Book Time vs. Naismith vs. Tobler: Comparing Hiking Time Formulas

When planning a hike, you'll encounter three major formulas for estimating hiking time: Book Time, Naismith's Rule, and Tobler's Hiking Function. Each has its strengths, limitations, and ideal use cases. This guide compares all three methods so you can choose the right one for your adventure.

Quick Comparison Table

| Formula | Origin | Best For | Typical Estimate | Complexity | |---------|--------|----------|-----------------|------------| | Book Time | White Mountains (1940s) | Beginners, conservative planning | Most conservative (slowest) | Very simple | | Naismith's Rule | Scotland (1892) | General hiking, moderate terrain | Middle estimate | Simple | | Tobler's Function | Academic study (1993) | Variable slopes, technical terrain | Accounts for slope angle | Mathematical |

Book Time: The Conservative Standard

What Is Book Time?

Book Time originated in the White Mountains of New Hampshire and was popularized by the Appalachian Mountain Club (AMC) in the 1940s. The name comes from its use in guidebooks and trail signs throughout the Northeast.

The Formula

Book Time is wonderfully simple:

Base Formula:

  • 30 minutes per mile of horizontal distance
  • 30 minutes per 1,000 feet of elevation gain

That's it. No complicated math—just add up miles and elevation.

Example Calculation

Planning a 6-mile hike with 2,500 feet of elevation gain:

  1. Distance time: 6 miles × 30 min/mile = 180 minutes (3 hours)
  2. Ascent time: 2,500 feet ÷ 1,000 = 2.5 × 30 min = 75 minutes (1 hour 15 minutes)
  3. Total Book Time: 3 hours + 1 hour 15 minutes = 4 hours 15 minutes

When to Use Book Time

Book Time is ideal for:

  • Beginners: If you're new to hiking, Book Time provides a conservative buffer
  • Group hikes: Larger groups move slower; Book Time accounts for this naturally
  • White Mountains: The formula was developed here and is calibrated for Northeast terrain
  • Family hikes: When hiking with kids or less experienced hikers
  • Conservative planning: When you want to ensure you finish before dark

Regional Variations

Different hiking regions have adapted Book Time to local conditions:

Adirondacks (New York):

  • 30 min/mile + 30 min/1,000 ft (same as White Mountains)
  • Some trails add "rugged terrain" notes suggesting +20% time

Colorado Rockies:

  • 30 min/mile + 30 min/1,000 ft for trails below treeline
  • 35-40 min/mile above treeline due to altitude

Pacific Crest Trail:

  • 25-30 min/mile for experienced thru-hikers
  • Book Time is considered too conservative for fit backpackers

Strengths of Book Time

  1. Extremely simple: Anyone can calculate it mentally
  2. Conservative: You're unlikely to be late if you use Book Time
  3. Well-tested: Decades of use in popular hiking areas
  4. Safe planning: Built-in buffer helps prevent after-dark finishes

Limitations of Book Time

  1. Often too slow: Fit hikers regularly beat Book Time by 30-40%
  2. No descent adjustment: Assumes downhill is "free" (not true on steep, rocky descents)
  3. Regional bias: Calibrated for Northeast trails, less accurate elsewhere
  4. No terrain adjustment: Same estimate for smooth trail vs. rocky scramble

Naismith's Rule: The Classic Standard

Background

Created by Scottish mountaineer William W. Naismith in 1892, this is the original hiking time formula. It's been refined over 130+ years and remains the international baseline.

The Formula

Naismith's Rule has two components:

Base Formula:

  • 5 kilometers per hour (3.1 mph) on flat ground
  • Add 1 hour for every 600 meters (about 2,000 feet) of ascent

In imperial units:

  • 3 mph on flat terrain
  • Add 30 minutes per 1,000 feet of climbing

Example Calculation

Same 6-mile hike with 2,500 feet of elevation gain:

  1. Distance time: 6 miles ÷ 3 mph = 2 hours
  2. Ascent time: 2,500 feet ÷ 1,000 = 2.5 × 30 min = 75 minutes (1 hour 15 minutes)
  3. Total Naismith: 2 hours + 1 hour 15 minutes = 3 hours 15 minutes

Note: Naismith is 1 hour faster than Book Time for the same hike!

When to Use Naismith's Rule

Naismith's Rule excels for:

  • Moderate terrain: Well-maintained trails with typical conditions
  • International hiking: Widely recognized worldwide
  • Average fitness hikers: Those with regular hiking experience
  • Quick estimates: Easy mental math while on the trail
  • General planning: When you don't need extreme precision

Strengths of Naismith's Rule

  1. Widely known: The "standard" hiking formula globally
  2. Well-calibrated: Accurate for average hikers on typical trails
  3. Simple math: Easy to calculate without a calculator
  4. Proven track record: 130+ years of refinement
  5. Basis for other methods: Many formulas are "Naismith + adjustments"

Limitations of Naismith's Rule

  1. Ignores descent: Original formula doesn't penalize downhill
  2. Assumes average fitness: May not match your personal pace
  3. No terrain factor: Rocky scrambles take longer than smooth trails
  4. Less accurate on extremes: Struggles with very steep or very gentle slopes

Common Modifications

Many hikers modify Naismith to better fit their needs:

Tranter's Corrections:

  • Adjust for fitness level (very fit to novice)
  • Add fatigue factors for long days (10+ hours)

Langmuir's Improvements:

  • Add 10 minutes per 1,000 feet of descent on steep trails
  • Adjust for rugged terrain (+15-50%)

Tobler's Hiking Function: The Physicist's Approach

Background

Developed by geographer Waldo Tobler in 1993, this formula takes a mathematical approach based on the physics of walking. Unlike Book Time and Naismith (which are empirical observations), Tobler's function models how slope angle affects walking speed.

The Formula

Tobler's function is more complex:

Speed (km/h) = 6 × e^(-3.5 × |slope + 0.05|)

Where:

  • slope = elevation change ÷ horizontal distance (as a decimal)
  • e is Euler's number (~2.718)
  • The optimal speed occurs at a -5% downhill grade (slope = -0.05)

Don't worry—you won't calculate this by hand! This is what our calculator is for.

How It Works

Tobler's function recognizes that:

  • Flat ground: You walk at a moderate pace (~5-6 km/h)
  • Gentle downhill (-5% grade): You walk fastest (~6 km/h)
  • Steep uphill: You slow down exponentially
  • Steep downhill: You also slow down (watching your footing)

This creates a curve where speed varies smoothly with slope angle.

Example Calculation

For our 6-mile hike with 2,500 feet of gain:

Manual calculation is complex, but the result is approximately:

Total Tobler Time: ~3 hours 20 minutes

This is close to Naismith but accounts for the specific slope profile.

When to Use Tobler's Function

Tobler is best for:

  • Variable terrain: Routes with changing slopes (up, down, flat sections)
  • Steep descents: Accurately models slowdown on steep downhills
  • Long-distance planning: More precise for multi-day trips
  • Off-trail travel: Better than Naismith for cross-country routes
  • Academic accuracy: When you need physics-based modeling

Strengths of Tobler's Function

  1. Slope-aware: Accounts for both ascent and descent with precision
  2. Continuous model: Smoothly adjusts for slope changes
  3. Scientifically grounded: Based on biomechanics research
  4. Accurate on extremes: Better than Naismith on very steep or gentle terrain
  5. No arbitrary constants: Formula derived from walking mechanics

Limitations of Tobler's Function

  1. Complex math: Requires a calculator or app
  2. Less intuitive: Hard to understand why it works
  3. Needs slope data: Requires detailed elevation profile
  4. Still doesn't account for terrain: Assumes consistent trail quality
  5. Less widely known: Not as universal as Naismith

Head-to-Head Comparison

Let's compare all three methods on real hiking routes:

Example 1: Mount Washington via Tuckerman Ravine Trail

Route Details:

  • Distance: 8.4 miles round trip
  • Elevation gain: 4,250 feet
  • Terrain: Rocky trail, above treeline

| Method | Estimate | Reality Check | |--------|----------|---------------| | Book Time | 6h 45m | Conservative (most hikers: 5-7 hours) | | Naismith | 5h 0m | Slightly optimistic (rocky terrain) | | Tobler | 5h 15m | Very accurate for average hikers |

Winner: Tobler, with Book Time as safe fallback

Example 2: Presidential Traverse (White Mountains)

Route Details:

  • Distance: 19-23 miles (route dependent)
  • Elevation gain: 8,500-9,000 feet
  • Terrain: Mix of rocky trail and exposed ridge

| Method | Estimate | Reality Check | |--------|----------|---------------| | Book Time | 13h 30m | Matches strong hikers; too conservative for very fit | | Naismith | 10h 0m | Too optimistic (doesn't account for difficulty) | | Tobler | 11h 15m | Good for fit hikers; add 20% for terrain |

Winner: Book Time for planning, Tobler with terrain adjustment for accuracy

Example 3: Moderate Day Hike (Well-Maintained Trail)

Route Details:

  • Distance: 5 miles round trip
  • Elevation gain: 1,200 feet
  • Terrain: Smooth, well-graded trail

| Method | Estimate | Reality Check | |--------|----------|---------------| | Book Time | 3h 6m | Too conservative (easy trail) | | Naismith | 2h 18m | Spot-on for average hikers | | Tobler | 2h 25m | Very close to Naismith |

Winner: Naismith for simplicity; all methods agree within 15 minutes

Which Formula Should You Use?

Choose Book Time If You're:

  • New to hiking or returning after a long break
  • Hiking with a group of varied abilities
  • Planning a trip in the White Mountains or Adirondacks
  • Prefer conservative estimates to avoid after-dark finishes
  • Not confident in your fitness level

Example scenario: Family hike with kids and elderly relatives on a New England 4000-footer.

Choose Naismith's Rule If You're:

  • An intermediate hiker with regular experience
  • Planning a moderate hike on well-maintained trails
  • Need a quick mental estimate while on the trail
  • Hiking solo or with similar-ability partners
  • Want an internationally recognized baseline

Example scenario: Weekend day hike on your local mountain, solo or with experienced friends.

Choose Tobler's Function If You're:

  • Planning a long-distance or multi-day trek
  • Dealing with significant elevation changes (lots of up and down)
  • Hiking on variable terrain with changing slopes
  • Want the most precise mathematical model
  • Have detailed elevation profile data

Example scenario: Planning a thru-hike on the John Muir Trail or calculating stage times for a multi-day backpacking trip.

Combining Methods for Best Results

Smart hikers often use multiple formulas:

The "Range Estimate" Approach

  1. Calculate Book Time for your worst-case scenario
  2. Calculate Naismith for your expected time
  3. Calculate Tobler for precision

Example result:

  • Book Time: 6 hours (plan to start by 10 AM if sunset is 6 PM)
  • Naismith: 4.5 hours (expect to finish around 3:30 PM)
  • Tobler: 4 hours 45 minutes (very close to Naismith)

This gives you a range of 4-6 hours, letting you plan conservatively while understanding your likely finish time.

Adjustments for All Methods

Regardless of which formula you use, add time for:

  • Breaks: 5-10 minutes per hour for water/snacks
  • Photos: 10-30 minutes for summit/scenic stops
  • Navigation: 5-15 minutes if route-finding is needed
  • Group dynamics: +20% for groups of 4+
  • Difficult terrain: +15-30% for rocky, muddy, or technical sections

Advanced: Weighted Average Approach

Our hiking time calculator uses a weighted average of all three methods:

Likely Time = (0.3 × Book Time) + (0.4 × Naismith) + (0.3 × Tobler)

This combines the conservative safety of Book Time, the proven accuracy of Naismith, and the slope precision of Tobler into a single, balanced estimate.

We also provide:

  • Best case: Optimistic estimate for fit hikers
  • Worst case: Conservative estimate accounting for challenges

This range gives you flexibility while keeping safety margins.

Practical Tips

Track Your Personal Multiplier

After 5-10 hikes, you'll notice patterns:

  • "I'm consistently 15% faster than Naismith" → Multiply Naismith by 0.85
  • "Book Time is always 30% too slow for me" → Multiply by 0.70
  • "Tobler is perfect for me" → Use Tobler as-is

Keep a hiking log and compare your actual vs. estimated times.

Adjust for Experience Level

Beginner (< 10 hikes):

  • Use Book Time or add 20-30% to Naismith
  • Plan for 1.5-2 mph pace instead of 3 mph

Intermediate (10-50 hikes):

  • Naismith or Tobler will likely match your pace
  • Trust the formulas but add break time

Advanced (50+ hikes, regular fitness):

  • You may beat Naismith by 10-20%
  • Consider Tobler with personal pace adjustments

Seasonal Adjustments

Summer:

  • Add 10-15% in extreme heat (>85°F)
  • Add 5-10% for high humidity

Winter:

  • Add 20-30% for snow travel (even with snowshoes)
  • Add 10-20% for ice (microspikes needed)

Mud Season:

  • Add 15-25% for slippery, slow trails

Conclusion

There's no single "best" formula—each has its place:

  • Book Time is your safe, conservative friend for uncertain conditions
  • Naismith's Rule is the reliable, universal standard for everyday hiking
  • Tobler's Function is the precise, mathematical model for detailed planning

For most hikers, starting with Naismith's Rule and adding 10-20% for safety is a great approach. As you gain experience, you'll develop intuition for when to switch methods or apply adjustments.

The most important thing? Track your actual hiking times and learn how your pace compares to the formulas. Your personal experience is the best calibration tool.

Ready to compare all three methods for your next hike? Use our hiking time calculator to see side-by-side estimates and make informed planning decisions.

Further Reading

References:

  • Naismith, W. W. (1892). "Excursions." Scottish Mountaineering Club Journal.
  • Appalachian Mountain Club (1940s-present). White Mountains guidebooks.
  • Tobler, W. (1993). "Three presentations on geographical analysis and modeling." Technical Report 93-1, NCGIA.
  • Langmuir, E. (1984). "Mountaincraft and Leadership."
  • Scarf, P. (1998). "Route planning and estimation of journey time." Journal of Navigation.