Coin flip results and statistics
Flip sequence
Heads and tails totals
Result percentages
Running frequency
Probability analysis
Trial comparison
| Trial | Heads | Tails | Heads % | Winner |
|---|
Merged result summary
No result yet.
Recent simulation history
| Date | Setup | First side | Second side | Winner | Seed |
|---|
Formula used
Experimental probability
Experimental probability uses observed outcomes. Divide matching results by total flips. Larger samples usually approach the chosen probability.
P(A) = successful outcomes ÷ total outcomes
Binomial probability
Binomial probability models repeated independent flips. Each flip keeps the same probability. Exact counts use combinations and two probability powers.
P(X=k) = C(n,k)pk(1-p)n-k
Fairness test
The chi-square statistic compares observed and expected counts. Small values suggest closer agreement. This calculator reports a simple two-category test.
χ² = Σ((observed − expected)² ÷ expected)
How to use
- Choose a preset or enter custom simulation values.
- Set fair or weighted probabilities and side labels.
- Add an optional seed for repeatable random results.
- Run instantly or add delay for animated flipping.
- Review statistics, charts, streaks, trials, and probabilities.
- Copy, download, print, or export the final result.
Example data
| Example | Flips | First probability | Trials | Useful purpose |
|---|---|---|---|---|
| Quick decision | 1 | 50% | 1 | Choose between two equal options. |
| Best of five | 5 | 50% | 1 | Use majority results for a contest. |
| Weighted test | 100 | 65% | 10 | Compare observed and expected frequencies. |
| Classroom study | 1000 | 50% | 5 | Explore the law of large numbers. |
Frequently asked questions
Is this coin flipper truly random?
It uses browser-generated pseudo-random values. Seeds create repeatable sequences. Unseeded results vary between runs.
What is a weighted coin?
A weighted coin gives unequal side probabilities. You can set either side indirectly. Both probabilities always total one hundred percent.
Why use a random seed?
A seed recreates the same sequence. It supports demonstrations and testing. Share the seed to repeat results.
How are streaks measured?
The calculator scans results in order. It tracks repeated identical sides. Longest and current streaks are reported separately.
What does the chi-square value mean?
It measures disagreement with expected counts. Smaller values indicate closer agreement. Large samples provide more useful comparisons.
Can I flip several coins each round?
Yes, choose coins per round. Total flips equal rounds times coins. Every result remains available for analysis.
Can I pause a long simulation?
Pause works during delayed automatic mode. Resume continues the same run. Stop keeps completed flips and finalises them.
How does exact probability work?
It uses the binomial distribution. Enter a target first-side count. The calculator shows exact, minimum, and maximum probabilities.
Where is my history stored?
History stays in this browser. It uses local device storage. Clearing browser data can remove saved sessions.