Estimate Number of Particles from Particle Size Distribution Calculator

Analyze particle classes using mass fractions and diameters. View bin counts, totals, and concentration estimates. Export clean reports and compare assumptions with interactive charts.

Enter mass-based particle size distribution data, choose a representative diameter method, and estimate total particle count from density and particle volume assumptions.

Calculator Input

Large screens use three columns, smaller screens use two, and mobile uses one.
Reset
1.0 matches a sphere with the same diameter.

Particle Size Distribution Input

Enter mass percentage by size bin. The calculator will normalize the percentages if they do not sum to 100.
Lower size Upper size Mass % Row action

Formula Used

This calculator estimates particle number from a mass-based particle size distribution. Each size bin is treated as particles with one representative diameter.

1. Choose a representative diameter for each bin.

2. Convert that diameter to centimeters for volume consistency.

3. Compute particle volume:

Vp = shape factor × π/6 × d³

4. Compute single particle mass:

mp = density × Vp

5. Compute mass in each bin:

mbin = total sample mass × normalized mass fraction

6. Estimate particles in each bin:

Nbin = mbin / mp

7. Sum all bins for the total estimated particle count.

How to Use This Calculator

  1. Enter the total sample mass in grams.
  2. Enter the true material density in g/cm³.
  3. Set the shape factor. Use 1.0 for spherical particles.
  4. Select the particle size unit used in your distribution.
  5. Select a representative diameter method for each size bin.
  6. Enter lower size, upper size, and mass percentage for each bin.
  7. Click Estimate Particle Count.
  8. Review the summary, detailed table, and Plotly chart.
  9. Use the CSV or PDF buttons to export the result.

Example Data Table

Example assumptions: sample mass = 10 g, density = 2.65 g/cm³, shape factor = 1.00, size unit = µm, method = geometric mean.

Lower size (µm) Upper size (µm) Mass %
1510
51018
102024
204026
408022

FAQs

1. What does this calculator estimate?

It estimates how many particles are present in a sample when you know total mass, material density, and a mass-based particle size distribution. It converts each size bin into an estimated count using particle volume and mass.

2. Why do smaller particles create very large counts?

Particle mass scales with the cube of diameter. When diameter drops, each particle becomes much lighter, so the same bin mass is divided into many more particles. That is why fine fractions often dominate count.

3. Why is the result only an estimate?

Real particles are not identical inside a bin. The calculator uses one representative diameter for each range and assumes a constant density and shape factor. Those assumptions make the output useful for estimation, not exact counting.

4. Which representative diameter method should I choose?

Geometric mean is common for log-spaced size bins. Arithmetic mean is simple for narrow ranges. Harmonic mean can emphasize smaller particles. Lower and upper bounds help test sensitivity. Use the method that best matches your measurement practice.

5. Can this handle non-spherical particles?

Yes. Use the shape factor to adjust particle volume away from the ideal sphere. A value below or above 1 changes the estimated particle mass and count. Choose a factor from your own calibration or literature.

6. What happens if my mass percentages do not sum to 100?

The calculator normalizes the values automatically and warns you. This preserves the relative distribution while making the total usable. Still, you should check your data because large deviations may indicate missing fractions or transcription errors.

7. What units are supported for particle size?

You can enter nanometers, micrometers, millimeters, or centimeters. The calculator converts sizes internally to centimeters because density is entered in grams per cubic centimeter.

8. When is this calculator most useful in chemistry?

It is useful for powders, catalysts, precipitates, pigments, crystals, and other particulate solids where you have a measured size distribution and want a fast count estimate for comparison, screening, formulation, or reporting.

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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.