How to Calculate Log Volume: Smalian, Huber Formulas and Practical Methods

Before any log purchase, before any production planning, one fundamental question needs a precise answer: how much wood is in that log?

It sounds simple. But the right answer makes a difference of significant money per log at large volumes — and the wrong method can systematically favor buyer or seller depending on which formula each party uses.

In this article you'll learn the most common formulas for calculating log volume — Smalian, Huber, and Newton — when to apply each one, their advantages and limitations, and how to use these estimates in sawmill production planning.

Why log volume calculation matters

A log's volume determines:

• The purchase price when wood is traded by m³ or board-feet
• The expected yield in m³ of sawn lumber produced
• The estimated revenue per log before sawing
• The cost per m³ sawn, which defines gross margin

A systematic underestimate of just 5–10% in volume means — for a sawmill processing 500 logs per month — a difference of 25 to 50 logs in volume charged or paid for incorrectly every month.

The basic geometry of a log

A log is not a perfect cylinder. It tapers — it has a larger diameter at the butt end and a smaller diameter at the tip. This taper, combined with natural trunk irregularities, is what makes log volume calculation an estimation exercise, not an exercise in absolute precision.

The three classic formulas — Smalian, Huber, and Newton — deal with this taper in different ways, each with a different trade-off between measurement ease and result precision.

Required measurements

To apply any of the formulas, you need to measure:

• Length (L): from butt end to tip, in meters.
• Diameter at butt (D₁): measured with a diameter tape or calipers, in meters.
• Diameter at tip (D₂): same, in meters.
• Diameter at mid-length (Dm): measured at exactly the midpoint of the length — needed only for Huber and Newton.

All diameter measurements should be made without bark whenever possible, or with a bark deduction (typically 2–4 cm for eucalyptus, 3–6 cm for pine). Diameter is the average of two perpendicular measurements at the same cross-section.

Smalian Formula

Smalian is the simplest and most widely used formula in log trading. It calculates volume as if the log were a solid with cross-sectional area varying linearly between the two ends.

V = L × (A₁ + A₂) / 2

Where:

• V = volume in m³
• L = length in meters
• A₁ = cross-sectional area at butt = π × (D₁/2)²
• A₂ = cross-sectional area at tip = π × (D₂/2)²

Practical example

Log with: D₁ = 0.40 m, D₂ = 0.28 m, L = 5.0 m

• A₁ = π × (0.20)² = 0.1257 m²
• A₂ = π × (0.14)² = 0.0616 m²
• V = 5.0 × (0.1257 + 0.0616) / 2 = 0.468 m³

When to use Smalian

Smalian is recommended when you cannot access the middle section of the log (stacked logs, for example). It is the standard formula in the Brazilian and many other timber markets.

Smalian's limitation

Smalian overestimates volume on more tapered logs (where the difference between D₁ and D₂ is large). The error is systematically positive, which benefits the seller.

Huber Formula

Huber uses only the mid-length diameter to calculate volume, treating the log as a cylinder with the central cross-section area.

V = L × Am

Where Am = cross-sectional area at mid-length = π × (Dm/2)²

Practical example

Same log: Dm = 0.34 m, L = 5.0 m → V = 5.0 × π × (0.17)² = 0.454 m³

When to use Huber

Huber is more accurate than Smalian for regular logs and is the preferred formula in forest inventories and scientific research. It requires access to the log's midpoint.

Newton Formula (Prismatoid)

Newton combines all three measurements and is the most accurate of the three for logs with regular taper.

V = L × (A₁ + 4×Am + A₂) / 6

Same log: V = 5.0 × (0.1257 + 4×0.0908 + 0.0616) / 6 = 0.459 m³

When to use Newton

Newton is the most accurate option when precision is critical — technical reports, high-value purchases, formal inventories. Requires three measurements per log.

Formula comparison

Quick reference table: approximate volumes by diameter and length

Table calculated using Huber method (cylinder with mean diameter). Use as a quick field reference — for formal purchases, measure and calculate individually.

Log volume and expected yield

Knowing the log volume in m³ is the starting point — but what the sawmill converts into sellable product is always less than that volume. The difference goes to:

• Kerf (saw dust): 8–15% of volume
• Slabs and edgings discarded: 10–25% of volume
• Sawdust and chips from thin cuts

A yield of 50–60% is considered good for mid-sized logs with a typical dimension mix. Larger logs and mixes with few large dimensions can reach 65–70%.

In SawOptima, when you enter the log diameter and length, the system automatically calculates how many pieces fit within the circle and estimates utilized vs. lost volume — before you saw the first log.

Conclusion

Correctly calculating log volume is a fundamental skill for any sawmill that trades wood by m³ or wants to control its yield rigorously. The Smalian, Huber, and Newton formulas aren't complicated — they just require correct measurements and consistency in method.

The sawmill that knows exactly how much wood it buys, how much it converts, and how much it loses has a real advantage over competitors operating on guesswork. Measure to manage — that's the principle.