Hoppus formula – log volume from the quarter girth

A traditional British rule still used in the tropical hardwood and teak trade.

What is the Hoppus formula?

The Hoppus formula calculates log volume as a square prism whose side is a quarter of the mid-length girth. The result is 21.5% less than the true cylinder volume – the difference stands for the waste when a round log is squared.

Formula

V = (d · π / 4)² · L / 10,000

d = mid diameter in cm · L = length in m · V in Hoppus m³. From the girth: V = (G / 4)² · L, where G is the mid girth. Hoppus volume is π/4 = 78.5% of the true volume.

Worked example

A log with a 30 cm mid diameter and 4 m length: V = (30 · 3.1416 / 4)² · 4 / 10,000 = 0.222 Hoppus m³ (the true volume is 0.283 m³).

Where it is used

The United Kingdom and Ireland (historically), India, Malaysia, Myanmar and West Africa – mainly in the tropical hardwood and teak trade.

Frequently asked questions

Why does Hoppus give a smaller volume?

It measures a square prism inscribed in the log, not a cylinder. The result is always 78.5% of the true volume.

What is a Hoppus foot?

The imperial unit of Hoppus volume. One Hoppus foot equals about 1.27 cubic feet of true volume.

Can Hoppus be calculated from the girth?

Yes, that is how it originated – the girth is measured at mid-length and a quarter of it is squared. The app supports both inputs.

Other log scaling methods

All 22 methods in the app ›

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 Smalian formulaWhen you cannot reach the middle of the log – on a deck or a truck – you measure both ends.m³ · US · CA Doyle Log RuleThe oldest log rule still in wide use in the southern and midwestern United States.BF · US Scribner Decimal CA rule built by drawing boards into circles, today the standard for softwood logs in the western United States.BF · US · CA International ¼″ Log RuleIt allows for a ¼-inch kerf, shrinkage and log taper, so it comes closest to the real sawn timber 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 STN / ČSN 48 0009Table-based scaling under the Slovak standard STN 48 0009 and the Czech ČSN 48 0009: under-bark volume from tables by mid diameter, length and species. Commonly used in the roundwood trade in Slovakia and Czechia.m³ · SK · CZ More methodsMid-girth, Newton, GOST 2708-75, Brereton, Vermont, Universal (Daniels), Ontario Board Foot, Ontario Cubic, Roy, Alberta, BC Firmwood, Guo Biao (GB/T 4814)All 22 methods ›