Coin Toss Calculator

Work out coin toss instantly with clear inputs, formula shown and shareable results.

About Coin Toss Calculator

The streak probability is computed exactly with a dynamic programme that tracks the current run length and forbids it ever reaching the target, then takes one minus the survival probability. Runs are far more likely than intuition suggests: three heads in a row appears in about 83% of ten-toss sequences, which is why streaks are poor evidence of anything.

Formulas

Run probability

P(at least one run of k) = 1 - P(never reaching a run of k), computed by tracking run length

All the same

P = p^n + (1 - p)^n

Worked example

With the default values below, Coin Toss Calculator returns Chance of a heads streak that long of 50.7813%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Number of tossesaccepts 1–200: 10
Streak length you are asking aboutminimum 1: 3
Chance of headsaccepts 0.1–99.9 %: 50 %

Results

Chance of a heads streak that long: 50.7813%
Heads expected: 5.000
Chance every toss is the same: 0.195313%
Possible sequences (capped at 50 tosses): 1,024

Step by step

1Values used
2Run probability
3All the same
4Chance of a heads streak that long= 50.7813
5Heads expected= 5.000
6Chance every toss is the same= 0.195313
7Possible sequences (capped at 50 tosses)= 1,024

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Coin Toss figure worked out?

P(at least one run of k) = 1 - P(never reaching a run of k), computed by tracking run length. The streak probability is computed exactly with a dynamic programme that tracks the current run length and forbids it ever reaching the target, then takes one minus the survival probability.

Why does this matter?

Runs are far more likely than intuition suggests: three heads in a row appears in about 83% of ten-toss sequences, which is why streaks are poor evidence of anything.

What do I need to enter?

Enter number of tosses, streak length you are asking about, chance of heads. The defaults shown are a realistic worked example — swap in your own figures to get a result you can use.