Naismith or Tobler: Why Two Hiking Time Estimates Differ
Put a route into the Hiking Time Calculator and you get two times. The main one is the Naismith estimate. Underneath it sits a Tobler cross-check, which is usually shorter, sometimes by close to an hour. This guide explains where each number comes from, compares them on five hypothetical routes, and says which one to plan around and why.
Two different ideas of walking
Naismith's rule (1892) is additive. It charges a fixed price for distance, one hour per 5 km, and a separate fixed price for climbing, one hour per 600 m of ascent. Double the climb and you double the climbing time, whatever the distance it is spread over.
Tobler's hiking function (1993) is a speed curve. Waldo Tobler fitted an equation to observed walking speeds on different slopes: speed in km per hour equals 6 times e to the power of minus 3.5 times the absolute value of (slope plus 0.05). The fastest speed, 6 km per hour, comes on a gentle downhill of about 5%; walking speed falls away smoothly as the ground gets steeper in either direction. On level ground the function gives a little over 5 km per hour, which is why Naismith and Tobler agree almost exactly on flat routes.
The calculator applies Tobler's function to the route's average uphill slope: total ascent divided by total distance. That one choice explains most of the gap you will see.
Five routes compared
All at the "average" pace setting. The slope column is simply ascent divided by distance.
| Route | Average slope | Naismith | Tobler | Gap |
|---|---|---|---|---|
| 10 km, no climb | 0% | 2h 00m | 1h 59m | 1 min |
| 10 km, 100 m of climb | 1% | 2h 10m | 2h 04m | 6 min |
| 15 km, 600 m of climb | 4% | 4h 00m | 3h 26m | 34 min |
| 6 km, 900 m of climb | 15% | 2h 42m | 2h 01m | 41 min |
| 4 km, 1,000 m of climb | 25% | 2h 28m | 1h 55m | 33 min |
On flat and gently rolling routes the two methods are within a few minutes of each other. Once the route climbs seriously, Naismith comes out 30 to 40 minutes longer. As a share of the total, the gap is largest on the steep, short routes: on the 6 km route with 900 m of climb, Tobler's figure is about a quarter shorter than Naismith's.
Why Tobler comes out shorter on hill routes
Most day hikes are out-and-back or loops. Half the distance is climbing and much of the rest is descending. When the calculator divides total ascent by total distance, it spreads the climb across the whole route, including the half where you are going down. The 6 km route with 900 m of ascent really climbs 900 m in about 3 km, a 30% gradient, then descends it. Averaged over 6 km, the slope looks like 15%.
Tobler's curve punishes steep slopes heavily, so averaging the steepness away makes the route look easier than it is. At the same time, the descending half of the route is treated as climbing at that average slope, which the function charges more for than a gentle descent. The two effects partly cancel, but on steep routes the first one wins and the cross-check comes out short.
Naismith's rule does not have this problem with averaging. It charges for every metre of ascent at the same rate, wherever it falls. Its weakness is the opposite one: it adds nothing at all for descent, which on a steep, rough path can take as long as the climb.
Which number to plan around
The calculator recommends the Naismith figure, and for planning a hill day that is the right default, for three reasons:
- It is usually the more conservative of the two on routes with real climb, and when a time estimate is wrong, being too short is the costly direction. A plan that is 40 minutes too optimistic can mean the last hour on the trail in the dark.
- It counts all the climbing honestly. Total ascent is the number most trail descriptions and mapping apps give you, and Naismith uses it directly.
- It is easy to check by hand. 12 minutes per km plus 10 minutes per 100 m of climb. If the calculator's answer surprises you, you can see at once which input drove it.
The Tobler figure is useful as a sense check. If the two numbers are close, the route is gentle and either will do. If they are far apart, the route is steep, and you should expect the real day to sit nearer the longer figure, or beyond it on rough ground.
What neither method knows
Both are estimates for a fit adult on a reasonable trail in decent conditions. Neither one includes:
- Stops. Breaks for food, water, photographs and navigation are extra. Add them yourself.
- Footing. Scree, boulder fields, snow, mud, sand and scrambling can halve your speed. Tobler's original data included off-path walking at roughly three fifths of on-path speed, but the calculator uses the on-path curve.
- Load and fatigue. A heavy pack and a long day slow you down, especially late on. The "leisurely / heavy pack" setting scales both figures by 1.25; on the 15 km route with 600 m of climb it moves the Naismith estimate from 4h 00m to 5h 00m.
- Altitude, heat and weather. All of them slow you down, and none of them is in either formula.
- The way back. On a long day, most people come back more slowly than they went out. The Daylight Turnaround Calculator allows 25% more time for the return leg by default for exactly this reason.
Calibrating against your own hikes
The best way to know which setting describes you is to compare the calculator with your own record. After your next few hikes, note the total distance, total ascent and your moving time (most watches and phone apps separate moving time from stopped time). Put the distance and ascent into the calculator and see which pace setting comes closest to what you actually did.
A walker who consistently beats the brisk figure on well-made paths should still be careful on unfamiliar or rough ground, where the rule's assumptions no longer hold. A walker who always lands near the leisurely figure has a reliable planning number and should use it every time, rather than hoping today will be quicker.
Putting it together
For a hypothetical 15 km route with 600 m of climb at average pace, a sensible plan might read: Naismith 4h 00m, Tobler 3h 26m, so plan on the longer figure. Add 40 minutes of breaks and a further 20 minutes because the route description mentions a rocky section, and plan around five hours. Put those five hours into the turnaround calculator with your start and sunset times to get the time you must turn back, and put them into the Water Needs Calculator for a water figure.
Then carry what the numbers cannot replace: a map and navigation, layers, food and water, first aid, a headlamp and a charged phone. Leave your route and expected return time with someone at home, and check the land manager's current trail conditions before you go. If the day starts running slower than the plan, believe the clock, not the estimate, and turn around on time.
For a deeper look at the main estimate on its own, read Naismith's rule worked through.