Nanoparticle Concentration Calculator

Convert between mass concentration, molarity, and particle number density

Particle Properties

Required

Particle Model

Solid particle Core-shell

Total Diameter (d) TEM or hydrodynamic diameter

Diameter must be greater than zero

Material Density (ρ) Bulk density of particle material

g/cm³

Density must be greater than zero

Polydispersity Index (PDI) Optional – from DLS measurement

Leave blank for monodisperse. PDI = (σ/d)² where σ is std. deviation.

PDI must be between 0 and 1

Single particle mass: —

Effective density: —

Molecular weight: —

Concentration Input

Any One

Mass Concentration

Concentration must be ≥ 0

Molar Concentration

Concentration must be ≥ 0

Number Density

Accepts scientific notation (e.g., 1e12 or 1×10¹²)

Number density must be ≥ 0

Enter a value in any field above. The other two will be calculated automatically.

Converted Values

Mass Concentration

— mg/mL

Molar Concentration

— nM

Number Density

— particles/mL

Understanding Nanoparticle Concentration Units

Nanoparticle concentrations can be expressed in three fundamentally different ways. Converting between them requires knowing both the particle size and material density.

Core-Shell Particles

For particles with surface coatings (citrate, PEG, proteins), using bulk core density with the hydrodynamic diameter overestimates particle mass. The core-shell mode calculates effective density by weighting core and shell volumes. For a 20 nm gold core with 5 nm PEG shell, effective density drops from 19.3 to ~6.5 g/cm³.

Polydispersity Considerations

Real samples have size distributions characterized by PDI. Because mass scales with d³, larger particles dominate mass concentration:

PDI < 0.1: Monodisperse, calculations are accurate
PDI 0.1–0.2: Moderate polydispersity, ~10–20% error
PDI 0.2–0.4: Broad distribution, ~20–50% error
PDI > 0.4: Very polydisperse, consider fractionating

Sources & Citations

Haiss, W., et al. (2007). Determination of size and concentration of gold nanoparticles from UV-Vis spectra. Analytical Chemistry, 79(11), 4215–4221.

Pace, H. E., et al. (2011). Determining transport efficiency for counting and sizing nanoparticles via single particle ICP-MS. Analytical Chemistry, 83(24), 9361–9369.

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