Hiking time
calculator
Estimate how long a hike or backpacking leg will take from its distance and elevation gain. Naismith's rule, with Langmuir's descent correction and Scarf's distance–climb equivalence — imperial or metric, and honest about what the rule leaves out.
How the math works
Hiking time is dominated by two things: how far you go and how much you climb. Naismith's rule (William W. Naismith, Scottish Mountaineering Club Journal, 1892) sets both with one line — "an hour for every three miles on the map, with an additional hour for every 2,000 feet of ascent." So the base estimate is your flat walking time plus a fixed penalty for the vertical.
Naismith base: forward_speed = 3 mph · climb rate = 1 hour / 2,000 ft
metric: 2,000 ft = 609.6 m, so the climb term ≈ 1 hour / 600 m
(Langmuir's rounding: 5 km/h + 1 minute per 10 m of ascent)
Langmuir descent correction (Langmuir 1984), per 300 m of descent:
gentle slope (5–12°): − 10 minutes / 300 m (saves time)
steep slope (> 12°): + 10 minutes / 300 m (costs time)
shallow slope (< 5°): no correction
Equivalent flat distance (Scarf 2007, "Naismith's number"):
equivalent_distance = distance + 7.92 × ascent_height
(so 2,000 ft of climb = 3 miles of flat; 100 m of climb ≈ 0.79 km)
Naismith himself said nothing about going down. Eric Langmuir, in Mountaincraft and Leadership (1984, the official handbook of the UK Mountain Leader Training Boards), added the correction that is still taught: a gentle descent is faster than flat ground, so subtract 10 minutes per 300 m dropped on slopes of 5–12°; a steep descent is slower than flat, so add 10 minutes per 300 m on slopes over 12°. The correction changes sign at 12°, which is the part generic calculators miss.
The third piece re-expresses the whole route as one number. Philip Scarf (J Sports Sci, 2007) showed Naismith's rule is equivalent to treating 1 unit of climb as 7.92 units of horizontal distance — "Naismith's number." That turns a short, steep route and a long, flat one into comparable equivalent flat distances, and Scarf found the 7.92 ratio held up well against fell-running times.
Worked example
A day hike of 8 miles (12.9 km) with 2,500 ft (762 m) of ascent, at Naismith's 3 mph (4.8 km/h), no descent correction:
- On the flat: 8 mi ÷ 3 mph = 2 h 40 m (160 min)
- For the climb: 2,500 ft ÷ 2,000 ft/h = 1 h 15 m (75 min)
- Naismith total: 3 h 55 m (235 min), moving time, before breaks
- Equivalent flat distance: 8 mi + 2,500 ft × 7.92 = 8 + 3.75 = 11.75 mi (18.9 km) — the climb alone is worth the time of 3.75 mi of flat walking
Now a steeper hillwalk: 6 miles (9.66 km), 1,800 ft (548.6 m) of ascent and the same descent on steep (> 12°) ground. Base time is 2 h (flat) + 54 min (climb) = 2 h 54 m. The steep descent adds 548.6 m ÷ 300 × 10 ≈ 18 min, for 3 h 12 m. Had that descent been gentle (5–12°), Langmuir would subtract the same 18 min instead — 2 h 36 m. Same descent, 36 minutes apart.
When this calculator is wrong
Naismith's rule is a planning floor, not a prediction. It assumes a fit walker on reasonable ground, measures the map distance (your GPS track and the real trail are longer), and counts zero break time — no lunch, no photos, no navigation stops. On a loaded multi-day carry, in heat, or over rough ground, the real time runs well over the estimate. The one refinement that matters is Langmuir's descent correction, and even that is coarse: it changes sign at 12°, so a calculator that treats all downhill as free is wrong on steep ground and one that ignores descent is wrong on gentle ground.
The counter-case: the rule isn't always conservative. On smooth, gently-descending trail a fit party can beat it, because a gentle downhill is genuinely faster than flat and Naismith's base pace is modest. And the climb penalty itself is sound — Scarf (2007) found the 7.92 distance–climb equivalence reliable against fell-running times. What the base rule gets wrong is almost always the stuff it leaves out (breaks, terrain, load, fatigue late in the day), not the climb arithmetic.
- Breaks aren't in it. A long day with a lunch stop and a few navigation checks can add an hour or more that the rule never sees. Add your own rest time on top.
- Map distance understates the walk. Switchbacks, boulder fields, and GPS wander make the ground you actually cover longer than the line on the map.
- Pack weight and fatigue aren't modelled. Naismith assumed a fit, lightly-laden walker. Drop the forward-speed setting for a heavy pack, and expect the late miles of a big day to run slower than the early ones.
What to do with the result
Use the estimate as a minimum moving time and build a day around it. Add your planned break time, then set a turnaround time: the clock at which you head back regardless of whether you've reached the top, so you finish with daylight to spare. For multi-day planning, the equivalent flat distance is the number to compare legs with — a 10-mile day with 4,000 ft of climb (about 16 equivalent miles) is a bigger day than a flat 14-miler, even though it's shorter on the map.
Then calibrate against yourself. Time a few known hikes and compare them to the rule: if you consistently come in 15% over Naismith once breaks are counted, apply that factor to future plans. The rule is the starting point; your own splits are the measurement. Pair this with the pace calculator for flat-ground splits, the hiking calorie calculator to plan food for the climb, and the treadmill incline pace calculator to train the vertical before the trip.
Common questions
- What is Naismith's rule?
- A rule of thumb for hiking time from William W. Naismith (1892): allow 1 hour per 3 miles of distance plus 1 hour per 2,000 feet of ascent. In metric that's roughly 5 km/h plus 1 minute for every 10 m of climb. It estimates moving time for a fit walker and includes no allowance for breaks.
- How long does it take to hike a mile?
- On the flat at Naismith's 3 mph, about 20 minutes a mile. But climb dominates: every 2,000 ft of ascent adds a full hour no matter the distance, so a mile with 1,000 ft of gain takes roughly 20 min walking plus 30 min climbing — about 50 minutes. That's why steep miles feel so much longer than flat ones.
- Does Naismith's rule account for going downhill?
- Not on its own — Naismith only added time for distance and ascent. The widely taught fix is Langmuir's correction (1984): on a gentle descent (slopes 5–12°) subtract 10 minutes per 300 m dropped, and on a steep descent (over 12°) add 10 minutes per 300 m. The sign flips at 12°, which is why steep downhills slow you down rather than speed you up.
- What is the equivalent flat distance?
- A way to compare routes with different amounts of climb on one number. Scarf (2007) showed Naismith's rule treats 1 unit of ascent as 7.92 units of horizontal distance, so 2,000 ft of climb is worth 3 miles of flat (100 m of climb ≈ 0.79 km). Add 7.92 × your total ascent to your distance and you get a single "equivalent flat distance" that ranks the real effort of each leg.
- How accurate is Naismith's rule for backpacking?
- Treat it as a floor. With a full pack, on rough or unfamiliar ground, and once breaks are counted, real times commonly run 20–30% over the estimate — more in heat, snow, or late in a long day. Lower the forward-speed setting for a heavy load, add your break time, and calibrate the whole thing against a few of your own timed hikes.
- Why does my GPS say the hike is longer than I planned?
- Naismith uses map distance; your GPS logs the ground you actually cover, which is longer because of switchbacks, detours, and small position errors that accumulate. The elevation your watch records can also exceed the map's, and climb is the expensive part. If your device reads consistently long, plan from its numbers rather than the map's.