Tobler's hiking function
Tobler's hiking function is an exponential function determining the hiking speed, taking into account the slope angle. It was formulated by Waldo Tobler. This function was estimated from empirical data of the Swiss cartography professor Eduard Imhof.
Formula
Walking velocity:where
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.
Pace
Pace is the reciprocal of speed. For Tobler's hiking function it can be calculated from the following conversion:where
Sample values
| Slope | Gradient | Speed | Speed | Pace | Pace | Pace |
| Slope | Gradient | km / h | mi / h | min / km | min / mi | s / m |
| -60 | -1.73 | 0.02 | 0.01 | 3603.9 | 5799.9 | 216.23 |
| -50 | -1.19 | 0.11 | 0.07 | 543.9 | 875.3 | 32.63 |
| -40 | -0.84 | 0.38 | 0.24 | 158.3 | 254.7 | 9.50 |
| -30 | -0.58 | 0.95 | 0.59 | 63.3 | 101.9 | 3.80 |
| -25 | -0.47 | 1.40 | 0.87 | 42.9 | 69.1 | 2.58 |
| -20 | -0.36 | 2.00 | 1.24 | 30.0 | 48.3 | 1.80 |
| -15 | -0.27 | 2.80 | 1.74 | 21.4 | 34.5 | 1.29 |
| -10 | -0.18 | 3.86 | 2.40 | 15.6 | 25.0 | 0.93 |
| -5 | -0.09 | 5.26 | 3.27 | 11.4 | 18.3 | 0.68 |
| -2.8624 | -0.05 | 6.00 | 3.73 | 10.0 | 16.1 | 0.60 |
| 0 | 0 | 5.04 | 3.13 | 11.9 | 19.2 | 0.71 |
| 1 | 0.02 | 4.74 | 2.94 | 12.7 | 20.4 | 0.76 |
| 5 | 0.09 | 3.71 | 2.30 | 16.2 | 26.0 | 0.97 |
| 10 | 0.18 | 2.72 | 1.69 | 22.1 | 35.5 | 1.32 |
| 15 | 0.27 | 1.97 | 1.23 | 30.4 | 49.0 | 1.83 |
| 20 | 0.36 | 1.41 | 0.88 | 42.6 | 68.5 | 2.56 |
| 25 | 0.47 | 0.98 | 0.61 | 60.9 | 98.1 | 3.66 |
| 30 | 0.58 | 0.67 | 0.41 | 89.9 | 144.6 | 5.39 |
| 40 | 0.84 | 0.27 | 0.17 | 224.6 | 361.5 | 13.48 |
| 50 | 1.19 | 0.08 | 0.05 | 771.8 | 1242.1 | 46.31 |