How to Calculate Timber Volume: Logs and Standing Trees
For a felled log — Smalian's formula: V = (A₁ + A₂) / 2 × L. Average the cross-sectional area at each end, multiply by length.
For a standing tree: V = basal area × merchantable height × form factor. Basal area = π(DBH/2)²; form factor is typically 0.42–0.50.
Cross-sectional area A = π × (diameter / 2)². Keep diameter and length in the same unit system.
Log Volume: Three Formulas
| Formula | Equation | Needs | Accuracy |
|---|---|---|---|
| Smalian | V = (A₁ + A₂) / 2 × L | Both end diameters | Good; over-estimates strongly tapered logs |
| Huber | V = Amid × L | Mid diameter | Better, if you can reach the middle |
| Newton | V = (A₁ + 4Amid + A₂) / 6 × L | All three | Best |
Worked example. A log 6m long, 25cm at the small end, 35cm at the large end, 30cm at the middle:
- A₁ = π(0.125)² = 0.0491 m² · A₂ = π(0.175)² = 0.0962 m² · Amid = π(0.15)² = 0.0707 m²
- Smalian: (0.0491 + 0.0962) / 2 × 6 = 0.436 m³
- Huber: 0.0707 × 6 = 0.424 m³
- Newton: (0.0491 + 4(0.0707) + 0.0962) / 6 × 6 = 0.428 m³
The spread between them tells you something: a large gap means the log is irregular or strongly tapered. On a straight, lightly tapered log the three converge.
Standing Tree Volume
You cannot measure the ends of a standing tree, so you estimate from diameter, height and a shape correction.
V = BA × H × f
- BA = basal area = π × (DBH / 2)², where DBH is diameter at breast height
- H = merchantable height, not total height — measure to the top of usable stem
- f = form factor, the fraction of a cylinder the stem actually fills
- Worked: DBH 30cm, merchantable height 6m, form factor 0.45. BA = π(0.15)² = 0.0707 m². V = 0.0707 × 6 × 0.45 = 0.191 m³
DBH is measured at 1.3m above ground in most of the world (4.5 feet in the United States). On sloping ground, measure from the uphill side.
Choosing a Form Factor
| Stem type | Form factor |
|---|---|
| Straight conifers — pine, spruce, fir | 0.45 – 0.50 |
| Well-stocked plantation eucalyptus | 0.42 – 0.48 |
| Teak, well-formed hardwood plantation | 0.45 – 0.50 |
| Open-grown or heavily branched trees | 0.35 – 0.42 |
| General default when you have nothing better | 0.45 |
Form factor varies with species, age, stocking and site. Locally derived volume equations always beat a generic factor — if your national forestry service publishes species and site-class tables, use them instead.
Selling a stand? An estimate is not an inventory. We measure properly.
How to Measure Properly
- Take two diameter readings at right angles and average them. Logs and stems are rarely circular.
- Be consistent about bark. Over bark or under bark — pick one and tell your buyer which. Mixing them is a common cause of dispute.
- Measure merchantable length, not total length. Stop where the stem stops being usable.
- Use a diameter tape or callipers, not a ruler across the face.
- Record every measurement. A buyer can verify a written record; they cannot verify a recollection.
Scaling Up to a Whole Stand
Measuring a few convenient trees and multiplying is the classic error. Stands are patchy — better on the mid-slope, worse on the ridge — and trees you can easily reach are not a random sample.
A real inventory means:
- Systematic sample plots laid out on a grid or transect, not chosen by convenience
- A plot intensity matched to the precision you need — a transaction needs more plots than an internal estimate
- Every tree in the plot measured, including the poor ones
- Volume calculated by grade, because price is set by grade, not by total cubic metres
- Methodology stated so a buyer can check it rather than doubt it
Where Disputes Come From
Four recurring arguments, all avoidable
- Bark. One party measured over bark, the other under. Agree it in writing before measuring.
- Which formula. Smalian and Newton differ on tapered logs. State the method in the contract.
- Merchantable top. Where does the usable stem end? Define the minimum top diameter.
- Sample bias. The seller measured the good corner; the buyer measured the poor one. Systematic plots settle it.
Frequently Asked Questions
How do you calculate the volume of a log?
Smalian's formula is the most widely used: average the cross-sectional area at each end and multiply by length. V = (A1 + A2) / 2 × L, where A = π(diameter/2)².
Huber's formula (mid area × length) is more accurate if you can reach the middle of the log, 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, where basal area = π(DBH/2)² and DBH is diameter at breast height, 1.3m above ground in most countries.
The form factor corrects for taper and is typically 0.42–0.50, with 0.45 a reasonable default.
What is basal area?
The cross-sectional area of a stem at breast height — π(DBH/2)². For a 30cm DBH tree that is about 0.0707 square metres.
At stand level, basal area per hectare (the sum of all stems' basal areas) is one of the standard measures of stocking and competition.
Why do different formulas 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; Newton weights all three and is most accurate.
On a straight, lightly tapered log they converge. A large gap between them tells you the log is irregular.
Can I estimate my whole plantation from a few trees?
Not reliably. Stands are patchy, and the trees you can conveniently reach are not a random sample — measuring the accessible edge and multiplying is the classic error.
A real inventory uses systematic plots on a grid, measures every tree in each plot, and reports volume by grade with the methodology stated.
Should I measure over bark or under bark?
Either, as long as you are consistent and you tell the buyer which. Mixing the two is one of the most common causes of dispute in timber sales.
Agree the convention in writing before anyone starts measuring, along with the volume formula and the minimum merchantable top diameter.
An Estimate Is Not an Inventory
If you are selling, financing or valuing, you need systematic plots and a stated methodology a buyer can verify. That is what we do.
Over a decade establishing, measuring and managing eucalyptus, pine and indigenous plantations across Uganda. Based in Wakiso, Kampala. Reviewed and updated September 6, 2026.
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These apply the same way in any country.
