Tobler's Hiking Function Calculator (Walking Speed on Slopes)
Walking speed and time for a stretch of path from its gradient, using Tobler's hiking function, which makes you fastest on a gentle downhill, with a correction for off-path ground.
Results
The dashed line marks the value you entered.
What this tool does
Waldo Tobler fitted a curve to measured walking speeds in 1993: 6 × e^(−3.5 |S + 0.05|) km/h, where S is the slope as a fraction. It peaks at 6 km/h on a gentle downhill of about 5 %, falls on flat ground to about 5 km/h, and drops quickly on steep slopes either way, steep descents being slow too. Off a path he multiplies by 0.6. It describes fit walkers carrying little, so add time for rests, a heavy pack or rough footing.
Formula
v = 6 × e^(−3.5 × |S + 0.05|) km/h (S = gradient as a fraction; × 0.6 off the path) · time = distance ÷ v
Variables
| Symbol | Meaning | Unit |
|---|---|---|
gr | Gradient (positive uphill, negative downhill) | % |
d | Distance along the path | km |
sf | Terrain | — |
V | Walking speed | km/h |
TM | Time for the distance | min |
TH | The same in hours | h |
PC | Pace | min/km |
Worked example
- Gradient (positive uphill, negative downhill)10 %
- Distance along the path8 km
- Terrain1
- Walking speed3.55 km/h
- Time for the distance135 min
- The same in hours2.25 h
- Pace16.9 min/km
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.