Light Scattering Calculator

Calculator

White theme • Responsive grid inputs

Choose a model, enter your parameters, then calculate. Results appear above this form.

Scattering model

Rayleigh fits very small particles (x ≪ 1).

Wavelength (nm)

Visible light is roughly 380–750 nm.

Scattering angle (deg)

0° forward, 180° backward scattering.

Incident intensity (arb.)

Use 1 for normalized, relative results.

Particle radius (nm)

Smaller radius increases Rayleigh validity.

Relative refractive index (m)

m = n_particle / n_medium (unitless).

Number density (1/m³)

Particle count per cubic meter of medium.

Path length (m)

Distance through scattering medium.

Scattering coefficient μ_s (1/m)

Use when you know bulk scattering of a medium.

Anisotropy g (−0.99 to 0.99)

g > 0 favors forward scattering.

Path length (m)

Same meaning as Rayleigh path length.

Reset

Example Data Table

These sample rows show typical inputs and relative outputs.

Model	λ (nm)	θ (deg)	r (nm)	m	N (1/m³)	L (m)	Relative I (arb.)
Rayleigh	550	30	50	1.2	1.0e12	1	≈ 4.2e-06
Rayleigh	450	90	40	1.15	2.0e12	0.5	≈ 1.8e-05
HG	650	20	—	—	—	0.2	≈ 1.3e-01

Formula Used

Rayleigh (small spheres)

Cross-section (sphere):

σ_s = (8π³/3) · (r⁶/λ⁴) · [(m²−1)/(m²+2)]²

Phase function:

P(θ) = (3/(16π)) · (1 + cos²θ)

With b = N·σ_s and τ = b·L, we report: I = I0·τ·P(θ).

Henyey–Greenstein (anisotropic)

Phase function:

P(θ) = (1−g²) / [4π · (1 + g² − 2g cosθ)^3/2]

Using bulk scattering μ_s, we set τ = μ_s·L and report: I = I0·τ·P(θ).

These outputs provide a consistent, normalized comparison across angles and parameters. For full radiometry, include detector geometry and calibration.

How to Use This Calculator

Select a model: Rayleigh for very small particles, or Henyey–Greenstein for directional scattering.
Enter wavelength, scattering angle, and incident intensity.
Provide model parameters (particle values for Rayleigh, μ_s and g for Henyey–Greenstein).
Press Calculate to view results above the form.
Use Download CSV or Download PDF to export your last result.