Tobler's hiking function

Formula

Walking velocity:

${\displaystyle W=6e^{{\displaystyle -3.5\left|\frac{dh}{dx}+0.05\right|}}}$

${\displaystyle \frac{dh}{dx}=S=\tan \theta }$

where

W = walking velocity [km/h]

dh = elevation difference,

dx = distance,

S = slope,

θ = angle of slope (inclination).

The velocity on the flat terrain is 5 km / h, the maximum speed of 6 km / h is achieved roughly at -2.86°.

On flat terrain this formula works out to 5 km/h. For off-path travel, this value should be multiplied by 3/5, for horseback by 5/4.