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Angle of gradient equation and calculator

Power Transmission Design and Engineering
Engineering and Design Applications

Angle of uphill or downhill gradient equation and calculator

The angle of the uphill or downhill gradient α is calculated using the following formula:

tan α = p / 100

α = arctan ( p /100 )

Sin α = h / c

α = arcsin ( h / c )

Where:

α = Angle of gradient, in °
p = Uphill/downhill gradient, in %
h = Vertical height of an uphill/downhill gradient, in m
c = Distance travelled, in m

Example of a calculation:
Gradient p = 25%. what is the angle of the gradient?

tan α = p / 100 = 25 / 100

α = arctan 0.25

α = 14 °