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Log Taper CalculatorDiameter Change and Form Factor Analysis

Calculate log taper rate, IS 1902 taper class, form factor, and volume loss due to taper. Essential for quality grading, sawmill yield planning and purchase price negotiation.

Why this calculation matters

Taper decides which volume formula is honest and how much width you can expect from the butt versus the top.

IS 1902 Taper ClassesForm FactorVolume Loss %Price Impact INRPDF Report
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Log Taper Calculator

Diameter Change and Form Factor Analysis

Unit System and Species

This picker does not change the answer. Taper depends only on the dimensions you enter, not on the species — that is what makes it a rule rather than an estimate. The species is here so you can note it on a printout.

INR/m3
Diameter Measurements
cm
cm
metres
cm

Leave 0 to auto-calculate as average of two ends.

logs
IS 1902 Classes:
Class 1: <=0.5 cm/m (slight)
Class 2: 0.5-1.5 cm/m (moderate)
Class 3: >1.5 cm/m (excessive)
OK
Taper Analysis Results
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cm/m
Taper Rate
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form factor
Form Factor f
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IS 1902
Taper Class
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%
Volume Loss vs Cylinder
MeasurementValueMethodNote
Taper Analysis

About Log Taper Calculator

Taper is the reduction in diameter from butt to top end of a log. High taper reduces sawmill yield, causes skewed boards, and lowers log grade and price. IS 1902:2015 India classifies taper into three grades for pricing purposes. It applies a standard log taper formula so you can predict the diameter at any height along the stem before deciding where to buck.

Where Used?

Log Grading IS 1902Sawmill Yield PlanningTimber PurchaseForest Dept IndiaImport Quality Control

Formulas

Taper = (D_large - D_small) / L cm per metreForm factor f = V_huber / V_cylinderIS 1902 Class 1: taper <= 0.5 cm/m (slight)IS 1902 Class 2: 0.5 to 1.5 cm/m (moderate)IS 1902 Class 3: > 1.5 cm/m (excessive)
Sources & verification
  • Taper = (D_large − D_small) / L
  • IS 1902 taper classes 1–3
  • Form factor = (D_mid/D_large)²

Formula checked against the sources above by an automated regression test (tests/verify-phase3a.js) that derives each expected value independently of this page. Last reviewed .

FAQ

How does taper affect sawmill yield?
A log with 2 cm/m taper and 5m length loses roughly 18-25% of sawn lumber vs a uniform cylinder. Tapered logs require offset cuts, wasted edging, and irregular board widths. Mills pay 5-15% less per m3 for Class 3 logs.
Is more taper always a bad thing for a log?
For lumber recovery, generally yes — a strongly tapering log yields shorter or narrower boards and more slabwood waste than a cylindrical one of the same butt diameter, because the sawyer has to work around the shrinking width. But taper isn't all downside: it's natural, it tells you something about how the tree grew, and for some products like tapered poles or certain veneer logs it's not a problem at all. The key is to know the taper before you saw so you can plan the cutting pattern around it.
How do I measure taper accurately in the field?
Measure the diameter (inside bark) at both ends of the log, subtract the smaller from the larger, and divide by the log's length to get taper per unit length — that's exactly what this calculator does. For consistency, always measure at the same reference points and take two readings at right angles at each end to average out any out-of-roundness. Doing it the same way every time matters more than the absolute method, so your figures stay comparable from log to log.

Wood species data

Density, hardness and movement for 60 timbers

Browse all species

How the calculation works

Three standard volume methods are shown side by side because they disagree, and the disagreement is the useful part. Smalian averages the two ends and reads high on a tapered log; Huber uses the middle and reads closer to truth; Newton weights the middle four times as heavily and is the most accurate of the three when all three diameters are measured.

Show the formula
Taper = (butt diameter - top diameter) / length. Huber volume = mid-point area x length. Smalian volume = mean of the two end areas x length. Newton volume = (butt area + 4 x mid area + top area) / 6 x length. Form factor = Huber volume / cylinder volume computed on the butt diameter.

Huber, Smalian and Newton are standard published volume formulas and Newton is the reference where all three diameters are measured. The taper CLASSES shown alongside are a presentational convention of this site — no standard defines slight, moderate or excessive taper — so read the taper rate itself rather than the label.

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

Reports taper between the points measured. It does not account for irregular taper along the stem, ovality, or the difference between butt and upper logs from the same tree.

Do not use this for Sale settlement or grading decisions.

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.

How to use this tool

  1. Enter the log measurements below, then press Calculate.
  2. Fill in price per m3, large-end diameter, small-end diameter, log length.
  3. Press Calculate.

Worked example

With the tool's starting values — price per m3 = 18000, large-end diameter = 52, small-end diameter = 36, log length = 5, mid-point diameter = 44 — pressing Calculate gives: 3.200 cm/m (taper rate); 0.7160 form factor (form factor f); Class 3 IS 1902 (taper class).

Common mistakes to avoid