Naismith's rule & terrain difficulty

Two flat-distance numbers can describe wildly different efforts. A 20 km flat coastal walk and a 12 km Alpine ascent take the same time and burn similar calories. Naismith's rule, plus the derived terrain difficulty index, lets us compare them fairly.

Naismith's rule (1892)

A Scottish mountaineer named William W. Naismith published the formula in 1892. In its original form:

Allow 1 hour per 3 miles, plus 1 hour for every 2,000 feet of ascent.

Modernised:

time = (distance_km / v_walk) + (gain_m / r_climb)

With v_walk = 5 km/h and r_climb = 600 m/h, this matches the original almost exactly. We use these defaults; both are adjustable per-user.

Equivalent flat distance

Time isn't the most useful number to a casual user — they'd rather see "how far would this trip have been on flat ground?" Solve Naismith for distance:

distance_flat_eq = distance_km + (gain_m / r_climb) * v_walk

A 12 km walk with 800 m of climb has flat-equivalent distance:

12 + (800 / 600) * 5 = 12 + 6.67 = 18.67 km

So that 12 km Alpine walk "costs" the same as a 19 km flat coastal walk.

Terrain difficulty index

A normalised score (0–100) so trips can be ranked by toughness regardless of length:

terrain_index = min(100, max(0, ((flat_eq / actual) - 1) * 250))

Where:

• 0 = perfectly flat (flat_eq == actual_distance).
• 100 = a vertical staircase (40% climb-to-distance ratio).

Examples:

Pace efficiency

For trips where you actually walked the route:

pace_efficiency = (flat_eq / actual_distance) * 100

100% = the route was flat. 130% = you climbed 30% more than a flat equivalent. Useful for comparing your honest pace across varied terrain — if you walked Mt. Snowdon at 4 km/h actual, that's a 5.2 km/h flat-equivalent pace, which suggests you're fitter than the actual number suggests.

Why we don't use Tobler's hiking function

Tobler's function is a more accurate exponential model of speed-vs-slope. We don't use it because:

• It's a per-step model — needs slope per segment, not just total gain.
• The added accuracy (~5% better than Naismith) doesn't justify the implementation complexity for a leisure trip.
• Naismith is intuitive: "every 100 m up = 10 minutes". You can do the math in your head.

Related

• Analytics glossary — where these numbers appear in the dashboard.
• Altitude smoothing — the upstream that makes the climb number trustworthy.

Need help? Contact support · Where Is Tereza?