Calculating Board Feet in Logs: Complete Guide to Log Scaling Rules

Calculating board feet in round logs is fundamentally different from calculating board feet in sawn lumber. While lumber uses a simple formula, logs require specialized scaling rules that account for the circular cross-section, bark, taper, and sawing waste.

Last reviewed: November 8, 2025 by the Board Foot Calculator forestry advisor panel.

This comprehensive guide explains the three major international log scaling rules—Doyle, Scribner, and International—and helps you choose the right one for your needs.

Related: New to board feet? Start with What is a Board Foot? | For sawn lumber, see Board Foot Formula

In this guide:

• The fundamental differences between log and lumber calculations
• Detailed explanation of all three major scaling rules
• Side-by-side comparisons with real examples
• How to choose the right rule for your situation
• Understanding recovery rates and practical applications

Quick Navigation: Use our Log Calculator to compare all three rules instantly.

Log vs Lumber Calculation: Key Differences

Before diving into the scaling rules, it’s crucial to understand why log calculations are so different from lumber calculations.

Difference 1: Cross-Section Shape

Lumber (Rectangular):

• Sawn lumber has a rectangular cross-section
• Dimensions are straightforward: thickness × width × length
• Formula applies directly: (T × W × L) / 144

Logs (Circular):

• Round logs have a circular cross-section
• Must account for conversion from circle to rectangles
• Significant waste when sawing round logs into square boards
• The larger the log, the better the recovery rate

Difference 2: Loss Factors

Lumber:

• Already processed into standard sizes
• Loss already reflected in nominal vs actual dimensions
• Minimal additional waste

Logs:

• Bark must be removed (typically 10-15% of diameter)
• Sapwood may be unusable depending on species
• Saw kerf (blade thickness) removes material
• Defects, knots, and rot reduce usable wood
• Taper from one end to the other affects yield

Difference 3: Measurement Methods

Lumber:

• Direct measurement with tape or ruler
• Three simple dimensions: T, W, L

Logs:

• Small End Diameter (SED): Measured at the smaller end, inside bark
• Large End Diameter: Sometimes measured for taper calculation
• Length: Measured along the log, excluding severe defects
• Taper: The gradual decrease in diameter from butt to top

Difference 4: Standardization

Lumber:

• Universal formula worldwide
• Consistent calculation method

Logs:

• Multiple scaling rules in use
• Different regions prefer different rules
• Results can vary by 50-500% for the same log!
• Choice of rule significantly impacts pricing

Key Variables in Log Measurement

Understanding these variables is essential for accurate log scaling.

Small End Diameter (SED)

Definition: The diameter of the log at its smaller end, measured inside the bark (after bark removal).

Why it matters:

• All three major scaling rules use SED as the primary measurement
• SED determines the maximum size of boards that can be cut
• Measuring the wrong end (large end) will significantly overestimate yield

How to measure:

• Use a diameter tape or calipers
• Measure across the center of the log
• Take two measurements at 90° angles and average them
• Measure inside bark (deduct bark thickness if measuring outside)

Common mistake: Using the large end diameter instead of small end can overestimate yield by 20-40%.

Length

Definition: The usable length of the log, measured from small end to large end.

Industry standards:

• Typically sold in 2-foot or 4-foot increments
• Common lengths: 8’, 10’, 12’, 14’, 16’
• Longer logs (20’+ ) are less common and may command premium prices

Measurement tips:

• Exclude sections with severe defects, rot, or excessive crook
• Round down to the nearest standard length
• Some rules require specific length increments

Taper

Definition: The gradual decrease in diameter from the large end (butt) to the small end (top).

Impact on calculations:

• Greater taper = lower usable yield
• Doyle rule: Uses only SED, implicitly accounts for taper
• Scribner rule: Based on SED, conservative for tapered logs
• International rule: Mathematically accounts for taper in the formula

Typical taper rates:

• Conifers (pine, fir): 0.5-1 inch per 8 feet
• Hardwoods (oak, maple): 0.75-1.5 inches per 8 feet

Defect Deduction

Types of defects:

• Rot and decay: Reduces usable length or diameter
• Cracks and splits: May require trimming
• Excessive knots: Affects grade and usability
• Crook (bend): Reduces straight board yield

How defects are handled:

• Severe defects: Deduct from length
• Minor defects: May reduce grade but not volume
• Standards vary by region and industry

The Three Major Log Scaling Rules

Now let’s explore each of the three internationally recognized scaling rules in detail.

Doyle Rule

The Doyle Rule is the oldest and simplest log scaling formula, widely used in North American hardwood markets.

Formula

Board Feet = [(D - 4)² × L] / 16

Where:

• D = Small End Diameter (inches, inside bark)
• L = Length (feet)
• 4 = Assumed loss for bark, slab, and saw kerf (inches)
• 16 = Conversion factor

Example Calculation

For a log with D = 20 inches, L = 12 feet:

Board Feet = [(20 - 4)² × 12] / 16
           = [16² × 12] / 16
           = [256 × 12] / 16
           = 3,072 / 16
           = 192 board feet

Historical Background

• Developed in 1825 by Edward Doyle
• First widely adopted log scaling rule in North America
• Based on simple arithmetic for easy field calculation
• Still used in traditional hardwood markets, especially in the eastern United States

Advantages

✅ Extremely simple - Easy to calculate mentally in the field
✅ Traditional acceptance - Long history in hardwood markets
✅ Conservative for small logs - Protects buyers from overestimating
✅ Reasonable for large logs - Accuracy improves with diameter

Disadvantages

❌ Severely underestimates small logs - Logs under 16” are drastically undervalued
❌ Unfair to sellers of small timber - Can underestimate by 50-70%
❌ Not suitable for D < 12” - Results become unrealistic
❌ Exaggerates diameter differences - Small diameter changes cause large volume swings

Best Use Cases

• Hardwood markets in the eastern United States
• Buyer’s market situations (conservative estimates)
• Large diameter logs (D ≥ 20 inches)
• Traditional transactions where Doyle is the established standard

⚠️ Avoid using Doyle for: Small diameter logs (< 16”), softwood markets, or situations requiring accurate yield estimates.

Scribner Rule

The Scribner Rule is based on actual diagrams of board layouts and is the most widely used rule in North American softwood markets.

Formula

The Scribner Rule uses a lookup table called the “Scribner Decimal C” scale. However, an approximate formula exists:

Board Feet ≈ (0.79 × D² × L) - (2 × D × L)

Where:

• D = Small End Diameter (inches, inside bark)
• L = Length (feet)

Note: Professional use relies on official Scribner tables, not the approximation formula.

Example Calculation

For a log with D = 20 inches, L = 12 feet:

Using the approximation:

Board Feet ≈ (0.79 × 20² × 12) - (2 × 20 × 12)
           ≈ (0.79 × 400 × 12) - (480)
           ≈ 3,792 - 480
           ≈ 3,312 / 16
           ≈ 207 board feet

Using official Scribner Decimal C table: 230 board feet

(The approximation is less accurate; always use official tables when available.)

Historical Background

• Developed in 1846 by J.M. Scribner
• Based on hand-drawn diagrams of 1-inch boards laid out on log cross-sections
• Scribner physically drew circles representing log ends and fit rectangles inside
• Published as the “Scribner Decimal C” table (rounded to nearest 10 board feet)
• Official standard for U.S. National Forest System

Advantages

✅ Based on actual board layouts - More realistic than pure mathematical formulas
✅ Balanced for buyers and sellers - Fair middle ground
✅ Wide diameter range - Works well from 12” to 60”
✅ Industry standard - Most common rule in U.S. softwood markets
✅ Official government standard - Used for federal timber sales

Disadvantages

❌ Requires lookup table - Cannot easily calculate mentally
❌ Still underestimates small logs - Though less severe than Doyle
❌ Assumes 1/4” saw kerf - Modern thin-kerf saws waste less
❌ Rounded values - Decimal C rounds to nearest 10 BF

Best Use Cases

• Softwood markets (pine, fir, spruce)
• U.S. National Forest timber sales
• Balanced transactions between buyers and sellers
• Sawmill log purchases
• General-purpose scaling when no specific rule is mandated

Recommended for: Most general applications in North America, especially softwood species.

International Rule (1/4” and 1/8”)

The International Rule is a mathematically derived formula based on cylinder geometry and is considered the most accurate modern scaling rule.

Formulas

International 1/4” (Traditional sawmills):

Board Feet = (0.22 × D² × L) - (0.71 × D × L)

International 1/8” (Modern thin-kerf saws):

Board Feet = (0.22 × D² × L) - (0.36 × D × L)

Where:

• D = Small End Diameter (inches, inside bark)
• L = Length (feet)
• 0.22 = Cylinder volume conversion factor
• 0.71 or 0.36 = Saw kerf deduction (1/4” or 1/8” blade)

Example Calculations

For a log with D = 20 inches, L = 12 feet:

International 1/4”:

Board Feet = (0.22 × 20² × 12) - (0.71 × 20 × 12)
           = (0.22 × 400 × 12) - (170.4)
           = 1,056 - 170.4
           = 885.6 board feet

International 1/8”:

Board Feet = (0.22 × 20² × 12) - (0.36 × 20 × 12)
           = (0.22 × 400 × 12) - (86.4)
           = 1,056 - 86.4
           = 969.6 board feet

Historical Background

• Developed 1906-1917 by Judson F. Clark
• Based on mathematical cylinder volume calculations
• Accounts for taper by treating log as a frustum (truncated cone)
• Two versions for different saw kerf widths
• Recommended by international forestry organizations

Advantages

✅ Mathematically rigorous - Based on solid geometry principles
✅ No lookup tables needed - Can be calculated with a formula
✅ Fair across all diameters - Doesn’t penalize small logs
✅ Accounts for modern equipment - 1/8” version matches thin-kerf saws
✅ International standard - Facilitates cross-border comparisons
✅ Most accurate estimates - Closest to actual mill recovery

Disadvantages

❌ Complex formula - Difficult to calculate mentally
❌ Higher estimates - Results favor sellers, buyers may resist
❌ Less traditional acceptance - Not standard in many U.S. markets
❌ Requires calculator - Not practical for quick field estimates

Best Use Cases

• International timber trade
• Modern sawmills with thin-kerf equipment (use 1/8” version)
• Scientific research and forestry statistics
• Seller’s market situations
• Accurate yield planning
• Cross-regional comparisons

Recommended for: Operations prioritizing accuracy, modern equipment, or international standards.

Comparison Examples: Same Log, Different Rules

Let’s see how dramatically the three rules differ when applied to the same logs.

Example A: Small Diameter Log (12” × 16’)

Data from the US Forest Service log scaling tables show that a 12-inch small-end log, 16 feet long, scales very differently depending on the rule you apply:

Takeaway: Doyle understates small logs by roughly 30% compared with International 1/4”. If you are selling small-diameter hardwoods, insist on a rule that credits the additional recoverable lumber.

Example B: Medium Diameter Log (20” × 16’)

Takeaway: At common saw-log diameters (18”–22”), Doyle can reduce the payable volume by more than 30% relative to International. Scribner sits between the two and is typically chosen for balanced transactions in softwood markets.

Example C: Large Diameter Log (32” × 16’)

Takeaway: Differences shrink for very large logs, but International 1/4” still reports ~15% more yield than Doyle. Mills with thin-kerf equipment routinely approach the International values in production.

Summary Comparison Table

Key Takeaway: The choice of scaling rule has enormous impact on calculated volume, especially for small to medium diameter logs. Always clarify which rule is being used in timber transactions and, when possible, cite the same published tables to keep negotiations transparent.

How to Choose the Right Scaling Rule

Selecting the appropriate scaling rule depends on your specific situation, regional standards, and log characteristics.

Decision Framework

Step 1: Check Regional Standards

Different regions have established preferences:

Step 2: Consider Your Role

Step 3: Evaluate Log Diameter

Quick Selection Guide

Use Doyle if:

• ✅ Required by local market tradition (eastern U.S. hardwoods)
• ✅ You’re the buyer and want conservative estimates
• ✅ Log diameter is consistently > 20 inches
• ❌ Avoid for logs < 16 inches

Use Scribner if:

• ✅ Selling to U.S. National Forest System
• ✅ You want a balanced, widely accepted standard
• ✅ Working with softwood species
• ✅ Need a middle ground between buyer and seller

Use International 1/4” if:

• ✅ Engaged in international timber trade
• ✅ Need scientific accuracy for research
• ✅ Working with traditional sawmill equipment
• ✅ Want fair estimates across all log sizes

Use International 1/8” if:

• ✅ Operating modern thin-kerf sawmill
• ✅ Want most accurate yield predictions
• ✅ Selling logs and want maximum value
• ✅ Planning production with precision equipment

Log to Lumber Conversion: Understanding Recovery Rates

Log board feet (calculated by scaling rules) ≠ Actual lumber board feet (what you get from the mill)

Typical Recovery Rates

Recovery rate = (Actual lumber output / Log scale input) × 100%

Factors Affecting Recovery Rate

1. Sawing Method

• Plain sawn (flat sawn): Fastest, moderate recovery (50-60%)
• Quarter sawn: Slower, lower recovery (40-50%), premium lumber
• Rift sawn: Slowest, lowest recovery (35-45%), highest quality

2. Equipment Precision

• Traditional circular saws: 1/4” kerf, more waste
• Modern band saws: 1/8” kerf, less waste
• Thin-kerf technology: < 1/8” kerf, maximum recovery

3. Log Quality

• Straight, clear logs: 55-65% recovery
• Moderate defects: 45-55% recovery
• Severe defects, crook: 30-45% recovery

4. Operator Skill

• Experienced sawyer: +5-10% recovery improvement
• Optimized cutting patterns: Maximize board yield
• Defect management: Minimize waste from knots and rot

Practical Application

When purchasing logs:

• Budget for 80-90% of the scaled volume as actual lumber
• Add 10-15% buffer for defects and waste
• Example: Need 1,000 BF of lumber → Purchase logs scaling to 1,150-1,250 BF

When selling logs:

• Understand that buyers expect recovery rates < 100%
• Price negotiations often factor in expected waste
• Doyle-scaled logs may sell at higher $/BF to compensate for underestimation

Frequently Asked Questions

Why do different log scaling rules give such different results?

Each rule was developed at a different time, for different purposes, and with different assumptions about sawing technology and waste.

Doyle (1825) assumed very crude sawing with thick blades and significant waste, plus a simple formula for field calculation. It works reasonably well for large logs but severely underestimates small logs because the fixed 4-inch deduction represents a much larger percentage of small diameters.

Scribner (1846) was based on actual hand-drawn board layouts, making it more realistic. However, it still assumes 1/4-inch saw kerf and rounds to the nearest 10 board feet, introducing some inaccuracy.

International (1906-1917) uses mathematical cylinder geometry and can account for modern thin-kerf saws (1/8” version). It’s the most accurate but also the most generous, which is why some buyers resist it.

The differences can exceed 500% for small logs because the rules make fundamentally different assumptions about waste and recovery.

Which scaling rule should I use for my logs?

Short answer: Use whatever rule is standard in your region and market, unless you have a specific reason to choose differently.

Detailed guidance:

1. Check local standards first - Most timber markets have an established rule
2. Consider your role - Buyers prefer conservative rules (Doyle/Scribner), sellers prefer generous rules (International)
3. Match your equipment - Modern thin-kerf mills should use International 1/8”
4. Avoid Doyle for small logs - Never use Doyle for logs under 16 inches diameter

For most general purposes: Scribner is the safest choice as it’s widely accepted and reasonably balanced.

Should I measure the small end or large end diameter?

Always measure the small end diameter (SED) for all three major scaling rules.

Why the small end?

• The small end limits the maximum board size you can cut
• Using the large end would overestimate yield by 20-40%
• All official scaling rules specify small end measurement
• Industry standard practice worldwide

How to measure correctly:

• Measure inside the bark (after debarking, or estimate bark thickness)
• Take two measurements at 90° angles
• Average the two measurements
• Round to the nearest inch

Exception: Some specialized rules (like the Huber formula) use the mid-point diameter, but these are rare and not covered in this guide.

How do I handle logs with significant taper?

Taper (the decrease in diameter from butt to top) is automatically accounted for in all three major rules, though in different ways:

Doyle and Scribner:

• Use only the small end diameter
• Implicitly conservative for tapered logs
• No additional calculation needed

International:

• Mathematical formula accounts for typical taper
• Assumes log is a frustum (truncated cone)
• More accurate for heavily tapered logs

For extremely tapered logs:

• Consider scaling in sections (e.g., two 8’ logs instead of one 16’ log)
• Measure each section’s small end diameter
• Sum the board feet from each section
• This gives a more accurate estimate but requires more work

Practical tip: If taper exceeds 2 inches over 8 feet, consider sectioning the log for more accurate scaling.

Do I need to account for bark when measuring diameter?

Yes, absolutely. All three major scaling rules require inside-bark diameter measurements.

Why it matters:

• Bark is not usable lumber
• Bark thickness varies by species (0.5” to 2”+)
• Using outside-bark measurements overestimates volume by 10-25%

How to measure inside bark:

Option 1: After debarking (most accurate)

• Measure the log after bark removal
• Direct measurement of usable wood diameter

Option 2: Estimate bark thickness

• Measure outside bark diameter
• Deduct 2× bark thickness (both sides)
• Example: 14” outside bark, 0.75” bark thickness → 14” - (2 × 0.75”) = 12.5” inside bark

Typical bark thickness by species:

• Thin bark (0.25-0.5”): Birch, beech, maple
• Medium bark (0.5-1”): Oak, ash, pine
• Thick bark (1-2”+): Hickory, old-growth conifers, cork oak

Can I convert between different scaling rules?

No simple conversion exists because the rules use fundamentally different calculation methods. However, you can use approximate conversion factors for rough estimates:

Rough conversion factors (for medium logs, 16-24” diameter):

• Doyle to Scribner: Multiply by 1.2-1.3
• Doyle to International 1/4”: Multiply by 1.4-1.6
• Scribner to International 1/4”: Multiply by 1.15-1.25

⚠️ Warning: These factors are very approximate and vary significantly with log diameter. For accurate conversions, you must recalculate using the actual rule formulas or tables.

Best practice: Always specify which rule was used and recalculate if a different rule is required. Use our Log Calculator to compare all three rules instantly.

What’s the difference between log board feet and lumber tally?

Log board feet (Log Scale):

• Estimated volume calculated using a scaling rule
• Measured on standing trees or felled logs
• Used for pricing and timber sales
• Always an approximation

Lumber tally:

• Actual board feet of lumber produced after sawing
• Measured after milling is complete
• Reflects real yield after all waste
• The true usable volume

Key differences:

Typical relationship: Lumber tally is usually 40-60% of log scale, depending on the scaling rule, sawing method, and log quality.

Are there other log scaling rules besides these three?

Yes, several other rules exist, though they’re less common:

Regional rules:

• Roy Rule: Used in Quebec, Canada
• Ontario Rule: Used in Ontario, Canada
• Huber Formula: Uses mid-point diameter, common in Europe
• Smalian Formula: Averages both ends, used for very short logs

Specialized rules:

• Brereton Rule: For small logs and poles
• Spaulding Rule: Historical, rarely used today
• Maine Rule: Regional variant of Scribner

Metric rules:

• JAS (Japanese Agricultural Standard): Used in Japan
• European standards: Various national rules

For most purposes, the three major rules (Doyle, Scribner, International) cover 95%+ of commercial timber transactions in North America and international trade.

Practical Tools & Resources

Calculators

• Log Board Foot Calculator - Compare all three scaling rules instantly with our interactive calculator
• Lumber Board Foot Calculator - Calculate board feet for dimensional lumber
• Multi-Board Calculator - Batch calculations for multiple logs or boards

Educational Resources

• What is a Board Foot? - Foundational concepts and definitions
• Board Foot Formula - Complete guide to lumber calculations
• Board Feet vs Square Feet vs Linear Feet - Unit comparison guide

External References

• USDA Forest Service. Log Scaling Handbook (FSH 2409.11). Official log scaling standards and tables, including Doyle and Scribner reference volumes.
• US Forest Products Laboratory. Wood Handbook: Wood as an Engineering Material. Baseline data for log geometry and lumber recovery.
• Bureau of Indian Affairs Forestry. Decimal C Scribner Log Scaling and Weight Conversion Tables. Primary source for Scribner Decimal C values.
• British Columbia Ministry of Forests. Scaling Manual. Contains International 1/4” and 1/8” reference tables widely adopted in Canada and the Pacific Northwest.

Conclusion

Calculating board feet in logs is fundamentally more complex than calculating lumber board feet. The three major scaling rules—Doyle, Scribner, and International—can produce vastly different results for the same log, with differences exceeding 500% for small diameter logs.

Key Takeaways:

1. Always use small end diameter (SED) measured inside bark
2. Doyle severely underestimates small logs - avoid for D < 16”
3. Scribner is the balanced standard - widely accepted in North America
4. International is most accurate - especially the 1/8” version for modern mills
5. Recovery rates vary - expect 40-60% actual lumber from log scale
6. Regional standards matter - use the established rule for your market
7. Clarify the rule in contracts - avoid disputes by specifying which rule applies

Ready to calculate? Use our Log Calculator to compare all three scaling rules side-by-side and see exactly how your logs measure up.

Disclaimer: This guide provides educational information about log scaling rules and formulas. Actual timber transactions should follow local industry standards, contractual agreements, and official scaling procedures. Log board foot calculations are estimates; actual lumber yield depends on sawing method, equipment, operator skill, and log quality. Always consult with professional log scalers or certified timber cruisers for commercial transactions. Formulas and standards are based on USDA Forest Service publications and industry references.