Replica Exchange Monte Carlo Calculator

Model replica swaps to improve sampling efficiency fast. Paste temperature and energy pairs, then compute. Export results as tables for reports and teaching use.

Calculator

Mode

Batch computes swaps between i and i+1.

k setting

Match energy units to the chosen constant.

Quick tips

Target swap acceptance is often 0.2 to 0.4. If p is tiny, reduce spacing between temperatures.

Random u (0 to 1)

Example data table

These values demonstrate adjacent-swap probabilities across four replicas.

Replica	Temperature (T)	Energy (E)	Notes
1	300	-25.0	Lower temperature, lower energy.
2	350	-24.6	Moderate spacing.
3	420	-24.1	Higher temperature, slightly higher energy.
4	520	-23.7	Hot replica helps barrier crossing.

Formula used

Replica exchange proposes swapping configurations between two replicas at temperatures T1 and T2. The Metropolis acceptance is

β = 1 / (k T)
Δ = (β1 − β2) (E2 − E1)
p_accept = min(1, exp(Δ))

A larger overlap between energy distributions across temperatures increases swap acceptance.

How to use this calculator

Choose Single swap to evaluate one proposed exchange.
Select a k setting that matches your energy units.
Enter temperatures and energies for the two replicas, then compute.
For many replicas, switch to Batch and paste one T, E pair per line.
Use the CSV or PDF buttons to export your computed results.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.