledr So this means a 1000 foot rise over 1000 feet is 50% grade and 45 degrees, for instance. So if you want to convert from % to degrees multiply the percent in decimal form (multiply by .01 I think) by 90.
No. 1000' in 1000' = 100%. Zero percent is perfectly flat, and straight up is infinite percent (no matter how far you climb, you never go forward, so you'd be dividing by zero, which is by definition infinity.

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09-11-11, 07:05 PM   #12
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IDK, I tell people my Garmin readings on here, and they call me a liar. Apparently there are no roads that peak out at 28% in the rest of the world.

 09-11-11, 08:23 PM #13 nhluhr John Wayne Toilet Paper     Join Date: Feb 2006 Location: Roanoke Bikes: BH carbon, Ritchey steel, Kona aluminum Posts: 1,950 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) Most people mistakenly use distance traveled as their denominator. That works only with some trigonometry. The correct "run" is the horizontal distance traveled. Still, for relatively low grades, it's close enough for bragging rights.
 09-11-11, 08:43 PM #14 canam73 Senior Member   Join Date: Jun 2007 Location: Haunchyville Bikes: Posts: 6,382 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 2 Post(s) For cycling purposes this really was answered with the first response 5 years ago. Even taking Soloist's extreme example of a 28% grade as an example the change between using the the hypotenuse and the flat leg as your denominator changes the result by a little over 1%. At 28% it won't help you. And for more common (i.e. lesser) pitches the difference will be less. At 10% the difference is .05% Hey, let's have the math dorks really whip it out by calculating pi to the nth decimal, where n=stupid.
 10-25-13, 08:04 PM #15 kocoman Newbie   Join Date: Oct 2009 Bikes: Posts: 1 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) Can I use the theodolite app to calculate it? thanks
 10-25-13, 09:17 PM #16 MikeyBoyAz Middle-Aged Member     Join Date: Apr 2011 Location: Mesa, AZ Bikes: Bianchi Infinito CV 2014, TREK HIFI 2011, Argon18 E-116 2013 Posts: 2,271 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 17 Post(s) Holy resurrected thread BatMan!
10-26-13, 04:09 AM   #17
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 Originally Posted by MikeyBoyAz Holy resurrected thread BatMan!
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 10-26-13, 05:24 AM #18 Cyclelogikal An Average Joe     Join Date: Jul 2013 Location: NC Bikes: '13 Orbea Orca Posts: 646 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) Rise over run................and multiply by 100 So 100/1320x100= 7.5% Last edited by Cyclelogikal; 10-26-13 at 05:28 AM.
04-05-14, 10:36 PM   #19
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I looked this up on wikipedia - and the popular answer here is incorrect

Wikipedia: Grade (slope) - Wikipedia, the free encyclopedia

Pertinent section:

Quote:
 as a percentage, the formula for which is 100 \frac{\text{rise****{\text{run**** which could also be expressed as the tangent of the angle of inclination times 100. In the U.S., this percentage "grade" is the most commonly used unit for communicating

So for the given case the answer is 100/(1320^2-100^2)^(1/2) ~= 7.60 degrees

However, the back-of-envelope calculation of simply taking rise/run diverges by a factor of < 0.005 for angles under 10% and exceeds 0.01 only for grades > 20%

E.g. 100/1320 is 7.57 - compared with the precise calculation of 7.60, an inaccuracy of just 0.28%

Last edited by javadba; 04-05-14 at 10:53 PM.

 04-05-14, 11:10 PM #20 Condor637 Senior Member     Join Date: Feb 2013 Location: Victorville Bikes: 2013 Cannondale SuperSix 3 Posts: 167 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s)
04-06-14, 12:17 AM   #21
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04-06-14, 07:43 AM   #22
gc3
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Quote:
 Originally Posted by javadba I looked this up on wikipedia - and the popular answer here is incorrect Wikipedia: Grade (slope) - Wikipedia, the free encyclopedia
that's because wikipedia didn't exist when the thread originated...
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 04-06-14, 11:14 AM #23 MinnMan Senior Member     Join Date: Aug 2009 Location: Minneapolis Bikes: 2016 Masi cxgr, 2011 Felt F3 Ltd, 2010 Trek 2.1, 2009 KHS Flite 220, 1991 Bianchi Osprey Posts: 2,352 Mentioned: 1 Post(s) Tagged: 0 Thread(s) Quoted: 181 Post(s) Just to beat this ancient dead horse a little more, AKAIK, GPS algorithms don't actually give you the distance traveled on a slope, but rather the distance on a map between two waypoints, not accounting for grade. This means that for hilly terrain, they actually underestimate distance traveled on the road by a very small amount. But it also means that they give you the "run" in rise over run, without needing to convert from the hypotenuse distance. OTOH, if your distance comes from a sensor on your wheel, you do have to convert. As a general rule, this consideration as well as pretty much all the rest in this thread, are less important than the fact that the measurements available (precise run, precise rise) are seldom accurate enough for the corrections to matter (particularly for grades less than, you know, 20% or so.
03-27-17, 07:05 PM   #24
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No it's not.

Quote:
 Originally Posted by bobbycorno No. 1000' in 1000' = 100%. Zero percent is perfectly flat, and straight up is infinite percent (no matter how far you climb, you never go forward, so you'd be dividing by zero, which is by definition infinity. Bend, OR
100% grade is when the run and rise are equal.
That would be a 45º angle. Beyond the the % grows exponentially to the point that at 84.6º you have 1000% grade and 90º is litterally infinity because you only travel up and not foreward at all.

 03-27-17, 07:48 PM #25 Doge  Senior Member     Join Date: Jan 2014 Location: Southern California, USA Bikes: 1979 Raleigh Team 753 Posts: 6,592 Mentioned: 80 Post(s) Tagged: 0 Thread(s) Quoted: 1458 Post(s) Goto https://ridewithgps.com draw a line along your road and see what the grade is.