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Hiking Time Calculator

Estimates the time for a hike from distance, ascent and descent with Naismith's rule (1 h per 5 km plus 1 h per 600 m of ascent), Naismith with Langmuir's descent corrections, or Tobler's hiking function (speed = 6·e^(−3.5·|slope + 0.05|) km/h), with a pace factor for slower parties and optional breaks; all three estimates are reported.

When to use

You need a planning time for a walk or mountain hike from map distance and elevation gain/loss, or want to compare the Naismith and Tobler estimates.

Do not use when: You need running pace or race predictions (use running-pace or race-time-predictor), the route involves scrambling, snow, heavy loads or trackless terrain (the rules assume walkable paths), or you have a full elevation profile (segment-wise Tobler is more accurate than the whole-route net gradient used here).

Formula

Naismith: t = distance_km / 5 + ascent_m / 600 (hours). Langmuir: t = Naismith − descent_m / 300 × 10 min (gentle 5–12° descent) or + descent_m / 300 × 10 min (descent steeper than 12°). Tobler: v = 6 · e^(−3.5 · |(ascent_m − descent_m) / (1000 · distance_km) + 0.05|) km/h, t = distance_km / v. moving_time_hours = t × pace_factor; time_hours = moving_time_hours × (1 + break_minutes_per_hour / 60)

Naismith's rule (1892) and Langmuir's corrections (1984) are planning heuristics for fit walkers on paths; Tobler's function (1993) is an exponential fit to Imhof's walking data with a maximum of 6 km/h on a slight −5 % downhill. Applying Tobler to a whole route uses the net gradient, so a route with equal ascent and descent is treated as flat and its time is underestimated; descents on slopes below 5° get no Langmuir correction and should be left out of descent_m.

Inputs

ParameterTypeUnitRequiredDescription
distance_kmnumberkmyesHorizontal (map) distance of the route in kilometres. Range: > 0, ≤ 500
ascent_mnumbermdefault 0Cumulative elevation gain in metres. Range: ≥ 0, ≤ 20000
descent_mnumbermdefault 0Cumulative elevation loss in metres (used by the Langmuir corrections and by Tobler's net slope). Range: ≥ 0, ≤ 20000
methodenum: naismith | naismith_langmuir | toblerdefault naismithRule used for the primary time; the other estimates are still reported.
descent_steepbooleandefault falseLangmuir only: true when the descent is on slopes steeper than 12° (adds 10 min per 300 m of descent); false treats it as a gentle 5–12° descent (subtracts 10 min per 300 m).
pace_factornumberdefault 1Multiplier on the moving time: 1.0 = fit walker (Naismith's 5 km/h), 1.25 = slower or laden group (Langmuir's 4 km/h), 1.5 = family with children. Range: ≥ 0.5, ≤ 3
break_minutes_per_hournumbermin/hdefault 0Rest time added per hour of moving time. Range: ≥ 0, ≤ 30

Outputs

OutputTypeUnitDescription
time_hoursnumberhMoving time by the chosen method plus breaks.
time_textstringTotal time as hours and minutes, e.g. '2 h 50 min'.
moving_time_hoursnumberhTime by the chosen method with pace_factor applied, without breaks.
average_speed_km_hnumberkm/hdistance_km / time_hours (breaks included).
ascent_time_minutesnumberminNaismith's ascent allowance: 1 minute per 10 m of ascent, × pace_factor.
naismith_time_hoursnumberhNaismith's rule moving time × pace_factor, always reported.
naismith_langmuir_time_hoursnumberhNaismith's rule with Langmuir's descent correction, × pace_factor, always reported.
tobler_time_hoursnumberhdistance_km / Tobler speed at the route's net slope (ascent − descent) / distance, × pace_factor, always reported.
tobler_speed_km_hnumberkm/h6·e^(−3.5·|slope + 0.05|) at the net slope; 5.04 km/h on the flat, 6 km/h maximum at a −5 % descent.

Example

10 km with 500 m ascent, Naismith: {"distance_km":10,"ascent_m":500,"method":"naismith"} → {"time_hours":2.83,"time_text":"2 h 50 min","moving_time_hours":2.83,"average_speed_km_h":3.53,"ascent_time_minutes":50,"naismith_time_hours":2.83,"tobler_time_hours":2.37,"tobler_speed_km_h":4.23}

12 km, 800 m up and down, Langmuir, 10 min breaks per hour: {"distance_km":12,"ascent_m":800,"descent_m":800,"method":"naismith_langmuir","break_minutes_per_hour":10} → {"moving_time_hours":3.29,"time_hours":3.84,"time_text":"3 h 50 min","naismith_time_hours":3.73,"naismith_langmuir_time_hours":3.29,"tobler_time_hours":2.38,"tobler_speed_km_h":5.04}

GET https://tttkmbb.com/api/v1/calculate/hiking-time?distance_km=10&ascent_m=500&method=naismith

Machine access

Sources

FAQ

Which method should I use?

Naismith for a first estimate on trails; add Langmuir's corrections when the route has long descents; Tobler when the gradient is fairly uniform (here it sees only the net gradient of the whole route).

Is distance_km the map distance or the GPS track length?

The horizontal map distance, which is what all three rules expect; a 3D track length is slightly longer on steep ground and would over-estimate the time.

How do I allow for a slower group?

pace_factor scales the moving time: 1.25 corresponds to Langmuir's 4 km/h base speed for less fit or heavily laden parties; breaks are added separately with break_minutes_per_hour.

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