How we estimate hiking time

Short version

Every day's Hiking number is time moving forward — walking, climbing, descending. The smaller total w/ breaks line underneath (~20% larger) is a rough wall-clock trailhead-to-camp estimate that includes normal rest stops, snacks, and water filtering. A photo-heavy or big-group day easily pushes past that. If yours consistently comes in faster or slower, bump your pace preset in Settings.

The formulas

Two well-known equations

Every hiking planner needs a math model for time. We use the two most-cited ones in outdoor navigation and academic geography, layered together.

Naismith's Rule (1892)

Baseline

Scottish mountaineer William W. Naismith proposed a walking-time rule in the Scottish Mountaineering Club Journal in 1892: "one hour for every three miles on the map, plus an additional hour for every 2,000 feet of ascent."

In modern form: time = distance ÷ 3 mph + 0.5 hr per 1,000 ft climb. It's the baseline every outdoor navigation tool still starts from. Naismith assumed an unloaded, fit hillwalker — which is why we scale it by your chosen pace instead of using it raw.

Source: Naismith, W. W. (1892). "Excursions." Scottish Mountaineering Club Journal, Vol. II, No. 3, pp. 135–136.

Tobler's Hiking Function (1993)

Grade-aware

Geographer Waldo Tobler published an exponential walking-velocity function that responds to local grade instead of a whole-day average:

v = 6 × e^{−3.5 × |slope + 0.05|} km/h

Peak velocity is at −5% grade (slight downhill, comfortable stride). Everything steeper than that — up or down — slows you exponentially. On the OLP, this catches the sustained steep pitches that a whole-day average smooths away.

We integrate Tobler across the trail's elevation profile in ~50 m chunks (short enough to see real grade changes, long enough to not amplify GPS noise) whenever we have full coordinates. When we only have distance + total gain (like on the trail summary cards), we fall back to Naismith.

Langmuir gentle-descent correction: Tobler's peak sits at exactly −5% grade and drops off symmetrically. In practice, walkers descend gentle-to-moderate downhills (roughly 6–22% grade) noticeably faster than Tobler predicts — Ellis Langmuir's Mountaincraft and Leadership (1984) added a rule subtracting ~10 minutes per 300 m of descent in that band. We apply the equivalent as a 12% speedup to any Tobler chunk with slope between −22% and −6%. Real trails with long descent sections (OLP day 3 out of Rock Run, LT east of Worlds End) come out closer to what experienced hikers actually clock.

Source: Tobler, W. (1993). "Three Presentations on Geographical Analysis and Modeling." National Center for Geographic Information and Analysis (NCGIA), Technical Report 93-1. Also widely reproduced in GIS + hiking-app documentation (e.g. GPS Visualizer, GRASS GIS r.walk).

Pace presets

Your pace scales the whole formula

Both Naismith and Tobler assume a specific flat-ground velocity. Naismith's paper was tuned for an unloaded, fit dayhiker — about 3 mph. Trail Sherpa's audience is mostly multi-day backpackers, so we scale the flat velocity by your chosen pace preset (Settings). Slower base velocity also proportionally slows climbing, since heavier loads and slower legs affect both.

Preset	Flat pace	Who it fits
Day hiker	~3.0 mph	Unloaded or a light daypack, fit legs. Naismith's original assumption.
Backpacker Default	~1.9 mph	Multi-day pack (25–35 lb), normal fitness. This is what we default new accounts to since Trail Sherpa is a backpacking planner.
Heavy load	~1.5 mph	Heavy pack, sustained steep climbs, or pacing for a slower partner.

Worked example

Why day 1 on the OLP comes out around 10 hours

The classic OLP clockwise day 1 — Masten to Pleasant Stream — is 10.07 miles with 4,804 ft of climbing. That's ~480 ft/mile of gain, which is genuinely steep by long-trail standards (the AT averages ~200 ft/mi, the PCT ~170 ft/mi). Let's break down the estimate at Backpacker (1.9 mph):

Step 1 · Naismith baseline (aggregate)

10.07 mi ÷ 1.9 mph = 5.30 hr flat

4,804 ft ÷ 2,000 ft × 1 hr × 1.61 (pace scale) = 3.87 hr climbing

→ Naismith alone ≈ 9 hr 16 min

Step 2 · Tobler + Langmuir across the actual profile

The Pleasant Stream day isn't a smooth climb — it front-loads with the Sprout Point ascent, then drops and climbs Sassafras Ridge. Tobler penalizes each steep pitch on its own terms rather than averaging them out; Langmuir gives back a bit on the moderate descent sections. Together they land ~10 hr of actual moving time — a bit above raw Naismith because the steep uphills cost more than the descents save.

→ Hiking = 10 hr 26 min · Total w/ breaks = 12 hr 31 min

The extra time vs. flat Naismith is honest — those steep sections really do slow you down more than the day-average grade suggests. That said, remember what the number covers:

Included

Time actively walking / climbing / descending
Grade penalty on every slope segment
Your pack's approximate slow-down (via pace preset)

Not included

Rest breaks, snacks, meals
Filtering water, changing layers, first-aid
Photo stops, viewpoints, exploration
Setting up or breaking camp

A rough rule of thumb: total wall-clock time = estimated hiking time × 1.15 to 1.30 for a typical day with normal breaks. A photo-heavy day or a group day can easily push past 1.5×. So the 10.5-hour Pleasant Stream day maps to roughly 12–13 hours of wall clock — trailhead to camp — for most people.

Tuning it to reality

If yours is consistently off, adjust the preset

The pace preset is the one knob that moves everything at once. If you consistently finish days 20% faster than the estimate, drop from Backpacker to Day hiker. If you're 20% slower — or hike with a slower partner — bump up to Heavy load.

We don't currently support per-day pace overrides (some days you're fresh, some days you're crawling), but that's on the roadmap.

Adjust your pace → Plan a multi-day trip