Filter Media Efficiency, Resistance & Quality Factor

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. The 6 inputs are read from the form on every keystroke: Basis Weight, Mean Fibre Diameter, Face Velocity, Capture Constant, Resistance Constant and Target Efficiency.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves Quality Factor together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Filtration Efficiency, Penetration, Pressure Drop, Resistance per Gram, Efficiency per Gram, Basis Weight for Target, Extra Weight Needed, Pressure Drop at Target and Resistance the Target Costs — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

The tool loads with this case already solved — the Quality Factor shown above is its answer. Change one value and the difference from this baseline is the sensitivity of the result to that variable.

How to use it

1. Work through the input groups in order — Media and Calibration & Target. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read Quality Factor in the dark results panel — that is the headline figure, expressed in 1/Pa.
4. Check the supporting rows underneath (Filtration Efficiency, Penetration, Pressure Drop, Resistance per Gram, Efficiency per Gram, Basis Weight for Target, Extra Weight Needed, Pressure Drop at Target and Resistance the Target Costs) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Process planning — establishing Quality Factor before a trial is booked, so machine time and material in Nonwovens, Filtration, Hygiene & Technical Webs are committed against a calculated figure rather than an estimate.
• Costing and quotation — Quality Factor is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Basis Weight) shows how much of the gap in Quality Factor each variable explains.
• Teaching and study — the accepted ranges bracket normal Nonwovens, Filtration, Hygiene & Technical Webs practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• Two constants drive this tool and they are not the same kind of number. The resistance constant comes from a model: by default it is the Davies correlation for a polypropylene web at 11% solidity, with its leading constant refitted on measured N95 filtering layers (8.3 in place of 64, O Shaughnessy and others, 2023), which gives the same web the same pressure drop as the Meltblown Pore Size tool. Davies as published would give 4.53, about eight times more, because he built the correlation on much coarser fibres. The capture constant is fitted: no model on this page predicts it, and its default describes no particular media. The capture term is a fitted single-parameter stand-in for classical single-fibre theory, which treats interception, impaction and diffusion separately and gives each a different dependence on velocity and particle size; the fitted form reproduces the exponential shape and the direction of every lever but cannot predict the most-penetrating particle size or how efficiency shifts with it, and near that size the real curve has a minimum this model does not. Fit the two constants on measured flat-sheet data at the velocity of interest and treat the model as an interpolator rather than a predictor. Electret media break the relationship entirely: a charged web achieves efficiencies far above what its structure alone would give, loses that advantage as the charge dissipates in service or on contact with oil aerosol, and a mechanical model will therefore be badly optimistic about its life and badly pessimistic about its initial performance. Pressure drop here is clean-media resistance; loading raises it through life, and the useful life of a filter is usually set by the terminal drop rather than by efficiency. Face velocity is the flat-sheet test condition and not the face velocity of a pleated element, where the media velocity is lower than the element velocity by the pleating ratio - which is precisely why elements are pleated.
• Every input is bounded to the range normal practice occupies (Basis Weight 1 to 300 g/m2, Mean Fibre Diameter 0.2 to 30 um and Face Velocity 0.5 to 60 cm/s, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Questions people ask