Read steepness straight off the map.
A map gradient averages the ground between two points and hides short steep steps, cliffs and loose ground. Contour accuracy and your measurement both limit it: 1 mm on a 1:25,000 map is 25 m. Tobler’s function is an empirical fit for walking speed, not a rule for any one person.
Model details & unit conventions ↗Tobler’s hiking function gives walking speed on a slope: 6 × e^(−3.5 |S + 0.05|) km/h. See the speed table, the flat value and a map-based example.
Calculate slope from contour lines: rise from the contour interval, run from the map scale, then grade and angle, with a worked 1:25,000 example.
Convert percent grade to degrees and back with the formulas, a conversion table, a worked 8% example and the error in the small-angle shortcut.
Map scale explained: 1:25,000 means 1 mm is 25 m on the ground. Convert map distance, compare common scales and measure winding routes accurately.
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