Huber formula – log volume from the mid diameter

The most widely used scaling method in Central Europe: one diameter at mid-length and the length.

What is the Huber formula?

The Huber formula calculates log volume as a cylinder whose diameter equals the log's diameter at half its length. It needs a single diameter measurement and is accurate to within a few percent for typical sawlogs, which is why it underlies the scaling of individual logs in Ireland, Germany, Austria and France, as well as Slovakia and Czechia. The European standard EN 1309-2 gives it as the default procedure where no national rule exists.

Formula

V = π/4 · d² · L

V = volume in m³ · d = diameter at mid-length in meters · L = length in meters. With the diameter in centimeters: V = π/40,000 · d² · L.

Worked example

A log with a 30 cm mid diameter and 4 m length: V = 3.1416 / 4 · 0.30² · 4 = 0.283 m³.

Where it is used

Ireland – mid diameter over bark. Germany – RVR rules, solid cubic meters under bark from the mid diameter. Austria – mid diameter under the ÖHU trade customs and ÖNORM L 1021. France – standard NF B53-020 (cylinder from the mid diameter, rounded down to whole cm). Partly Hungary (hardwoods by mid diameter, softwoods from small-end tables) and Poland (long stems by mid diameter, shorter logs by small-end diameter). Slovakia and Czechia – basis of the STN and ČSN 48 0009 standards.

Frequently asked questions

How accurate is the Huber formula?

It is exact for a paraboloid-shaped log and within a few percent for typical logs. The largest error occurs on butt logs with strong root flare.

Is the diameter measured over or under bark?

It depends on the contract and standard. Trade volume is usually under bark – either measured directly, or double bark thickness is deducted from the over-bark diameter.

What is the difference between Huber and STN/ČSN 48 0009?

The STN and ČSN standards are based on Huber, but volume is read from tables: the diameter is rounded down to whole centimeters, the length down to decimeters, and the tables already allow for bark by species.

Is the Huber formula named in the European standard?

Yes. The European standard EN 1309-2 (Round timber – requirements for measurement and volume calculation) says that where no national or regional rule exists, volume is calculated as a cylinder from the mid diameter and the length – that is, the Huber formula. The diameter is rounded down to whole centimeters and the length down to tenths of a meter.

Other log scaling methods

All 22 methods in the app ›

In your countryDoyle vs Scribner vs International ¼″Three US board foot rules, three different results for the same log. Clearly laid out, in numbers, with the reasons.BF · US · CA In your countrySmalian formulaWhen you cannot reach the middle of the log – on a deck or a truck – you measure both ends.m³ · US · CA In your countryDoyle Log RuleThe oldest log rule still in wide use in the southern and midwestern United States.BF · US In your countryScribner Decimal CA rule built by drawing boards into circles, today the standard for softwood logs in the western United States.BF · US · CA In your countryInternational ¼″ Log RuleIt allows for a ¼-inch kerf, shrinkage and log taper, so it comes closest to the real lumber yield.BF · US JAS (Japanese standard)The small-end diameter squared method, the standard for logs traded to Japan.m³ · JP Swedish scaling (toppmätning)Swedish sawmills pay by the small-end diameter: m³to is a cylinder from the top end.m³ · SE Hoppus formulaA traditional British rule still used in the tropical hardwood and teak trade.m³ · GB · IE · IN · GH · MY More methodsSTN 48 0009, ČSN 48 0009, Vermont, Universal (Daniels), Newton, GOST 2708-75, Brereton, Ontario Board Foot, Ontario Cubic, Roy, Alberta, BC Firmwood, Mid-girth, Guo Biao (GB/T 4814)All 22 methods ›