Daily, the team receive several questions regarding the use of different formulae for measuring Roundwood and timber from all over the world. From Argentina to Myanmar, from JAS Scale to Imperial Hoppus, we are always ready to help our community to find the best solutions, whether they work with eucalyptus or pine, whether they measure metric or imperial, whether they are buying, selling, transporting or controlling the quality of their log piles.

At Timbeter, by bringing solutions and making measurements easier and more precise, we will make the industry more sustainable and profitable for all. Inevitably, we understand that the world is changing - that’s why we need to make it better for everyone.

Within our application, there are 11 volume formulae and tables, popular in measurements all over the world, according to different regions and industry, and specific company requirements.

Below, you can find our 11 formulae and tables, briefly explained:

Cylindrical formula

JAS Scale

GOST 2708-75

Doyle Log Scale

International 1/4" Rule

Roy Log Rule

Scribner Decimal C Rule

Ontario Scaler's Rule

Nilson (Estonian formula)

Lithuanian formula

Hoppus

**Cylindrical Formula**

The Cylindrical Formula is the most straightforward and used formula for fast measurements. It doesn’t mean that the method is the most accurate and should not be used to calculate all kinds of logs, due to their unique structures and timber being a highly valued and prized commodity. Cylindrical formula is mostly used to measure pulp-and fuelwood and is the conventional method used in Central-Europe.

*Formula:*

V = π x r² x h

**JAS Scale**

The Japanese Agricultural Standard Scale was developed for measuring roundwood in the late 1940s and became popular in Eastern Asia, Oceania (including Australia) and Chile. Used by companies exporting timber to China and Japan.

*Formula:*

For logs less than 6m long:

V(m3) = (D²*L)/10000

Where:

D - small-end diameter(cm), for less than 14 cm the diameter is rounded down and after 14cm the diameter is rounded down to the nearest even integer.

L - Length(m)

For logs equal to or greater than 6m:

V(m3) = (D + [L'-4]/2)^2*(L/10000)

Where:

D - small-end diameter(cm), for less than 14 cm the diameter is rounded down and after 14cm the diameter is rounded down to the nearest even integer.

L - Length(m)

L' - length in meters rounded down to nearest whole number

**GOST 2708-75**

The Interstate Standard GOST 2708-75, called “Round Timber. Tables volumes” was a table implemented by the Soviet government in 1977, in which the standard volume of Roundwood is determined by the thickness of the upper end and the length of the logs. This table is still commonly used in Russia and some CIS countries as a standard of quality for log measurements.

**Doyle Log Rule**

The Doyle Log Rule is used in East and Central parts of North America, originated in 1825. Differently, from Scribner rule, Doyle is based on a formula.

*Formula: *

bf volume = (small-end diameter in inches - 4)² x length /16

**International 1/4’’ Log Rule**

This rule was published in 1917 and used primarily in the eastern half of North America, especially popular in the New England and Quebec regions. Also, it’s been adopted by the US Forest Service in several regions.

*Formula:*V = (0.199 x diameter in inches²) - (0.642 x diameter in inches);

Where:

V = volume in board feet for 4-foot section

D = d.i.b on small end of 4-foot length

**Roy Log Rule**

This formula is used in the Province of Quebec, Canada. It’s quite accurate for 14 and 16 foot logs.

Formula:

BF = (d - 1)² L / 20

Where:

BF = board feet

d = scaling diameter in inches inside the bark on the small end of the log

L = log length in feet

**Scribner Decimal C**

The Scribner Decimal C is used in the Midwestern and Northern regions of North America. It was published in 1945 in the University of Minnesota and uses the help of a table.

*Formula:*

(0.79*D² - 2D - 4) * L/16 = FBM rounded to the nearest 10 FBM (313 ~ 310, 317 ~ 320 etc.)

D – small-end diameter in inches, rounding half down if the diameter is exactly .5

L - Length in feet

**Ontario Scaler’s Rule**

Used by mills in the Province of Ontario, Canada, it was adopted as the official rule in 1952.

*Formula: *

BF = (0.55D² - 1.2D) * L/12

Where:

BF = board feet

D = scaling diameter in inches inside the bark on the small end of the log

L = log length in feet

**Lithuanian**

The system used in this Baltic country are based on Timber Volume Tables, which represent the norms for eight main tree species (pine, spruce, birch, aspen, black alder, grey alder, oak and ash). The measurements can include or exclude the bark.

**Nilson**

Estonians use this formula developed by Arthur Nilson to calculate the volume of logs. This method uses both a formula and a support table with coefficients, depending on tree type.

*Formula:*

cbm = (d² * L*(a1+a2*L)+a3*L²)/10 000

d – small-end diameter

L – Length in dm

a1, a2, a3 – coefficients, that are defined by the tree species.

For Pine a1= 0.0799, a2=0.000146, a3=0.0411

For Spruce a1= 0.07995, a2=0.00016105, a3=0.04948

For Birch and other Hardwoods a1=0.0783, a2=0.000236, a3=0.045

For other Conifers a1=0.0800, a2=0.000154, a3=0.0453

**Hoppus**

This older system of measurement was practiced in the UK and former British colonies. It was made popular in 1736, and it’s still used in Asia, Africa, South America and Oceania. It can both be used in metric and imperial systems.

*Formulae:*

*Imperial:*

Hoppus ft³ via girth = (mid-girth in inches/4)² x length in feet / 144

*NB!* Round to the nearest tenth ft³

Hoppus ft³ via diameter = mid-diameter in inches² x length in feet x 0.004283

*NB!* Round to the nearest tenth ft³

Hoppus superficial feet = Hoppus ft³ x 12

Hoppus ton = hoppus ft³ / 50

*Metric:*Hoppus m³ via girth = (mid-girth in cm/4)² x length in metres / 10.000

*NB!* Round to the nearest three decimal points

Hoppus m³ via diameter = mid-diameter in cm² x length in metres x 0.000061685

*NB!* Round to the nearest three decimal points

**References:**

The Measurement of Roundwood - Methodologies and Conversion Ratios from M. A. Fonseca

http://www.lnmma.lt/EN/Apvaliosios%20medienos%20matavimo%20taisykles%20EN.pdf

http://www2.dnr.cornell.edu/ext/info/pubs/management/CC%20selling%20and%20Scalling%20Sawlogs.pdf

http://rmk.ee/sale-o/sale-of-t/measurement-of-timber

http://vsegost.com/Catalog/41/4110.shtml

https://conservancy.umn.edu/bitstream/handle/11299/188336/Scribner%20Decimal%20C%20Log%20Rule.pdf?sequence=1&isAllowed=y