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  • percent grade to angle degree

    How do you convert a % grade to the angle of degree. If you have a 14% grade, how do you find the degree?

  • #2
    Re: percent grade to angle degree

    Originally posted by Unregistered
    How do you convert a % grade to the angle of degree. If you have a 14% grade, how do you find the degree?
    Make sure it is the ratio of vertical rise to the horizontal run, not the slant length, Then angle = arctan(rise/run).

    In this case, express as the percent as a decimal and plug in

    angle = arctan(0.14) = 7.97

    (If it is rise/slant_length, use the arcsin function)

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    • #3
      Re: percent grade to angle degree

      thanks, you just helped me with my performance assesment for my physics class.

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      • #4
        Re: percent grade to angle degree

        Thanks JohnS, your simple explanation is exactly what I needed for my surveying homework.

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        • #5
          Re: percent grade to angle degree

          So a 100% grade is a 45 degree climb. As the grade goes from zero to 100, the angle goes from zero to 45 degrees. Is that relationship linear? If it was, then 1 degree would be 1/45 of 100, or 2.222%.

          Or did I miss something? Also, what's a 50 degree grade (assuming we might find it in, say, San Francisco?

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          • #6
            Re: percent grade to angle degree

            Originally posted by Larry View Post
            So a 100% grade is a 45 degree climb. As the grade goes from zero to 100, the angle goes from zero to 45 degrees. Is that relationship linear? If it was, then 1 degree would be 1/45 of 100, or 2.222%.

            Or did I miss something? Also, what's a 50 degree grade (assuming we might find it in, say, San Francisco?
            The relation is nonlinear, angle = arctan(rise/run)
            or rise/run = tan(angle)

            tan(1) = 0.01746 = 1.746%
            It is pretty linear for small angles (under 6) but gets quite non linear for larger angles.
            tan(50) = 1.19175, the rise is larger than the run. You might find it on a roof, probably not on a road.

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            • #7
              Re: percent grade to angle degree

              Yes. It's clear if you look at the tangent graph. Leaving zero it moves in a direction up and to the right. But it's rate of climb increases as it goes, passing 1 at 45 degrees, and heading for straight up and infinity at 90 degrees.

              Thanks for the comeback,
              Larry

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              • #8
                Re: percent grade to angle degree

                Thanks for the conversion formula. I ride a road bike and have wondered when fellow road bikers tell their stories of how hard the hill they just rode was and it was a (XX) % grade just what angle of rise it was, thanks.

                Bob

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                • #9
                  Re: percent grade to angle degree

                  Originally posted by Unregistered View Post
                  How do you convert a % grade to the angle of degree. If you have a 14% grade, how do you find the degree?
                  14% grade= 14' rise for every

                  Cos = (√ 100 SQ - 14 SQ ) / 100
                  Degree = -Cos

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                  • #10
                    Re: percent grade to angle degree

                    Originally posted by Unregistered View Post
                    How do you convert a % grade to the angle of degree. If you have a 14% grade, how do you find the degree?
                    18 degree grade what is the angle of degree

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                    • #11
                      Re: percent grade to angle degree

                      My employer is unwilling to fork out the cash to purchase a couple of "slope meters" so I'm considering the generic alternative of using an angle meter (such as the Johnson Level & Tool 700 Magnetic Angle Locator as a "get-me-by". I will be measuring slopes in the 2 to 8 percent range.

                      How do I convert the angles to get the corresponding slopes for each percent of slope (2, 3, 4, 5, 6, 7 and 8 percent)? It doesn't have to be "NASA-accurate" - obviously since I plan to use an angle gauge. But I'm hoping it will give me a close enough idea as to what percent slope my guys are setting.

                      Is this even possible or am I wasting my time?

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                      • #12
                        Re: percent grade to angle degree

                        Originally posted by That1Guy View Post
                        My employer is unwilling to fork out the cash to purchase a couple of "slope meters" so I'm considering the generic alternative of using an angle meter (such as the Johnson Level & Tool 700 Magnetic Angle Locator as a "get-me-by". I will be measuring slopes in the 2 to 8 percent range.

                        How do I convert the angles to get the corresponding slopes for each percent of slope (2, 3, 4, 5, 6, 7 and 8 percent)? It doesn't have to be "NASA-accurate" - obviously since I plan to use an angle gauge. But I'm hoping it will give me a close enough idea as to what percent slope my guys are setting.

                        Is this even possible or am I wasting my time?
                        Use any scientific calculator with the tangent and arctangent functions (usually abbreviated TAN and either ATAN or TAN followed by a -1 superscript)

                        As a decimal fraction slope = rise/run = tan(angle). If you want percent multiply the decimal by 100%

                        Example 4 angle is meaured. Slope = tan(4) = 0.0699
                        In percent, this is 6.99% (or about 7%)

                        In reverse, take the slope in percent and divide by 100 so it is a decimal fraction. Take the arctangent
                        7% = 0.07
                        ATAN(0.07) = 4.004 or about 4 with sensible rounding.

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                        • #13
                          Re: percent grade to angle degree

                          if i have a 4 to 1 slope what would that be as a percentage

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                          • #14
                            Re: percent grade to angle degree

                            Originally posted by wildman View Post
                            if i have a 4 to 1 slope what would that be as a percentage
                            If rise/run is 1/4, that is 25%

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