There are several methods to calculate log volume, each with its own formula and approach. The most common and popular methods are:

• Doyle Formula
• Scribner Rule

Doyle Formula

$\mathrm{The\; Doyle\; log\; rule\; is\; a\; common\; method\; used\; to\; estimate\; the\; volume\; of\; lumber\; that\; can\; be\; sawn\; from\; a\; log.\; The\; Doyle\; rule\; tends\; to\; underestimate\; log\; volumes\; for\; smaller\; logs\; and\; overestimate\; for\; larger\; ones.\; Here\text{'}s\; the\; formula\; and\; method\; to\; calculate\; the\; log\; volume\; using\; the\; Doyle\; log\; rule:}$

$\frac{\mathrm{}}{}$$\text{Board Feet}={\left(\frac{D-4}{4}\right)}^2\times L$

Where:

• 𝐷 is the diameter of the log in inches (measured at the small end, inside the bark).
• 𝐿 is the length of the log in feet.

Steps to Calculate Log Volume using Doyle Rule

1. Measure the Diameter: Measure the diameter (D) of the log at the small end, inside the bark, in inches.
2. Measure the Length: Measure the length (L) of the log in feet.
3. Apply the Formula: Plug the values of D and L into the Doyle formula.

Example Calculation

Suppose you have a log with a diameter of 16 inches and a length of 12 feet:

1. Diameter (D): 16 inches
2. Length (L): 12 feet

Calculation:

$\text{Board Feet}={\left(\frac{16-4}{4}\right)}^2\times 12$

$\text{Board Feet}={\left(\frac{12}{4}\right)}^2\times \mathrm{12}$

$\text{Board Feet}={\left(3\right)}^2\times 12$

$\text{Board Feet}=9\times 12$

$\text{Board Feet}=108$

So, the log volume is estimated to be 108 board feet using the Doyle log rule.

Scribner log rule

The Scribner rule is typically represented by a set of tables, but it can also be estimated with the following formula

$v=\frac{(0.79D^2-2D-4)L}{16}$

Where:

• 𝐷 is the diameter of the log in inches (measured at the small end, inside the bark).
• 𝐿 is the length of the log in feet.

Example Calculation

Suppose you have a log with a diameter of 16 inches and a length of 12 feet:

1. Diameter (D): 16 inches
2. Length (L): 12 feet

Calculation:

Board Feet = (((0.79 x 16 x 16) - (2 x 16) - 4) x 12 ) / 16

Board Feet = ((202.24 - 32 - 4) x 12 ) / 16

Board Feet = (166.24 x 12 ) /16

Board Feet = 1994.88 / 16

Board Feet =  124.68