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Vriksai Timber Intelligence

Smalian FormulaTwo-End Area Volume Calculator

Calculates log volume using the average of two end cross-sectional areas multiplied by length. Standard in Scandinavia, used in India IS 1902, and common in international timber research.

Why this calculation matters

Volume decides what you pay and what you expect to recover. Smalian is reliable on cylindrical logs and over-reads on tapered ones.

Two-End Area MethodIS 1902 IndiaNewton ComparisonForest InventoryPDF Report
SM

Smalian Formula

Two-End Area Volume Calculator

Unit System and Species
Log End Diameters
cm
cm
metres
cm
cm
logs
OK
Smalian Volume Results
-
m3
Smalian Volume
-
m3
Huber Volume
-
m3
Newton (most accurate)
-
kg
Est. Weight
Cross-Section Areas
Area A1 (large end)-
Area A2 (small end)-
Mean area (A1+A2)/2-
Method Comparison
Smalian (avg 2 ends)-
Huber (mid-section)-
Newton (most accurate)-
Formula Trace
About Smalian Formula
Named after Christian Smalian (1838). Calculates volume as the arithmetic mean of two end cross-sectional areas multiplied by length. Standard in Scandinavia, used in India IS 1902:2015, and common in timber cruising worldwide. Tends to overestimate for highly tapered logs - compare with Huber and Newton for accuracy. Use it whenever you need the cubic metre volume of a log from its end diameters — the log volume formula used in sale and survey work worldwide.
Where Used?
IS 1902 IndiaScandinaviaForest InventoryExport DocumentationAcademic Research
Formulas
Smalian: V = ((A1 + A2) / 2) x L A = pi x (D/200)^2 D in cm, L in mHuber: V = A_mid x L A_mid at midpointNewton: V = (A1 + 4 x A_mid + A2) / 6 x L most accurate
Sources & verification
  • Smalian formula (published formula)
Formula checked against the sources above by an automated regression test (tests/test-calculators.js) that derives each expected value independently of this page. Last reviewed .
FAQ
Smalian vs Huber - which is more accurate?
Smalian overestimates for tapered logs because the butt end is disproportionately large. Huber (mid-section) is more accurate for typical taper. Newton is most accurate. IS 1902 India prefers Huber as primary method.
Why does Smalian overestimate the volume of tapered logs?
Because it only looks at the two ends and assumes the log swells smoothly between them, like a section of a cone. Real logs taper unevenly and are often fuller in the middle than that straight-line assumption predicts, so the average of the two end areas comes out a little high. The more taper a log has, the bigger the overestimate — which is exactly why standards like IS 1902 lean toward Huber's mid-point method for tapered Indian hardwoods.
When is Smalian the right formula to use anyway?
When you can't get at the middle of the log, which is most of the time in a stacked pile or on a loaded truck. Smalian only needs the two end diameters, both of which are easy to reach, so it's the practical workhorse for everyday scaling. On straight, low-taper logs the error is small and perfectly acceptable. Save Huber for individual high-value logs where you can measure the mid-point and the extra accuracy is worth the effort.
ResourcesView the formulasFormula Library
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Wood species data
Density, hardness and movement for 60 timbers
Browse all species 
How the calculation works
The area of each end of the log is worked out from its diameter, the two areas are averaged, and that average is multiplied by the length. It treats the log as if its cross-section changed evenly from one end to the other, which is why it reads high on a log that tapers sharply.
Show the formula
End areas A1 = pi x (D1/200)^2 and A2 = pi x (D2/200)^2 with D in cm. Smalian volume = ((A1 + A2) / 2) x length. The page also reports Huber (mid-area x length) and Newton ((A1 + 4 x Amid + A2)/6 x length) for comparison.
Smalian averages the two end areas and therefore over-reads on strongly tapered logs, because area varies with the square of diameter.
References and what each one provides
  • USDA Wood Handbook (FPL GTR-190)USDA Forest Products LaboratoryPublished density, moisture relationships, shrinkage coefficients and mechanical properties for a wide range of species. The reference dataset behind most wood-property figures on this site.
Unverified values are marked as such rather than presented as sourced.
Limitations of this calculation
Geometric volume assuming circular cross-sections and regular form. It does not account for ovality, sweep, taper irregularity, or hollow and defective centres.
Do not use this for Contract scaling or sale settlement without an agreed rule and joint measurement.
Figures are engineering estimates from the inputs and assumptions shown. Verify against the actual material and, where the result affects structure or safety, against a qualified professional.
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How to use this tool
  1. Enter the log measurements below, then press Calculate.
  2. Pick your bark status from the dropdown.
  3. Fill in large-end diameter d1, small-end diameter d2, log length, bark thickness - large end. 
  4. Press Calculate. 
Worked example
With the tool's starting values — large-end diameter d1 = 45, small-end diameter d2 = 32, log length = 5, bark thickness - large end = 2.5, bark thickness - small end = 1.8 — pressing Calculate gives: 0.59867 m3 (smalian volume); 0.58208 m3 (huber volume); 0.58761 m3 (newton (most accurate)). 
Common mistakes to avoid