Are these results number-weighted or volume-weighted?

Number-weighted (by count). Each measurement counts once. Laser-diffraction instruments report volume-weighted values, which are numerically different — often 2–5× larger for polydisperse samples. Do not compare the two directly.

Should I use the normal or lognormal fit?

Particle and microsphere size data is commonly lognormal (right-skewed). The tool fits both and reports which has the better goodness-of-fit (R²/KS). Use the recommended one unless your distribution is narrow and symmetric.

How many particles do I need?

For a stable distribution, aim for ≥ 2,000 measurements (≥ 5,000 for submission-grade D90 work). Below ~2,000 the tool flags results as Preliminary.

Does my data leave my computer?

No. All parsing and computation happen in your browser; nothing is uploaded.

ToolsConductScience tool

MicrospheresFree in-browser calculator

Microsphere Size Distribution Calculator.

Paste microsphere diameter measurements and get a count-per-bin histogram, normal and lognormal fits, D10/D50/D90, span, CV%, GSD, and QC spec pass/fail. Client-side — nothing is uploaded.

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Validated2026-06-19

CitableMethods and citation included

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Diameter measurements (paste CSV / one per line)

0 values

Unit

QC spec (optional)

D90 maxD10 minCV% maxSpan max

Paste at least two diameter values to see the distribution.

When to use

You have a list of particle/microsphere diameters and need D-values, span, and a histogram
You need a quick QC pass/fail against a size specification
You want to know whether your data is better described as normal or lognormal

Do not use for

You need volume-weighted D-values comparable to laser diffraction (this is number-weighted)
You are establishing regulatory compliance to a compendial method (USP/EP) without method comparability

Number-weighted ≠ volume-weighted

Do not compare these number-weighted D-values to laser-diffraction (volume-weighted) D-values; they differ by physics, not error.

Mind your sample size

Below ~2,000 measurements the tail percentiles (D90) are unstable. The tool flags small samples as Preliminary.

Method

Percentiles by linear interpolation on the sorted data; sample standard deviation; GSD = exp(SD of ln diameters). Normal and lognormal PDFs are fit by moment-matching and scored by R² against the histogram and a Kolmogorov–Smirnov statistic against the empirical CDF. Results are number-weighted.

Validated

Last validated 2026-06-19. Calculations are designed for planning and documentation support; verify procurement decisions against manufacturer specifications or institutional SOPs.

How to cite

How to Cite

ConductScience. Microsphere Size Distribution Calculator (v1.0.0). 2026.

ISO 9276-2:2014 Representation of results of particle size analysis — Calculation of average particle sizes and moments.

Limpert E, Stahel WA, Abbt M. Log-normal distributions across the sciences. BioScience. 2001;51(5):341-352. doi:10.1641/0006-3568(2001)051[0341:LNDATS]2.0.CO;2

Number-weighted vs volume-weighted

Image and count-based methods produce number-weighted distributions: every particle contributes once. Laser diffraction produces volume-weighted distributions: each particle contributes in proportion to its volume, so a few large particles dominate. The two give different D-values by design — this calculator reports number-weighted results.

Why lognormal?

Distributions from emulsification, milling, and polymerization are usually lognormal because each size-change step is multiplicative (Gibrat’s law). A lognormal distribution is symmetric on a log axis and never negative. A normal fit is reasonable only for narrow, symmetric distributions (CV below ~10–15%).

D10, D50, D90, and span

D10/D50/D90 are the diameters below which 10%, 50%, and 90% of particles fall (by count here). Span = (D90 − D10) / D50 measures breadth: smaller is more monodisperse. CV% and the geometric standard deviation (GSD) are complementary polydispersity measures.

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