Pair Correlation g(r) Calculator

Calculator Inputs

Dimension

Choose based on your coordinate columns.

Periodic boundaries

Use minimum-image convention

Recommended for bulk systems.

Particles (N)

If provided, must match lines pasted.

Box length Lx

Box length Ly

Box length Lz

Binning mode

Either specify Δr or bins count.

Bin width Δr

Number of bins

Maximum radius r_max

Use ≤ min(L)/2 for strict periodic consistency.

Override density ρ

Use manual density instead of N/V

Useful when units are reduced.

Coordinates (one particle per line)

Accepted separators: commas, spaces, tabs, semicolons. For 2D use x y, for 1D use x.

The pair correlation function g(r) measures how density varies with distance. This calculator builds a histogram of pair separations and normalizes by the ideal-gas neighbor count in a shell.

Histogram: neighbor counts in [r, r+Δr) from all particle pairs.
Shell factor: dV = 4πr²Δr (3D), dA = 2πrΔr (2D), dℓ = 2Δr (1D).
Normalization: g(r) = counts(r) / (N · ρ · dV).
Periodic option: minimum-image distances reduce finite-size artifacts.

Select the dimension that matches your data (1D/2D/3D).
Enter box lengths. For periodic systems, use your cell sizes.
Paste coordinates, one particle per line, using commas or spaces.
Choose bin settings: either Δr or a target number of bins.
Optionally set r_max. For periodic data, keep r_max ≤ min(L)/2.
Press Compute g(r). Results appear above the form.
Use Download CSV or Download PDF to export.

Sample g(r) values (illustrative only):

r	g(r)	Interpretation
0.50	0.02	Very few close neighbors due to repulsion.
1.05	2.30	First coordination shell peak.
1.55	0.85	Depletion after the first shell.
2.05	1.45	Second shell ordering.
3.00	1.05	Approaching uniform structure.
4.00	1.00	Long-range limit, ideal-gas behavior.

Pair Correlation g(r) Calculator

Calculator Inputs

Formula Used

How to Use This Calculator

Example Data Table

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