Markov Chain Calculator
Enter a stochastic transition matrix and an initial distribution to get the steady-state vector and the k-step distribution instantly.
Transition Matrix P
Row i = probabilities of moving FROM state i. Each row must sum to 1.
Initial Distribution v0
Probability of starting in each state. Must sum to 1.
Steady-State Distribution (π)
Converged after ? power-iteration steps.
Distribution after 5 Steps
vk = v0 × Pk
Pk (Transition Matrix after 5 Steps)
Summary
Enter a stochastic transition matrix and an initial distribution to get the steady-state vector and the k-step distribution instantly.
How it works
- Select the number of states n (2 to 6) to generate the n×n matrix grid.
- Fill in each cell with the transition probability from row-state i to column-state j.
- Each row must sum to 1; a live row-sum indicator confirms validity.
- Enter the initial probability distribution (must also sum to 1).
- Set the number of steps k and click Calculate.
- The tool runs power iteration to find the steady-state vector and matrix-multiplies the initial vector k times for the k-step distribution.
Use cases
- Model customer retention and churn across subscription tiers.
- Analyze page-rank style link graphs for small networks.
- Simulate weather-pattern Markov models in statistics coursework.
- Verify hand-calculated steady-state answers on homework problems.
- Prototype board-game or inventory-level Markov models quickly.
- Understand convergence behavior by comparing k-step vs. steady-state.
Frequently Asked Questions
Last updated: 2026-06-10 ·
Reviewed by Nham Vu