Naismith's rule at a glance
| Miles | Gain (ft) | Moving time |
|---|---|---|
| 1 | 0 | 20 min |
| 2 | 500 | 55 min |
| 3 | 1,000 | 1 h 30 min |
| 5 | 1,500 | 2 h 25 min |
| 8 | 2,500 | 3 h 55 min |
| 10 | 3,000 | 4 h 50 min |
| 12 | 4,000 | 6 h 0 min |
How the two methods work
Naismith's rule (1892) adds two parts: walking time at a flat pace, and climbing time. In the common U.S. form that is 3 miles per hour plus 30 minutes for every 1,000 feet of ascent. A 3.2-mile hike with 900 feet of gain comes to 64 minutes of walking plus 27 minutes of climbing, about 1 hour 31 minutes. Changing the flat pace above changes the first part only.
Tobler's hiking function (1993) estimates speed from the slope: 6 x e^(-3.5 x |slope + 0.05|) km per hour, fastest on a slight downhill. We apply it to the climbing part (the gain spread over half the distance) and to the rest as level ground, which gives a second, often slightly longer, estimate on steady uphill trails.
Both give moving time for a fit adult on maintained trail. Snow, scrambling, altitude above about 8,000 feet, heat and a heavy pack all slow people down, and neither formula counts breaks, photos or route finding.
Examples: trails to public hot springs
Round trip, using the one-way distance and gain from the managing agency on each page, with Naismith's rule.
- Terwilliger (Cougar) Hot Springs0.25 mi one way10 min
- Umpqua Hot Springs0.3 mi one way12 min
- Bagby Hot Springs1.4 mi one way56 min
- Goldbug Hot Springs (Elk Bend Hot Springs)2 mi one way, 1,350 ft2 h 1 min
Questions
How long does it take to hike a mile?
On flat, good trail most adults walk 2.5 to 3 miles per hour, so 20 to 24 minutes per mile. Naismith's rule uses 3 mph (20 minutes per mile) and adds time for climbing.
What is Naismith's rule?
A rule from 1892 by the Scottish mountaineer William Naismith: one hour for every three miles, plus one hour for every 2,000 feet of ascent. That is 30 minutes per 1,000 feet.
Does going downhill add time?
Naismith's rule ignores descents. Tobler's hiking function gives the fastest pace on a gentle downhill (about 5% grade) and slows down on steep descents.
Methods: W. W. Naismith (1892), Scottish Mountaineering Club Journal; W. Tobler (1993), "Three presentations on geographical analysis and modeling", NCGIA. Estimates for planning only.