Measuring log volume: formulas, stacks and scaling rules

A sawmill does not buy "logs". It buys a volume, a quality, a delivery date and a risk profile, and each is defined by a measurement rule. Log volume is the base of nearly every payment in the wood chain, so a systematic error never cancels in a large batch, while random errors do. This lesson covers volume rules from Europe and North America. Regional rules differ and are never interchangeable.

Germany: mid-diameter and the Huber formula

The German framework agreement for roundwood trade (RVR, voluntary, signed 2014, applied from 1 January 2015, 5th edition 2023) applies only when buyer and seller put it in the contract. It measures the mid-diameter without bark at the middle of the log: one reading up to 19 cm, two perpendicular readings from 20 cm, rounded down to whole centimetres. Volume in cubic metres solid without bark (Fm o.R.) is:

V = (pi / 4) x d^2 x L x 10^-4 (d in cm, L in m)

Worked example. A log with 30 cm mid-diameter and 5.00 m length: 0.7854 x 30^2 x 5 x 10^-4 = 0.7854 x 900 x 5 / 10000 = 0.353 m3, reported as 0.35 m3.

Because volume is proportional to d squared, a diameter error is amplified. For a 30 cm log, 1 cm of error is (31^2 - 30^2) / 30^2 = 61 / 900 = 6.8 percent of volume. A caliper that reads 1 cm high is therefore a price change on the whole batch, which is why rules fix rounding and require calibrated instruments for billing.

Stacked wood in Germany

For stacked wood the RVR gives factors from stacked cubic metres with bark (Rm m.R.) to Fm o.R.: 0.70 for 1 m lengths, 0.65 for 2 m and 0.60 for 3 m. For weight, 1 t oven-dry with bark equals 2.2 Fm o.R. for spruce and fir, 2.1 for pine and Douglas fir, 1.8 for larch, 1.5 for beech and 1.4 for oak. The brochure states that these are averages for internal and statistical use and must not serve as a sales measure.

Worked example. 100 Rm of 1 m spruce is 100 x 0.70 = 70 Fm o.R. on the average factor.

Sweden: volume built from the actual stack

The Swedish regulation (Biometria, 2025 for logs, 2026 for stacks) uses m3sub, the form-adjusted solid volume. For stacks, volume is the product of external dimensions (m3t) multiplied by a wood-volume percentage. Base percentages: 70 percent spruce, 68 pine, 66 aspen, 65 alder and oak, 64 birch, beech and ash, adjusted for bark, stacking, crookedness, snow and ice, logging waste, length and stack height. The regulation's own example is 6.00 x 3.01 x 1.08 = 19.505 m3t, which at 55 percent gives 19.505 x 0.55 = 10.73 m3sub.

Contrast with the German flat factors: the Swedish figure is built from the actual stack, and conditions such as snow and ice change it.

North America: board-foot rules

North American mills often use board-foot rules that estimate sawn recovery from small-end diameter and length. The USDA handbook NA-FR-15 prints these values for 16-foot logs (shown as printed; the Scribner and Doyle scaling note is unresolved in the source):

Worked example. At 16 in., Doyle gives (180 - 144) / 180 = 20 percent less than International. At 10 in. the gap is (65 - 36) / 65 = 44.6 percent, and at 30 in. the rules converge. A review (Spelter, 2004) found in its abstract that the three rules generally underestimate true recovery, inconsistently, with the undercount growing for smaller logs. A price in "per MBF Scribner" therefore cannot be compared with a European Fm o.R. price without a size-dependent conversion agreed in writing.

Key points

• Systematic measurement errors never cancel; random errors do in large batches.
• German RVR volume: V = (pi/4) x d^2 x L x 10^-4; a 30 cm, 5 m log is 0.35 m3, and 1 cm of diameter error on 30 cm is about 6.8 percent of volume.
• RVR stack factors (0.70, 0.65, 0.60 for 1, 2, 3 m) are statistical averages, not a sales measure.
• Swedish stack volume is external dimensions times a wood-volume percentage, adjusted for conditions.
• Board-foot rules differ by size; Doyle gives 20 percent less than International for a 16 in. log.