Toppmätning – log volume in Sweden

Swedish sawmills pay by the small-end diameter: m³to is a cylinder from the top end.

What is the Swedish scaling (toppmätning)?

In Sweden sawlogs are measured at the small end (toppmätning). Volume in m³to is calculated as a cylinder with the small-end diameter under bark and the log length. Diameter is recorded in whole centimeters and length in decimeters, and the class midpoint is used – diameter + 0.5 cm and length + 0.05 m.

Formula

V = π/4 · (D + 0.5)² · (L + 0.05) / 10,000

V in m³to · D = small-end diameter under bark in whole cm · L = length in m rounded down to decimeters. The 0.5 cm and 0.05 m additions are the class midpoints.

Worked example

A log with a 25 cm small-end diameter and 4.3 m length: V = 3.1416 / 4 · 25.5² · 4.35 / 10,000 = 0.222 m³to.

Where it is used

Sweden – sawlog (timmer) purchases by sawmills. Timber measurement in Sweden is carried out by the independent organization Biometria. Pulpwood (massaved) is usually measured differently, in m³fub.

Frequently asked questions

What does m³to mean?

A “toppmätt” cubic meter – cylinder volume calculated from the small-end diameter. It is less than the true log volume because it ignores taper.

Why is 0.5 cm added to the diameter?

Diameter is recorded rounded down to whole centimeters, so the true diameter is on average half a centimeter larger. The calculation therefore uses the class midpoint; likewise 5 cm is added to a length recorded in decimeters.

What is the difference between m³to and m³fub?

m³to is the cylinder volume from the small end (sawlogs); m³fub is the true solid volume under bark. For the same log, m³fub is higher.

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 Huber formulaThe most widely used scaling method in Central Europe: one diameter at mid-length and the length.m³ · SK · CZ · DE · AT · FR · IE JAS (Japanese standard)The small-end diameter squared method, the standard for logs traded to Japan.m³ · JP 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 ›