The degrees in an angle and the incline grade can be derived from each other.
(1) angle of incline in degrees
(2) grade of incline in percent
(3) sides of the triangle (horizontal, vertical, hypotenuse)
grade in percent =
= SIN(angle in degrees) * 100
angle in degrees =
= ARCSIN ((grade in percent) / 100)
SIN(angle in degrees) =
= (vertical rise in m) / (hypotenuse in m)
hypotenuse in m =
= SQRT (((horizontal distance in m)^2) + ((vertical distance in m)^2))
• Trigonometric functions in MS Excel require input in radians. Conversion between degrees and radians is done with the DEGREES and RADIANS functions.
For small angles (<= 6 degrees) the tangent for the angle approximates the sine fairly well.
tangent for angle =
= (vertical rise in meters) / (horizontal distance in meters))
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