Markov Chain One-Step Transition Calculator

Analyze one step transitions for any Markov process with a clear matrix editor and smart validation. Paste data or type values. Normalize rows if needed. Get next state probabilities and share results instantly. Supports initial state vectors or single state choice with examples and tips for students researchers engineers and data scientists worldwide today.

Transition Matrix P (rows i to columns j)
i \ j S1 S2 S3
S1
S2
S3

Each row represents probabilities of moving from state i to j in one step.


Values should sum to 1; enable Normalize to auto-scale.
Advanced
Tips
  • Rows should be non negative and sum to 1 for a proper transition matrix.
  • Enable Normalize to scale each row automatically.
  • Use a unit vector to represent a known current state.
  • Increase Decimals for more precision.
  • Paste mode accepts spaces or semicolons as separators.
Example (3×3)
P =
0.7 0.2 0.1
0.3 0.4 0.3
0.2 0.3 0.5

p = 0.6 0.3 0.1

With these values the next-step distribution is shown after you compute.

FAQs

What does one-step transition mean?

It is the probability distribution after exactly one transition. If p is the current distribution and P is the transition matrix, the next distribution is p' = p·P.

Do rows need to sum to one?

Yes. Each row represents probabilities that must add to 1. If your data does not, enable Normalize to rescale each row safely.

How do I model a known current state?

Choose Single state index and provide the index of the current state. This creates a unit vector so the one-step probabilities are just the selected row of P.

Can I paste matrices from spreadsheets?

Yes. Use Paste mode. Provide exactly n lines with n values per line separated by spaces or semicolons.

What precision should I use?

Use more decimals for sensitive comparisons. For reporting, 3–6 decimals are typical. The display does not affect internal arithmetic beyond rounding for readability.

Does this detect absorbing states?

Absorbing states have a row with 1 on the diagonal and 0 elsewhere. You can spot them directly in P. This tool focuses on one-step results rather than full classification.

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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.