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Calcimator

Nanoparticle Size Calculator

Size distribution processing from lab inputs.

Inputs

Results

Diffusion Coeff. (m²/s)

0

S/V Ratio (nm⁻¹)

0.12

Surface Area (nm²)7,853.98
Volume (nm³)65,449.85
Size Std Dev (nm)19.36
PDI Class (1-4)2
Sedimentation (m/s)0
Surface Area (m²)0
How to Use This Calculator
  1. Enter the hydrodynamic diameter (nm) from your DLS measurement.
  2. Set PDI (polydispersity index) to characterize size distribution width — below 0.2 indicates monodisperse.
  3. Enter solution temperature (°C) and solvent viscosity (mPa·s).
  4. Review diffusion coefficient (m²/s), surface area (nm²), volume (nm³), and surface-to-volume ratio.
  5. 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)
1,00000.01
3,50000
6,50000
9,00000

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

  1. Identify Input Parameters
    4 parameters
    Particle Diameter (nm) = 50, Polydispersity Index (PDI) = 0.15, Temperature (°C) = 25, Solvent Viscosity (mPa·s) = 0.89 = 4 input(s) provided
  2. Calculate Diffusion Coeff.
    Diffusion Coeff. = parseFloat(diffusionCoeff.toPrecision(4))
    9.815e-12 = 9.815e-12
  3. Calculate S/V Ratio
    S/V Ratio = 6 / diameterNm
    0.12 = 0.12
  4. Calculate Surface Area
    Surface Area = π * diameterNm * diameterNm
    7853.98 = 7853.98
  5. Calculate Volume
    Volume = (π / 6) * pow(diameterNm, 3)
    65449.85 = 65449.85

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