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Markov chain steady state calculator

The long-run distribution of a Markov chain: the probabilities the system settles into no matter where it starts. Enter the transition matrix (each row a state's outgoing probabilities) and it solves π·P = π by power iteration, showing the steady-state probability of each state.

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Open Markov chain steady state calculator and you get an answer straight away, with no account to create. It covers the probabilities the system settles into no matter where it starts. Enter the transition matrix (each row a state's outgoing probabilities) and it solves π·P = π by power iteration, showing the steady-state probability of each state — adjust any of them and the result follows immediately.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is Markov chain steady state calculator?

The long-run distribution of a Markov chain: the probabilities the system settles into no matter where it starts. Enter the transition matrix (each row a state's outgoing probabilities) and it solves π·P = π by power iteration, showing the steady-state probability of each state.

What does a concrete case look like?

P = [[0,9 ; 0,1], [0,5 ; 0,5]] → π = (5/6 ; 1/6) ≈ (0,833 ; 0,167) — the tool shows every step in between, not just the final figure.

What does it take into account?

It factors in the probabilities the system settles into no matter where it starts. Enter the transition matrix (each row a state's outgoing probabilities) and it solves π·P = π by power iteration, showing the steady-state probability of each state. Change any of them and the output follows immediately.

When would I actually use this?

Anything modelled as points and connections: a shortest route, a network's capacity, a schedule with dependencies, or a circuit reduced to its logic.

What is the most common mistake?

Assuming a shortest path stays shortest when a weight changes sign. Negative edges break the greedy argument Dijkstra rests on, and the algorithm returns a confident wrong answer rather than an error.

What else is filed next to it?

Bitwise Calculator, Delaunay triangulation generator and Dijkstra shortest path calculator share its section. They are not variants of it — being filed together is not the same as being alike — but that is where to look if this turned out not to be the tool you wanted.

Where do the figures come from?

The algorithms are the textbook ones and their results are exact for the graph you enter. What varies is cost: several of these problems have no known efficient solution, so large inputs are answered by heuristic and the tool says when that is the case.

Further reading

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