How do I work out the volume of a log? Using the calculator
- 1Measure the log: the diameter or girth halfway along it, or the diameter at both ends, and its length.
- 2Enter how many logs of this size you have, and the bark thickness if you want the volume under bark.
- 3Read the true volume in cubic metres or cubic feet, with the quarter-girth (Hoppus) and French measures underneath.
- 4For US log scale, switch on the log rules: the board feet by Doyle, Scribner Decimal C and International ¼-inch are worked out from the small end.
- 5The table below the results shows one log of each size, so you can read off a whole pile quickly.
Log volume formulas (Huber, Smalian, Hoppus, Doyle)
- 01Huber: V = π/4 × mid diameter² × length
- 02From the girth: V = girth² × length ÷ (4π)
- 03Smalian: V = (π/4 × small² + π/4 × large²) ÷ 2 × length
- 04Quarter-girth (Hoppus, 'au quart'): V = (girth ÷ 4)² × length
- 05Doyle: board feet = (D − 4)² × L ÷ 16 (D small end in inches, L in feet)
- 06International ¼-inch: per 4 ft section 0.905 × (0.22 D² − 0.71 D), D growing ½ in every 4 ft
A log is close to a cylinder whose cross-section is the one halfway along, so its volume is the area of that middle cross-section × the length: π/4 × d² × L. A 40 cm (0.4 m) log 4 m long holds π/4 × 0.16 × 4 = 0.503 m³. With a tape round the middle instead, the girth C gives the same thing as C² × L ÷ (4π).
The quarter-girth or Hoppus measure squares a quarter of the girth: the square beam you could cut from the log, about 78.5 % of the true volume. It survives in the UK and as the French 'cubage au quart'; the French 'au cinquième déduit' takes a fifth off the girth before quartering it, for oak with a wide sapwood.
US log rules estimate the boards a sawmill will cut, from the small end inside the bark. Doyle's formula takes 4 in off the diameter for slabs, which is why it gives so little for small logs; Scribner comes from drawn diagrams of boards and is read from its table; the International ¼-inch rule allows for ¼-inch saw kerf and the log's taper, and is probably the most accurate of the three.
Log volume calculation example
A log 4 m long with a mid diameter of 40 cm has a girth of 125.7 cm and holds 0.503 m³ of wood.
The quarter-girth (Hoppus) measure of the same log is 0.395 m³, and the French 'au cinquième déduit' 0.253 m³.
Cut and split into 33 cm pieces it stacks to about 0.7 m³ of firewood.
Tips before you buy
- Measure the diameter under the bark when you sell by the volume under bark, and take two measurements at right angles on an oval log.
- For a pile of logs of different sizes, work out each size class and add them up — the table below the results gives one log of each size.
- Agree on the measure first: a cubic metre quarter-girth and a cubic metre true volume differ by 27 %, and US board feet differ by up to 40 % between the log rules for small logs.
- For a standing tree, measure the girth at 1.30 m and the height to the cut: foresters use volume tables (French 'tarifs de cubage') for the taper, which this calculator does not include.
Frequently asked questions
How do you calculate the volume of a log?
Measure the diameter halfway along the log and multiply π/4 × diameter² × length, all in metres (Huber's formula). A log 4 m long with a 40 cm mid diameter: 0.7854 × 0.4² × 4 = 0.503 m³. With the girth instead: girth² × length ÷ 12.566.
How many board feet are in a log?
It depends on the log rule. A 16 ft log with a 16 in small end scales 144 board feet by Doyle, 160 by Scribner Decimal C and 180 by the International ¼-inch rule. A 12 in log of the same length: 64, 80 and 95.
Which log rule should I use?
The one your buyer uses — local tradition decides. Doyle is the most widely used, especially on private timber in the East and South; Scribner Decimal C was used by the Forest Service in the Lake States and the West; International ¼-inch is probably the most accurate but little used (Purdue Extension). On small logs Doyle gives only a fraction of the boards.
What is the Hoppus (quarter-girth) measure?
Volume = (girth ÷ 4)² × length. It gives the square beam inside the log, about 78.5 % of its true volume, so 1 Hoppus cubic foot is 1.273 true cubic feet. It is the same as the French 'cubage au quart sans déduction'.
How many cubic feet of wood are in a cord?
A cord is a stack 8 × 4 × 4 ft = 128 cubic feet, but the gaps between the pieces mean it holds only about 80–90 cubic feet of solid wood; 85 is the usual figure.
How do I measure a log properly?
Measure the length along the log and the diameter at the middle, at right angles to the log. From 20 cm (8 in) up, take two diameters at right angles and average them. Forest rules round down: the German RVR rounds the diameter down to whole cm, the UK Forestry Commission rounds the length down to 0.1 m.
How much does bark take off?
Usually 1–3 cm off the diameter, more on thick-barked trees. The German RVR takes 1 cm for spruce up to 26 cm, 2 cm for 27–50 cm and 3 cm above that; the UK Forestry Commission factors are 0.82–0.92 of the volume over bark, depending on the species.
Also searched as: log scale calculatorDoyle log scale calculatorScribner log rule calculatorboard feet in a log calculatorHoppus calculatortimber volume calculator for logscubic metres in a loghow much firewood is in a log
Sources
- RVR – Rahmenvereinbarung für den Rohholzhandel in Deutschland, 2023: Huber's formula, measuring rules, bark deductions, stacked-wood factors (German)
- Forestry Commission Booklet 49, Timber Measurement (Huber's formula, rounding, under-bark factors)
- Briggs, Measurement of Logs, ch. 2 (University of Washington): Huber, Smalian and Hoppus
- Purdue Extension FNR-191, log rules: Doyle formula, International ¼-inch and Scribner tables
- Idaho log scaling manual, ch. 1: Scribner Decimal C table and scaling rules
- Virginia Tech 420-085: how much wood is in a cord (80–90 ft³ in 128 ft³)
- LWF Merkblatt 12 (2024): solid, stacked and loose firewood conversion factors (German)
- CNPF: cubage des bois abattus – true volume C² × L ÷ 4π, the legal measure in France (French)
Formulas last reviewed: September 30, 2026 ·How we check our formulas