Naismith's rule gives 23 to 25 minutes for the 1.2 km main route up Bukit Timah, Singapore's highest hill, on a climb of roughly 83 to 103 m that we read off NParks' contour map. NParks' trail guide of 2012, still linked from its current hiking page, allows "approximately 45 minutes to an hour to reach the summit, at a leisurely pace". The rule, as W. W. Naismith wrote it in 1892, is an hour for every three miles on the map plus an hour for every 2,000 feet of ascent. NParks' January 2025 Central Catchment guide implies 1.75 to 3 km/h, on our arithmetic, against the rule's 5.
The walk in Naismith's 1892 note took in short halts
The rule appeared in the Scottish Mountaineering Club Journal, Vol. II, No. 3, September 1892, in a note on a day over Cruach Ardran, Stobinian and Ben More. Page 136 of the Internet Archive scan reads: "Distance, ten miles; total climb, 6,300 feet; time, six and a half hours (including short halts). This tallies exactly with a simple formula, that may be found useful in estimating what time men in fair condition should allow for easy expeditions, namely, an hour for every three miles on the map, with an additional hour for every 2,000 feet of ascent."
The formula gives 6 hours 29 minutes for that day, by our arithmetic. The note does not say Naismith built the rule from the walk, or how long the halts lasted, but the day he offered as matching it included stops. That "easy expedition" also took in cutting steps down a snow slope described as fifty degrees. His "total climb" supports counting every rise rather than the height of the top.
Metric rounding omits several minutes on a long walk
Three miles an hour is 4.83 km/h and 2,000 feet is 609.6 m, so 5 km and 600 m is a rounding; we could not establish who first made it. On Naismith's own day the metric version gives 6 hours 25 minutes. On a flat 24-mile day it gives 7 hours 43 against the 1892 wording's 8 hours.
We computed both versions for 651 days of 5 to 15 miles with 1,000 to 4,000 feet of climb, and every one differed. The metric version came out 2 to 10 minutes shorter, 6 at the median. The rounding also shifts weight onto climbing: a metre of ascent costs as much time as 7.92 m of map distance in the 1892 wording and 8.33 m in the metric one.
Halts dropped out of our calculator's version of the rule
Until 7 October 2026 our Naismith hiking time calculator called its answer moving time only, in its result, its facts and its FAQ. Its miles-and-feet mode applied the metric rounding, so across 5,151 combinations of up to 25 miles and 10,000 feet it differed from the 1892 rule in 94.4% of them.
The revision made that day applies three miles and 2,000 feet in miles mode and drops the moving-time claim; the live page may show the old version until it is deployed. The revised page's 30 minutes for Bukit Timah counts the hill's full 163 m as climb, an upper bound, since the start sits at roughly 60 to 80 m on our reading of the map. The page's slowest pace factor, ×1.5, labelled as our own convention, falls short of every park figure below.
Published park times in Singapore and Sabah contain far more than the rule
NParks' Bukit Timah hiking page, dated March 2025, lists Route 1 as 1.2 km "via the main road" and gives no time. The time is from the 2012 guide it links, which also allows "another 30 minutes to reach the foot of the hill", where the rule, ignoring descent, gives 14. On our climb estimate the 2012 allowance is 1.8 to 2.6 times the rule.
The Central Catchment TreeTop Walk guide times six routes. Its 7 km trail to the TreeTop Walk is given 3 to 4 hours; the rule's distance term alone gives 84 minutes. Across the six, the published times are 1.7 to 2.9 times the distance-only figure, on our arithmetic; NParks gives no climb, and any climb would lengthen the rule's estimate, so these are upper bounds.
Sabah Parks' Kinabalu itinerary, as it stood on 7 October 2026, places supper and the start of the ascent between 2:00 and 3:30 am and has climbers reach Sayat-Sayat "by 5:30 am". Its summit trail brochure puts Laban Rata Resthouse at 3,272.70 m and Sayat Sayat Hut at 3,665 m, 392 m higher and 0.5 to 1.5 km on. The rule gives 45 to 57 minutes; the itinerary allows 2 to 3.5 hours, supper included. The descent window is shaped differently: check-out by 10:30 am and Timpohon Gate before 4:00 pm leaves 5 hours 30 minutes at the deadline, and up to 8 hours 30 for a climber leaving at 7:30, when check-out opens. Both are schedule allowances, and they do not show the parks or the rule to be wrong.
Tobler's function covers the descent that Naismith's rule ignores
Tobler's hiking function, in NCGIA Technical Report 93-1 of February 1993, reads: "For walking on footpaths in hilly terrain: W = 6 exp { -3.5 * abs(S + 0.05)}", with W in km/h and S the slope. Estimated from Imhof's 1950 data, it gives 5 km/h on the flat and peaks at 6 km/h on a 5% descent, about 2.9 degrees on our conversion.
On 1,084 out-and-back routes we modelled at a steady grade, the rule gave more time than Tobler below an average grade of about 14 degrees, and up to 37% less above it. Langmuir's descent adjustment and Tranter's corrections are commonly cited; we could not check either against its original publication. A 2023 PLOS ONE study by Wood and colleagues, using about 88,000 km of UK GPS tracks, found its own model and every existing one it tested, Naismith's included, averaged 13.5–15.5% error over whole routes.
Scarf's ratio packs eight metres of distance into each metre of climb
Scarf's 2007 paper in the Journal of Sports Sciences finds that Naismith's rule "implies that 1 m of ascent is equivalent to 7.92 m of horizontal travel". From fell-running records it recommends "that male runners and walkers use a 1:8 equivalence ratio and females a 1:10 ratio": a metre of climb counts as about 8 m of distance for men and 10 m for women. The abstract contrasts treadmill experiments at 1:3.3 and a mountain road-relay at 1:4.4, and says nothing about descent or fatigue.
Official Rinjani sources we could reach include no stage times
For Gunung Rinjani on Lombok we found no official distance, climb or time for any stage of any route. Rinjani's climbing procedure is set by the park office head's Decree No. 19 of 2022, according to a Tourism Ministry statement Antara reported in June 2025; we did not open the decree. The office's website returned an error on 7 October 2026. The times and rules for each of these trails are Balai Taman Nasional Gunung Rinjani's, NParks' and Sabah Parks' to publish.
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