Analyze component sizes with practical distribution tools. Choose models or measurements and set custom bins. See fractions, percentiles, and exports in one view instantly.
Goal: compute the fraction of components that fall within size bins, plus key percentiles (D10, D50, D90).
If ln(d) is normally distributed with median dg and spread σg, then:
F(d) = Φ( (ln(d) − ln(dg)) / ln(σg) )
Φ is the standard normal cumulative function.
A common particle-size form for undersize cumulative fraction:
F(d) = 1 − exp( −(d/λ)k )
λ is the characteristic size and k controls spread.
If d is normally distributed with mean μ and standard deviation σ:
F(d) = Φ( (d − μ) / σ )
This model can assign probability to negative sizes.
Between dmin and dmax, a scale-free model:
p(d) ∝ d−α, d ∈ [dmin, dmax]
Useful for fragmentation and multiscale component populations.
For bin edges di to di+1, the number fraction is:
fi = F(di+1) − F(di)
Area or volume/mass weighting applies w(d)=dp using bin midpoints, then re-normalizes all bins to sum to 1.
Example size–value pairs you can paste into measured-data mode:
| Size (micron) | Value (counts) |
|---|---|
| 5 | 12 |
| 10 | 30 |
| 20 | 26 |
| 40 | 18 |
| 80 | 14 |
Component size distribution describes how many parts fall within size ranges, such as 1–2, 2–5, or 5–10 micron. In quality control and materials processing, distribution shape often matters more than a single average. This calculator summarizes the distribution with cumulative fractions and standard percentiles, then formats the results for export.
Two batches can share the same mean size while behaving differently in flow, packing, surface reactivity, or optical scattering. A broader spread can increase fines (small sizes) and oversize tails (large sizes). Percentiles such as D10 and D90 quantify these tails, helping you compare batches using consistent metrics.
Counting components emphasizes small sizes because they are more numerous. Surface-area weighting scales roughly with d2, so larger particles gain importance for reactions or coatings. Volume or mass weighting scales with d3, matching many bulk-property applications. This tool applies the selected weighting and then normalizes fractions to 1.00.
Bin edges control resolution and noise. Narrow bins reveal structure but can look jagged with limited data. Wider bins smooth the curve and are easier to report. A common workflow is to start with log-spaced edges (for example 1, 2, 5, 10, 20, 50, 100) and refine around critical process limits.
The cumulative column shows the fraction below each bin’s upper edge, which should rise from 0 toward 1. D10 is the size where 10% of the chosen basis lies below it; D50 is the median; D90 captures the upper tail. Reporting D10/D50/D90 together is a compact way to describe spread and skew.
Lognormal is common for multiplicative growth processes and many particle populations. Rosin–Rammler (Weibull) often fits milled or crushed materials. Normal is useful when variations are symmetric, but it can imply negative sizes. Power-law models suit fragmentation cascades within dmin and dmax. Use models when you need a smooth predictive curve.
In measured-data mode, paste size,value pairs such as 5,12 and 10,30. Values may be counts, mass, or any nonnegative weight. The calculator sorts by size, re-normalizes values to fractions, and computes cumulative totals and D-values by interpolation. Ensure sizes are positive and use consistent units across all rows.
After calculation, the results block provides a metric summary and a detailed table suitable for technical notes and QA records. CSV export preserves the full table for spreadsheets and plotting. PDF export captures the results block for quick sharing, versioned reports, and review workflows.
D50 is the median size for the selected basis. Half of the normalized fraction lies below D50 and half lies above it, based on number, area, or volume weighting.
Use number for counting components, area for surface-driven effects like coatings, and volume/mass for bulk properties. The calculator weights by d² or d³ and re-normalizes to fractions.
The tool converts inputs to normalized fractions that sum to 1.00. In area or volume basis, values are additionally weighted by size, which changes relative contributions across sizes.
Start with log-spaced edges like 1, 2, 5, 10, 20, 50, 100. Then tighten bins near specification limits or where the distribution changes rapidly.
Lognormal is a strong default when size is produced by multiplicative processes or growth variability. It often represents particle populations with a right-skewed tail.
Yes. Run each batch with identical bin edges and basis. Compare D10, D50, D90, and the cumulative table to see differences in tails and overall spread.
A normal distribution can assign probability to negative sizes. The calculator reports results, but you should confirm that μ and σ keep nearly all probability in the physically valid range.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.