Nanoparticle Size Calculator
Size distribution processing from lab inputs.
About this calculator
This calculator turns a single hydrodynamic diameter measurement — the kind of number a Dynamic Light Scattering (DLS) instrument reports as the Z-average — into a fuller physical picture of the particle. It runs the number backward through the Stokes-Einstein relation (D = kT / (3πηd)) to recover the diffusion coefficient that would have produced that size at your stated temperature and solvent viscosity, so you can sanity-check instrument settings or compare across measurement conditions. From the diameter alone it also derives geometric quantities: surface area (πd²) and volume ((π/6)d³) for a single idealized sphere, plus the surface-to-volume ratio (6/d), which matters because a nanoparticle's reactivity, catalytic activity, and dissolution rate all scale with how much surface it exposes per unit of material — smaller particles react disproportionately faster.
The polydispersity index (PDI) you enter is translated into a size standard deviation estimate (σ = d·√PDI) and bucketed into a monodisperse/moderate/broad/very-broad classification, the standard shorthand DLS users rely on to judge sample quality. Finally, a Stokes settling velocity is computed assuming a gold nanoparticle in water (fixed densities of 19,300 and 997 kg/m³) — useful as a reference case, but swap in your own material's density if it isn't gold. Because the model treats every particle as a perfect, non-interacting sphere, real aggregation, non-spherical shapes, or concentrated suspensions will shift actual behavior away from these idealized numbers.
Inputs
Results
Diffusion Coeff. (m²/s)
0
S/V Ratio (nm⁻¹)
0.12
How to Use This Calculator
- Enter the hydrodynamic diameter (nm) from your DLS measurement.
- Set PDI (polydispersity index) to characterize size distribution width — below 0.2 indicates monodisperse.
- Enter solution temperature (°C) and solvent viscosity (mPa·s).
- Review diffusion coefficient (m²/s), surface area (nm²), volume (nm³), and surface-to-volume ratio.
- Size standard deviation (nm) helps assess whether your synthesis produces a tight size distribution.
How the result changes with Particle Diameter (nm)
| Particle Diameter (nm) | Diffusion Coeff. (m²/s) | S/V Ratio (nm⁻¹) |
|---|---|---|
| 25 | 0 | 0.24 |
| 38 | 0 | 0.16 |
| 75 | 0 | 0.08 |
| 125 | 0 | 0.05 |
What each input means
- Particle Diameter (nm)
- Hydrodynamic diameter (Z-average) from DLS.
- Polydispersity Index (PDI)
- <0.1 monodisperse, 0.1-0.3 moderate, >0.3 broad.
- Temperature (°C)
- Measurement temperature.
- Solvent Viscosity (mPa·s)
- Water at 25°C = 0.89 mPa·s.
What each result means
- Diffusion Coeff. (m²/s)
- D = kT/(3πηd). Stokes-Einstein diffusion coefficient.
- Surface Area (nm²)
- Single particle surface area.
- Volume (nm³)
- Single particle volume.
- S/V Ratio (nm⁻¹)
- 6/d for spheres. Higher = more reactive surface.
- Size Std Dev (nm)
- Estimated σ = d·√PDI.
- PDI Class (1-4)
- 1=monodisperse, 2=moderate, 3=broad, 4=very broad.
- Sedimentation (m/s)
- Stokes settling velocity (gold NP in water).
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersParticle Diameter (nm) = 50, Polydispersity Index (PDI) = 0.15, Temperature (°C) = 25, Solvent Viscosity (mPa·s) = 0.89 = 4 input(s) provided
- Calculate Diffusion Coeff.Diffusion Coeff. = parseFloat(diffusionCoeff.toPrecision(4))9.815e-12 = 9.815e-12
- Calculate S/V RatioS/V Ratio = 6 / diameterNm0.12 = 0.12
- Calculate Surface AreaSurface Area = π * diameterNm * diameterNm7853.98 = 7853.98
- Calculate VolumeVolume = (π / 6) * pow(diameterNm, 3)65449.85 = 65449.85
Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does lowering the temperature or raising viscosity change the diffusion coefficient for the same particle size?
Because diffusion coefficient is derived, not measured, here — it's back-calculated from Stokes-Einstein: D = kT/(3πηd). Increasing temperature raises D (particles diffuse faster), while raising viscosity lowers D (a thicker solvent damps motion) even though you entered the same diameter. That's why you should log the actual measurement temperature and solvent viscosity alongside your DLS diameter, not just the diameter number itself.
What does the PDI classification (1-4) actually mean for my sample?
PDI class buckets your polydispersity index into a quality read: 1 (PDI<0.1) is monodisperse — a tight, uniform size population; 2 (0.1-0.3) is moderate; 3 (0.3-0.5) is broad; 4 (>0.5) is very broad, suggesting aggregation or a multimodal mixture. It's derived straight from the same PDI thresholds DLS instrument software itself uses, so it should match what your instrument's own report calls the sample.
Why is the sedimentation velocity fixed to gold nanoparticles in water?
The Stokes settling calculation needs a particle density and a fluid density, and the engine hardcodes gold (19,300 kg/m³) and water (997 kg/m³) rather than asking you for material properties. If your nanoparticle is a different material — silica, polystyrene, iron oxide — the real settling velocity will differ substantially since it scales with the density difference between particle and fluid, so treat this output as illustrative unless you're actually working with gold in water.
Why does the surface-to-volume ratio matter for nanoparticle behavior?
S/V ratio (6/d for a sphere) quantifies how much surface area exists per unit of material, and it climbs sharply as diameter shrinks — a 10 nm particle has ten times the S/V ratio of a 100 nm particle. Because catalytic activity, dissolution rate, and surface reactivity all scale with exposed surface area rather than volume, this single number is often a better predictor of a nanoparticle's chemical behavior than diameter alone.
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