The Formulas
| Method | Formula | When to use it |
|---|---|---|
| Smalian | V = (A₁ + A₂) / 2 × L | The workhorse. Needs both end diameters. Slightly over-estimates on strongly tapered logs. |
| Huber | V = Amid × L | More accurate than Smalian when you can reach the middle of the log. |
| Newton | V = (A₁ + 4Amid + A₂) / 6 × L | Most accurate of the three. Needs all three diameters. |
| Standing tree | V = BA × H × f | BA = π(DBH/2)². f is the form factor. |
| Doyle (board feet) | BF = ((D − 4)/4)² × L | US log rule. D = small-end inches, L = feet. |
A = cross-sectional area = π × (diameter / 2)². Keep diameter and length in the same unit system and the volume comes out in cubic units of that system.
Choosing a Form Factor
A tree is not a cylinder — it tapers. The form factor is the fraction of a cylinder the stem actually fills.
| Stem type | Typical form factor |
|---|---|
| Straight conifers (pine, spruce, fir) | 0.45 – 0.50 |
| Plantation eucalyptus, well stocked | 0.42 – 0.48 |
| Open-grown or heavily branched trees | 0.35 – 0.42 |
| General default when unsure | 0.45 |
Form factor varies with species, age, stocking and site. Locally derived volume equations always beat a generic factor — if your country's forestry service publishes species tables, use those.
Getting an Accurate Measurement
- Measure diameter over bark or under bark consistently — and tell your buyer which you used. Mixing the two is a common source of dispute.
- Take two diameter readings at right angles and average them. Logs are rarely circular.
- DBH is measured at 1.3m above ground in most countries (4.5ft in the US). On a slope, measure from the uphill side.
- Measure length to the merchantable top, not the tip of the tree.
- Do not scale a stand from one tree. For a whole block you need systematic plots, not a sample of convenience — that is what a proper inventory is.
A Word on Board Feet
Board-foot log rules are US conventions that estimate sawn output rather than solid wood volume, so they are not directly comparable to cubic metres.
- Doyle is simple but under-measures small logs severely — a 10-inch log scales at roughly half what other rules give.
- Scribner and International ¼-inch are table-based; approximating them with a formula introduces error, so we do not.
- Outside North America, sell in cubic metres. It is unambiguous.
Frequently Asked Questions
How do you calculate the volume of a log?
The most widely used method is Smalian's formula: average the cross-sectional area at each end and multiply by the length. V = (A1 + A2) / 2 × L, where A = π(diameter/2)².
If you can measure the middle of the log, Huber's formula (mid area × length) is more accurate, and Newton's using all three diameters is more accurate still.
How do you calculate standing tree volume?
Volume = basal area × merchantable height × form factor. Basal area is π(DBH/2)², where DBH is diameter at breast height — 1.3m above ground in most countries.
The form factor accounts for taper and is typically 0.42–0.50, with 0.45 a reasonable default when you have nothing better.
What is a form factor in forestry?
The fraction of a cylinder that a tree stem actually fills. A perfect cylinder would be 1.0; real stems taper, so they are lower.
Straight conifers run 0.45–0.50, plantation eucalyptus 0.42–0.48, and open-grown branchy trees as low as 0.35. Locally derived species equations always beat a generic factor.
What is the Doyle log rule?
A US board-foot rule: BF = ((D − 4) / 4)² × L, where D is small-end diameter in inches and L is length in feet.
It under-measures small logs severely — which is why sellers of small timber dislike it and buyers often prefer it. Outside North America, sell in cubic metres.
Why do Smalian, Huber and Newton give different answers?
Because each assumes a different stem shape. Smalian averages the two ends and slightly over-estimates strongly tapered logs; Huber uses the middle and is usually closer; Newton weights all three and is most accurate.
On a straight, lightly tapered log the three converge. Big differences between them tell you the log is irregular.
Can I use this to value my whole plantation?
Not from a few trees. Scaling a stand requires systematic sample plots laid out to a design, measured consistently, with volume calculated by grade — that is a forest inventory, not a calculation.
Buyers price unmeasured timber defensively, so a proper inventory routinely pays for itself in the improved offer.