Particle Size Calculator
Mean, median, standard deviation and D-values from individually measured particle diameters.
Calculator
One value per line, space- or semicolon-separated. At least 2 measurements.
Theory & method
Unlike the Size Distribution Calculator — which starts from sieve masses retained per aperture, a mass-weighted distribution — this calculator starts from particle diameters measured individually: under a microscope, from image analysis, or with a caliper or reticle. Each measurement counts as one point in the distribution, not a mass fraction.
The empirical cumulative distribution sorts the measurements and assigns 1/n to each; D-values follow by log-linear interpolation on that curve — the same `dValue` engine used by every calculator on this site. A percentile outside the range actually covered by the measurements is left undetermined ("—") rather than extrapolated.
Cu and Cc follow the same ASTM D2487 definitions used elsewhere on this site, but computed here on a count-based (number of particles) distribution rather than a mass-based one — the two are not directly comparable when particle size varies widely: a few large particles dominate a mass distribution but count the same as small ones in a count distribution.
How to use
- 01Measure or obtain individual particle diameters (microscopy, image analysis, caliper, reticle) — the same unit throughout (µm).
- 02Enter one value per line (or separated by spaces/semicolons) — comma is the decimal separator, as everywhere on this site.
- 03Read the mean, median and standard deviation, and the D-values, Cu, Cc and span derived from the empirical distribution.
Frequently asked questions
How is this different from the Size Distribution Calculator?
The Size Distribution Calculator starts from sieve masses retained per aperture — a mass-weighted distribution. This calculator starts from individually measured diameters (e.g. under a microscope) — a count-weighted (number-based) distribution. The two are not directly comparable when particle sizes vary widely: a handful of large particles dominate a mass distribution but count the same as small ones in a count distribution.
Why do some D-values show "—"?
A D-value only exists within the range actually spanned by your measurements' cumulative percentages — this engine never extrapolates beyond what was measured. With few measurements, or measurements clustered away from a percentile (e.g. D10 with only 3 values), that percentile falls outside the covered range and is left undetermined rather than guessed.
How many measurements do I need?
At least 2 to compute a distribution at all. Meaningful D10/D90 estimates typically need enough measurements that the extremes of your sample actually reach the 10th/90th percentile — with very few points, expect several results to read "—".
Normative references
- ISO 9276-1 — Representation of results of particle size analysis — Part 1: Graphical representation.
- ISO 9276-2 — Representation of results of particle size analysis — Part 2: Calculation of average particle sizes/diameters and moments from particle size distributions.
- ASTM D2487 — Standard Practice for Classification of Soils for Engineering Purposes (Unified Soil Classification System) — Cu/Cc definitions.