VIDEO: Convert percent to degrees

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Percent in the gradient triangle

In many everyday situations you will encounter slopes in a percentage that you want to convert into a slope angle (in degrees). Especially on inclines while driving.

  • The best thing to do is to make the percentage clear using a slope in the triangle. Draw a right triangle and name the slope angle Alpha.
  • The incline is always calculated at 100 meters. With a gradient of 12% = 12/100 this means that at 100 meters in the horizontal (i.e. horizontally) it goes up 12 meters.
  • However, you want that angle to calculate. For this you need the tangent as an angle function. The tangent of an angle is always the ratio of the opposite side to the adjacent side.
  • In your case, the opposite cathetus is the distance that lies opposite the slope angle alpha. This is 12 meters long in the example.
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  • The adjacent is the line that connects to the alpha angle and which forms the right angle at the end. With percentages, this is always 100 meters long.

How to calculate the angle

  • Now you need yours calculator, namely the inverse function of the tangent function TAN-1because you want to calculate the angle. Now enter the following: TAN-1(12/100) = 6,84°. In some pocket calculators, this inverse function is expressed as "arctan" (the arctangent).
  • If you now want to convert the number of degrees of the angle back into a slope in percent, proceed as follows. The equation is converted according to the gradient in percent and reads: 100 * TAN (6.84 °) = 12%.

The formula is for everyone Conversions valid of this kind. You should now be able to easily master the conversion from percent to degrees.

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