Appropriate
- Order-of-magnitude planning
- Comparing ideal counts across sizes
- Designing an initial dilution range
- Estimating whether a direct count method is feasible
Planning calculation
Estimate idealized silica particles from size and mass.
Enter the nominal diameter, assumed particle density, silica mass concentration and sample volume. The calculator treats every particle as a solid sphere of one diameter.
Model
The geometry behind the estimate
Sphere volume = (4/3)πr³ | mass per particle = density × volume | count = total silica mass ÷ mass per particle| Assumption | Why it can fail | Better evidence |
|---|---|---|
| One exact diameter | Real particles have a distribution | Lot-specific distribution and count method |
| Solid nonporous sphere | Porosity or coatings change effective density | Product-specific density / structure evidence |
| All silica mass is particles | Residuals or formulation components may be included | Certified solids or chemical analysis |
| No aggregates | Association changes effective entities | DLS, microscopy or application-specific count |
| No transfer loss | Particles can adsorb, settle or remain in vessels | Validated recovery study |
Use and misuse
Use the estimate for scale—not release decisions.
Not appropriate
- Certifying number concentration
- Replacing a lot certificate
- Assigning deposited wafer count
- Proving all powder redispersed
- Setting a regulated release value
Upgrade the model
- Use a measured size distribution
- Use product-specific density
- Measure solids concentration
- Validate recovery and aggregation
- Compare against an independent count method
Questions engineers ask
Frequently asked questions
Is the estimated count a certified number concentration?
No. It is a geometric estimate based on ideal spheres, one diameter and user-entered density and mass concentration.
Why does count change so sharply with diameter?
Ideal sphere volume and mass scale with diameter cubed. Doubling diameter produces eight times the mass per particle at constant density.
Can I use bulk silica density for porous particles?
Only as a rough assumption. Effective particle density can differ with porosity, coating and structure.
Sources and verification
Technical basis
- NIST measurement protocols — Supports distinguishing model estimates from measured results.
- NIST traceability policy — Supports traceability and uncertainty boundaries.
- Applied Physics silica microsphere family — Commercial size-family context.
Commercial specifications should be confirmed against the current Applied Physics quotation, certificate, lot documentation and product page before purchase or protocol use.
Continue the research
Related technical guidance
Particle distribution
Replace single-diameter assumptions with a population.
Dry powders
Control powder mass and redispersion.
Dilution calculator
Calculate ideal preparation volumes.
Applied Physics technical pathway
Need a particle specification reviewed?
Send the target size, medium, concentration, application, certificate requirements and shipping destination. Applied Physics can evaluate the appropriate silica family or custom pathway.