How to use it
- Choose Units, then type the Distance from the map.
- Type the Total ascent and Total descent of the route, and choose the Steepness of the descent that fits most of it.
- Type your Walking speed on flat ground.
- Read Time by Naismith's rule and Time by Tobler's hiking function, then the working under Working, step by step.
How the time is calculated
Naismith's rule was published in 1892 by W. W. Naismith in the Scottish Mountaineering Club Journal. It allows one hour for every 5 km (3 miles) forward, plus one hour for every 600 m (2,000 ft) of ascent. Langmuir's handbook "Mountaincraft and Leadership" (1984) adds a correction for descent: on a gentle decline of 5 to 12 degrees, 10 minutes are taken off for every 300 m of descent; on a steep decline over 12 degrees, 10 minutes are added. The source gives no correction for slopes under 5 degrees, so none is applied here. The sources are listed below.
Tobler's hiking function, from Waldo Tobler's 1993 report, gives walking speed on a slope. Its speed on flat ground is 5.04 km/h, the fastest is about 6 km/h on a gentle downhill slope of 5%, and it is slower uphill. This page applies it to the average slope of the whole route, with the speed scaled so that flat ground gives the speed you type.
Naismith: T = D ÷ 5 km/h + A ÷ 600 m per hour (A in feet: A ÷ 2,000 per hour)
Langmuir, gentle descent 5 to 12 degrees: minus 10 minutes per 300 m of descent
Langmuir, steep descent over 12 degrees: plus 10 minutes per 300 m of descent
Tobler: W = 6 × e^(−3.5 × |S + 0.05|) km/h, with S = (ascent − descent) ÷ horizontal distance- The Naismith total is never below zero.
- The Tobler slope uses the map distance as the horizontal distance, in the same metres as the ascent and descent.
Why the two methods differ
Naismith adds a fixed hour for each 600 m of climb, whatever the slope of each section. Tobler's function only sees the slope of each part of the path, so this page feeds it the average slope of the whole route. A route with a long climb and a long flat part can therefore average out to a gentle slope, and Tobler then gives a faster time than Naismith. Read the two figures as a range, and plan with the longer one.
What this calculator does not include
- Pack weight. Neither method here includes a load correction: no equation for a pack could be confirmed from a source, so none is applied. A heavy pack makes the real time longer than either figure.
- Rest stops, photographs, route-finding, mud, snow, heat and the walker's fitness beyond the speed you type.
- The real path length: on steep ground the path is longer than the map distance.
Worked example: 10 km with 800 m of climb and 300 m of descent
On the flat at 5 km/h, 10 km takes 2 hours. The climb adds 800 ÷ 600 = 1 hour 20 minutes. The gentle descent takes 300 m ÷ 300 m × 10 minutes = 10 minutes off. Naismith's total is 2:00:00 + 1:20:00 − 0:10:00 = 3:10:00, an average of 3.2 km/h.
For Tobler, the average slope is (800 − 300) m ÷ 10,000 m = 5%. The speed on that slope is about 4.20 km/h (the page uses the unrounded speed), so 10 km takes 2:22:57, an average of 4.2 km/h. The two methods differ by about 47 minutes, which is why the page shows both.
| Method | Time | Average speed |
|---|---|---|
| Naismith’s rule with Langmuir correction | 3:10:00 | 3.2 km/h |
| Tobler’s hiking function | 2:22:57 | 4.2 km/h |
Frequently asked questions
What is Naismith's rule?
Naismith's rule, published in 1892, allows one hour for every 5 km (3 miles) on the flat and one more hour for every 600 m (2,000 ft) of ascent. It is a planning rule for walkers, not a guarantee.
What does Langmuir's correction change?
It takes 10 minutes off for every 300 m of descent on a gentle slope of 5 to 12 degrees, and adds 10 minutes for every 300 m on a slope steeper than 12 degrees. No correction is given under 5 degrees.
What is Tobler's hiking function?
It is a formula for walking speed on a slope, published by Waldo Tobler in 1993. Walking speed is about 5 km/h on flat ground, fastest at about 6 km/h on a gentle downhill, and slower on steeper slopes.
Which of the two times should I plan with?
Neither is exact. Plan with the longer time, and add time for rest stops, weather and the weight of your pack, which neither method includes.
Why does the page ask for my walking speed on the flat?
Naismith's rule assumes 5 km/h. Tobler's function is scaled so that flat ground gives the speed you type, so the two methods start from the same pace.
Does the calculator include the weight of my pack?
No. A load correction could not be confirmed from a source, so no pack factor is applied. A heavy pack makes the real time longer than either figure.
Are my route figures stored or sent anywhere?
No. The calculation runs in your browser, and nothing you type is stored or sent.
Sources
- Wikipedia: Naismith's rule (the 1892 rule, the Langmuir descent correction, the 1984 handbook and the 1892 journal reference)
- Wikipedia: Tobler's hiking function (the formula, the flat-ground speed and the 1993 report by Waldo Tobler)
Figures and text last checked on Tuesday, November 10, 2026.