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Old 04-05-14, 10:36 PM
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javadba
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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:

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.
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