Hiking Time Calculator (Naismith & Tobler)

Understanding the hiking time calculator — concept and principle

Knowing roughly how long a hike will take helps you plan start time, daylight, water and food. This calculator gives two classic estimates from the distance and the total ascent: Naismith's rule, a simple rule of thumb from Scottish mountaineering, and Tobler's hiking function, a formula that turns slope into walking speed.

How it is calculated

• Naismith's rule: time (h) = distance (km) ÷ 5 + ascent (m) ÷ 600. One hour for every 5 km on the flat, plus one hour for every 600 m of climbing.
• Tobler's hiking function: speed (km/h) = 6 × e^(−3.5 × |s + 0.05|), where s is the slope as a fraction (rise ÷ run). Here s is the average gradient, ascent ÷ (distance × 1000), and time = distance ÷ speed.

Neither result includes breaks.

The principle

Walking uphill costs time in two ways: you cover horizontal distance, and you lift your body weight. Naismith (1892) simply adds the two: 5 km/h on level ground plus a fixed time cost for height gained. Tobler (1993) fitted an exponential curve to observed walking speeds. It peaks at 6 km/h on a slight downhill of about −5%, gives about 5 km/h on the flat and falls off steeply as the path becomes steeper in either direction. A single average gradient smooths the route into one even slope, so Tobler often gives a shorter time than Naismith on hilly routes.

Worked example

1. Inputs: distance 10 km, total ascent 800 m.
2. Naismith: 10 ÷ 5 = 2 h, plus 800 ÷ 600 = 1.333 h, total 3.333 h = 200 min = 3 h 20 min.
3. Tobler gradient: 800 ÷ 10,000 = 0.08; 0.08 + 0.05 = 0.13.
4. Speed: 6 × e^(−3.5 × 0.13) = 6 × e^(−0.455) = 3.81 km/h.
5. Time: 10 ÷ 3.81 = 2.627 h = 157.6 min, rounded to 2 h 38 min.

How to read the result

Treat the two numbers as a range of moving time for a reasonably fit walker with a light pack on good paths. The gap here (about 40 minutes) shows how much the method matters. Add rest stops (often 10 minutes per hour), time for photos and meals, and a margin for weather. Rough ground, snow, heavy loads and long descents all slow you down; after a few hikes, scale the estimates by your own factor.

Common mistakes

• Using net height difference instead of total ascent; every climb counts, even if you descend between peaks.
• Forgetting that steep descents are slow too; both methods here underweight them.
• Treating the result as total trip time instead of moving time.

Frequently asked questions

Which method is more accurate?

Neither is universally better. Naismith is often closer on routes with big, concentrated climbs; Tobler is better suited to applying slope segment by segment, as in GIS route planning.

Does Naismith account for going downhill?

The basic rule does not. Later refinements, such as Langmuir's corrections, add or subtract time for descents depending on steepness.

Sources: Naismith W. W., Scottish Mountaineering Club Journal, 1892 · Tobler W., Three Presentations on Geographical Analysis and Modeling, NCGIA Technical Report 93-1, 1993