Hoppus Formula Explained: Quarter-Girth Log Measurement
The Hoppus (quarter-girth) formula h = (C/4)² × L/144, why it reads about 78.5% of true volume, Hoppus tons, and worked examples in imperial and metric.
The formula
Hoppus volume uses the quarter-girth rule: h ft³ = (C/4)² × L ÷ 144 with girth C in inches measured at mid-length and length L in feet; in metric, h m³ = (C/4)² × L ÷ 10,000 (C in cm, L in m). Dividing the circumference by 4 instead of by π embeds the factor 4/π, so a Hoppus reading is deliberately about 78.5% of true content — multiply by 1.273 to recover true volume.
History and trade units
The rule was published by Edward Hoppus in 1736 and became the standard of the British Empire timber trade. It still prices plantation teak and eucalyptus in India, Myanmar and parts of Africa and Latin America. Trade units: 1 Hoppus ton (HT) = 50 h ft³ ≈ 1.80 m³ true, 1 h ft³ ≈ 0.0361 m³ true, and the commercial shortcut 1 h ft³ ≈ 10 board feet (geometry says ≈ 12.7 BF — the 10 BF convention bakes in sawmill losses).
Worked examples
Imperial: a log with 36 in girth at mid-length, 16 ft long gives (36/4)² × 16 ÷ 144 = 9 h ft³ ≈ 11.5 ft³ true ≈ 90 BF commercial. Metric: girth 100 cm, 5 m long gives (100/4)² × 5 ÷ 10,000 = 0.3125 h m³ ≈ 0.40 m³ true. One tape reading, one multiplication — that is why the rule survived three centuries.
Hoppus to true volume
| Hoppus reading | True volume |
|---|---|
| 1 h ft³ | 0.0361 m³ |
| 10 h ft³ | 0.361 m³ |
| 50 h ft³ (= 1 HT) | 1.803 m³ |
| 100 h ft³ | 3.605 m³ |
| 1 h m³ | 1.273 m³ |
When to use Hoppus
Use it for quick field estimates and wherever the contract is written in Hoppus units — and never mix scales within one deal. Standing volume for a plantation sale, container loads of round teak, and legacy concessions are the classic cases. For comparison, JAS scaling is explained in JAS Log Scaling: The Japanese Agricultural Standard Explained, board-foot log rules in Doyle, Scribner and International Log Rules Compared, and Hoppus volume computes Hoppus volume, true volume and Hoppus tons from a single girth and length.