Skip to main content
Calcimator

Paper Opacity Calculator

Estimate paper opacity from basis weight, filler content, TiO2 loading, fiber type, and calendering. Uses Kubelka-Munk scattering theory.

About this calculator

This calculator estimates how opaque a sheet of paper will be — how much light it blocks rather than lets through — using a simplified form of Kubelka-Munk scattering theory: opacity = 1 − e^(−S × basis weight / 1000), where S is a total light-scattering coefficient built up from your inputs. Each fiber type starts with its own base scattering value (mechanical/groundwood pulp scatters light far more than chemical/kraft pulp, because its fiber fragments and lignin create more internal air-fiber interfaces), and a blend sits between the two. Filler loading adds to that scattering: ordinary mineral fillers like calcium carbonate or clay contribute a modest amount per percentage point, while titanium dioxide contributes roughly six times as much per point because of its very high refractive index — the calculator separates out the TiO2 portion of your filler percentage specifically to capture this.

Calendering, which presses and smooths the sheet under heat and pressure, works against opacity by collapsing the air pockets between fibers that do most of the scattering, so each step up in calendering level trims the total coefficient. The result is reported two ways: printing opacity (the raw scattering-based estimate) and a TAPPI-style contrast-ratio opacity that runs a few points lower, plus a qualitative show-through risk rating. Treat this as a formulation-planning estimate, not a substitute for an actual TAPPI T 425 opacity meter reading — real sheets vary with pulp refining, wet-end chemistry, and moisture in ways this simplified model doesn't capture.

Inputs

%
%

Results

Printing opacity (%)

99.75

TAPPI opacity (%)96.76
Scattering coeff (m²/kg)75
Show-through risk0
Total filler (%)15
How to Use This Calculator
  1. Enter the paper basis weight (GSM) for the grade being evaluated.
  2. Input total filler (%) and TiO2 percentage of that filler from your formulation.
  3. Select fiber type (chemical kraft, mechanical, or blend).
  4. Choose calendering level (0 = none to 3 = heavy supercalender).
  5. Review Printing Opacity (%), TAPPI Opacity, Scattering Coefficient, and Show-Through Risk.

How the result changes with Basis weight (GSM)

Basis weight (GSM)Printing opacity (%)
4095.02
6098.89
12099.99
200100

What each input means

Basis weight (GSM)
Paper grammage in grams per square meter.
Total filler (%)
Total mineral filler loading as percentage of sheet weight (includes TiO2).
TiO2 in filler (%)
Titanium dioxide portion of filler. TiO2 has very high light-scattering power.
Fiber type
0 = Chemical (kraft), 1 = Mechanical (groundwood), 2 = Blend.
Calendering level
0 = None, 1 = Light, 2 = Moderate, 3 = Heavy supercalendered.

What each result means

Printing opacity (%)
Estimated printing opacity percentage (0-100).
TAPPI opacity (%)
TAPPI T 425 contrast ratio opacity estimate.
Scattering coeff (m²/kg)
Total light scattering coefficient.
Show-through risk
Print show-through risk: 0 = None, 1 = Low, 2 = Moderate, 3 = High.
Total filler (%)
Confirmed total filler loading percentage.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Basis weight (GSM) = 80, Total filler (%) = 15, TiO2 in filler (%) = 0, Fiber type = 0 = 5 input(s) provided
  2. Calculate Printing opacity
    Printing opacity = opacityFraction * 100
    99.75 = 99.75
  3. Calculate TAPPI opacity
    TAPPI opacity = min(100, opacityPct * 0.97)
    96.76 = 96.76
  4. Calculate Scattering coeff
    75 = 75

Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why does TiO2 loading raise opacity so much more than other fillers?

The calculator adds roughly 18 m²/kg of scattering per percentage point of TiO2 versus about 3 m²/kg for the rest of the filler blend — a six-to-one ratio built directly into the fillerS term. That gap reflects titanium dioxide's very high refractive index compared to calcium carbonate or clay, which lets a small TiO2 addition scatter far more light per unit weight than an equivalent amount of ordinary mineral filler.

Why does increasing the calendering level lower the reported opacity?

Calendering compresses the sheet under heat and pressure, squeezing out the air-fiber interfaces that scatter light in the first place. The calculator models this with a calenderReduction factor that cuts the total scattering coefficient by 6% per level (0 to 3), so a heavily supercalendered sheet (level 3) loses 18% of its scattering power compared to an uncalendered one with identical fiber and filler content.

Why is TAPPI opacity always slightly lower than printing opacity in the results?

The calculator applies a fixed 0.97 multiplier to the printing opacity figure to approximate TAPPI T 425 contrast-ratio opacity, which measures the sheet against a black backing rather than the simpler single-sheet transmission model used for printing opacity. This 3% offset is a typical-paper approximation baked into the formula, not a separately derived scattering calculation.

Does switching from kraft to groundwood fiber change opacity even with the same filler recipe?

Yes — mechanical (groundwood) pulp is assigned a base scattering coefficient of 55 m²/kg versus only 30 m²/kg for chemical (kraft) pulp, because groundwood's fiber fragments and residual lignin create many more internal light-scattering surfaces. With identical basis weight and filler loading, choosing groundwood over kraft can raise opacity noticeably before any filler is even added.

Related Calculators

The questions that sit next to this one — chosen by subject, including calculators filed under a different category.

Paper Science

Paper Basis Weight Calculator

Convert between GSM (metric) and US basis weight (lbs/ream) for any paper grade. Estimates caliper thickness and M-weight.

Paper Science

Paper Machine Speed Calculator

Calculate required paper machine wire speed from production rate, trim width, basis weight, and machine efficiency. Includes reel timing and section speeds.

Paper Science

Pulp Consistency Calculator

Calculate pulp stock consistency from fiber weight and slurry weight. Determine dilution water needed and fiber flow rates for paper machine approach systems.

More in Manufacturing, Industrial & Coatings.