Pharmaceutics
Surface Area & Particle Size Analyzer
Turns sieve or laser-diffraction data into D10, D50, D90, span, mean diameter and specific surface area for a pharmaceutical powder.
D50 — median particle size
172.5μm
Moderate distribution · span 1.91
Sieve analysis data
List sieves from the coarsest to the finest, ending with the pan (mesh 0, opening 0).
True density, needed for the surface area. Blank or 0 is treated as 1 g/cm³. Many drug powders are 1.2–1.6.
Try an example
Examples replace the sieve table only.
Results
Sizes in micrometres (μm).
Dissolution rate
D50 173 μm – Moderate dissolution.
Flowability
Span 1.91 – May need glidant.
Cumulative distribution
Cumulative % finer than each size. Dashed lines mark 10%, 50% and 90%.
Sizes below 1 μm (such as the pan) are drawn at 1 μm.
Working
Your numbers, plugged into each step.
| Opening (μm) | Cumulative % finer |
|---|---|
| 850 | 100.0% |
| 425 | 95.0% |
| 250 | 80.0% |
| 180 | 55.0% |
| 150 | 35.0% |
| 75 | 20.0% |
| 0 | 0.0% |
Cumulative % finer = 100 − running total of % retained (7 rows, total 100.0%).
D10 = 0 + (10 − 0.0) ÷ (20.0 − 0.0) × (75 − 0) = 37.5 μm
D50 = 150 + (50 − 35.0) ÷ (55.0 − 35.0) × (180 − 150) = 172.5 μm
D90 = 250 + (90 − 80.0) ÷ (95.0 − 80.0) × (425 − 250) = 366.7 μm
Span = (366.7 − 37.5) ÷ 172.5 = 1.91
Mean = √(37.5 × 366.7) = 117.3 μm
SSA = 6 ÷ (1.5 × 172.5 ÷ 1000) × 1000 = 23188.4 m²/kg
Cumulative % finer = 100 − Σ % retained (from the coarsest sieve down)
Dx = S₂ + (x − C₂) ÷ (C₁ − C₂) × (S₁ − S₂)
Span = (D90 − D10) ÷ D50
Mean (sieve) = √(D10 × D90) · Mean (laser) = Σ(size × %) ÷ 100
SSA = 6 ÷ (ρ × D50 ÷ 1000) × 1000 (m²/kg)
Dx is read off the cumulative curve by straight-line interpolation between the two rows that bracket x%: S₁ and C₁ are the size and cumulative % of the coarser row, S₂ and C₂ of the finer row. ρ is particle density in g/cm³ and D50 is in μm. The surface area treats every particle as a sphere of diameter D50 (area-to-volume ratio 6/d).
The distribution is read as narrow when span is below 1, broad above 2, and moderate in between. A span below 1.5 is read as good flow; a D50 below 50 μm as fast dissolution.
References
- Sinko PJ, editor. Martin's Physical Pharmacy and Pharmaceutical Sciences. 8th ed. Philadelphia: Wolters Kluwer; 2023.
- Aulton ME, Taylor KMG, editors. Aulton's Pharmaceutics: The Design and Manufacture of Medicines. 6th ed. Edinburgh: Elsevier; 2022.
Common questions
Each row is a share of the whole sample, so together they should account for all of it. Up to 5% either way is accepted to allow for handling losses on the sieves; beyond that the calculator asks you to recheck the data.
Add it as the last row with mesh 0 and opening 0, and enter the % of powder collected in it. Without the pan the cumulative curve never reaches 0% finer and the total will be short.
Smaller is more uniform. Below 1 is narrow; 1–2 is typical of milled or granulated material; above 2 is broad and more likely to segregate during mixing. Tablet granules usually aim for a span under 2.0.
For sieve data it is the geometric mean of D10 and D90. For laser diffraction it is the volume-weighted mean, each size multiplied by its % and divided by 100 — so the % column should total 100.
Specific surface area is area per unit mass. The same size of particle has less surface per gram when the material is denser, so the true (particle) density divides into the result.
Prepared by the PharmaWallah student team. Verify results with your textbook or instructor. Report an error · Editorial policy