Particle Size Distribution
Compute D10, D50, D90, span and mean from cumulative volume data.
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What it does
Laser diffraction and sieve analysis return a particle size distribution, but the raw cumulative curve is hard to compare between batches. This calculator reads cumulative volume percent versus diameter and returns the standard percentiles D10, D50 and D90, the span that describes width, and a volume-weighted mean. Powder technologists, ceramicists and formulation scientists use it to spec raw materials, judge milling progress and predict flow, packing and dissolution from a single set of numbers.
How it works
The tool interpolates linearly between your data points to find the diameter at 10, 50 and 90% of cumulative volume: D10 is the size below which 10% of the mass lies, D50 is the median, D90 the size above which 10% lies. Span measures relative breadth as (D90 - D10) / D50, a dimensionless number around 1-2 for narrow powders. The volume-weighted mean sums each interval's midpoint times its volume increment. Sizes are in whatever unit you enter (usually micrometers); only the diameter and its cumulative percent are used.
Worked example
Take a powder whose cumulative volume reaches 2.1% at 0.5 micrometer, 33.2% at 5 micrometers, 58.6% at 10 micrometers and 96.1% at 45 micrometers. Linear interpolation gives D10 near 1.4 micrometers, D50 near 8.3 micrometers and D90 near 34 micrometers. With D10 = 1.4 and D90 = 34, span = (34 - 1.4) / 8.3 = about 3.9, a broad distribution. The volume-weighted mean lands near 11 micrometers, confirming the bulk of the mass sits in the tens-of-micrometers range.
When to use it
Use D-values to write powder specifications, track a milling or spray-drying run, and predict behavior: small D50 aids dissolution but hurts flow, large D90 signals oversized grit, and high span means a wide spread. The main pitfall is that D50 is sensitive to agglomerates, so a sonicated sample gives a different number than an as-received one; report the dispersion method. Also keep diameters in one unit, since mixing micrometers and nanometers silently breaks the interpolation.
FAQ
- What do D10, D50 and D90 mean?
- They are percentiles of the cumulative volume distribution. D10 is the diameter below which 10% of the sample mass lies, D50 is the median (half the mass is finer), and D90 is the diameter below which 90% lies, so 10% is coarser. For the sample data, D10 is about 1.4 micrometers, D50 about 8.3 micrometers and D90 about 34 micrometers. They summarize a full curve in three comparable numbers.
- What is span and how is it calculated?
- Span is a dimensionless width measure: span = (D90 - D10) / D50. It normalizes the gap between the coarse and fine tails by the median, so a span of 1 means the D90-D10 range equals one D50. For the sample, (34 - 1.4) / 8.3 = about 3.9, a broad powder. Narrow, well-milled powders often show span near 1-2, while wide feeds exceed 3.
- Why is D50 sensitive to agglomerates?
- Laser diffraction and sedimentation see the scattering or settling size of whatever particle is in the liquid, so agglomerates count as one large particle. Sonication or surfactant can break them and drop D50 by microns, while an as-received slurry keeps them and reports a larger D50. Always state the dispersion method and time, because the same powder can give very different D50 values depending on how it was prepared.
- What units should I enter for size?
- Enter diameter in any single unit, usually micrometers, and cumulative volume percent as a number from 0 to 100. The calculator only interpolates the curve, so the output keeps your input unit; do not mix micrometers in one row with nanometers in another, or the percentiles will be wrong. A header line starting with # is ignored, and values may be split by comma, tab or space.