Data Source and Methodology
Authoritative sources:
- Appalachian Mountain Club (AMC) Book Time: 30 minutes per mile plus 30 minutes per 1,000 ft of ascent. Reference: AMC White Mountain Guide (latest edition). Official: AMC Outdoors – How to Estimate Hiking Time (2022).
- Naismith, W. W. (1892). “Naismith’s Rule” presented to the Scottish Mountaineering Club Journal.
- Langmuir, E. (1984, 2013). Mountaincraft and Leadership (Scottish Mountain Leader Training Board). Adds descent adjustments to Naismith.
All calculations strictly follow the formulas and data provided by these sources.
The Formulas Explained
AMC Book Time (imperial units)
$$t_{min} = 30\\cdot D_{mi} + 30\\cdot \\frac{G_{ft}}{1000}$$
Naismith (metric units)
$$t_{min} = 12\\cdot D_{km} + \\frac{G_{m}}{10}$$
Naismith–Langmuir (metric base)
$$t_{min} = 12\\cdot D_{km} + \\frac{G_{m}}{10} + A_{desc}$$
with descent adjustment
$$A_{desc} = \\begin{cases} -10\\cdot\\frac{L_m}{300}, & 5^\\circ \\le \\theta \\le 12^\\circ \\\\ +10\\cdot\\frac{L_m}{300}, & \\theta > 12^\\circ \\\\ 0, & \\theta < 5^\\circ \\end{cases} $$
where angle \(\\theta = \\arctan\\left(\\dfrac{\\text{descent}}{\\text{horizontal run}}\\right)\), approximated from total descent and route distance.
After the base formula, optional multipliers are applied: \(t' = t_{min} \\times M_{fitness} \\times M_{terrain} \\times M_{pack} + B\\), where \(B\) is planned breaks (minutes).
Glossary of Variables
- D_mi: Distance in miles (AMC Book Time).
- D_km: Distance in kilometers (Naismith variants).
- G_ft: Total elevation gain in feet (AMC).
- G_m: Total elevation gain in meters (Naismith variants).
- L_m: Total elevation loss in meters (used by Langmuir adjustment).
- θ: Average descent slope angle derived from descent over approximate horizontal distance.
- M_fitness: Fitness/pace multiplier (e.g., 1.25 leisurely, 1.0 average, 0.85 fast, 0.75 elite).
- M_terrain: Terrain multiplier (1.0 easy to 1.4 very rugged).
- M_pack: Pack weight multiplier (1.0 none to 1.12 heavy).
- B: Planned breaks in minutes added to total time.
- t_min: Calculated moving time in minutes before breaks.
- t': Total time in minutes after modifiers and breaks.
Come Funziona: Un Esempio Passo-Passo
Scenario: 10 miles with 3,000 ft of gain, average fitness, moderate terrain, daypack, 30 minutes breaks. Method: AMC Book Time.
- Compute distance time: 30 × 10 = 300 minutes.
- Compute ascent time: 30 × (3000 / 1000) = 90 minutes.
- Base moving time: 300 + 90 = 390 minutes = 6 h 30 min.
- Apply modifiers: Average fitness (1.0), Moderate terrain (1.1), Daypack (1.05) → multiplier ≈ 1.155. 390 × 1.155 ≈ 451 minutes.
- Add breaks: 451 + 30 ≈ 481 minutes ≈ 8 h 1 min total.
The calculator performs these steps automatically, converting units as needed.
Frequently Asked Questions (FAQ)
Is AMC Book Time too conservative?
It’s designed for trip planning with safety margins. Fast hikers may beat it; groups often match or exceed it.
How do I estimate elevation gain and loss?
Use a GPX track, digital topo map, or trusted hiking app. Avoid relying on net summit elevation only—total ascent is cumulative.
What if my hike is mostly downhill?
Use the Naismith–Langmuir method and enter your total descent. It subtracts time for moderate downhills and adds time for very steep ones.
Does altitude or heat affect the estimate?
Yes. High altitude, heat, snow, or mud can slow you significantly. Increase Terrain or Fitness multipliers to reflect conditions.
Can I plan group hikes?
Yes. Use “Leisurely” fitness, set Terrain appropriately, and add extra break time. Groups typically travel at the pace of the slowest member.
Will GPS pauses be included?
Moving time excludes breaks by definition. Add planned breaks to approximate total elapsed time.