Two figures in, a clear answer out. The birthday paradox calculator uses days in a year, number of people and one way to produce probability of sharing a birthday and number of pairs, applying the standard relationship for this problem in the order the calculation actually needs it.
What Is the Birthday Paradox Calculator?
The birthday paradox calculator turns a set of measurements into probability of sharing a birthday and number of pairs, with the uncertainty made explicit rather than left implied.
Statistics is easy to quote badly. A figure without its spread tells the reader far less than they assume it does, and this calculator puts both together.
How the Birthday Paradox Is Calculated
The calculation uses the standard relationship for this kind of estimate, applied to the figures you supply. The intermediate steps are exposed so you can see how much of the answer comes from each one.
Sample size matters more than most people expect. Doubling the number of observations improves the precision by a factor of about one and a half, not two.
What the Result Does and Does Not Tell You
A result describes the data you gave it. It does not tell you whether the sample was representative, whether the method was appropriate, or whether there is a confound in the way the figures were collected.
Report the result together with its uncertainty. A number on its own is much easier to misread than a number with a range attached.
A Worked Example
Working through an example, with days in a year set to 365, number of people set to 10, one way set to 5, the calculator returns probability of sharing a birthday of 0.12, and number of pairs of 45. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out probability of sharing a birthday?
Enter days in a year, number of people and one way. The calculator then works through the relationship and reports probability of sharing a birthday and number of pairs.
What does the birthday paradox actually calculate?
It takes days in a year, number of people and one way and converts them into probability of sharing a birthday and number of pairs using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter days in a year?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Why does a small change in one value move the answer so much?
That happens when an output depends on a ratio, because dividing by a small number magnifies any change in it. Check the units first, then check whether the value you entered is in the range the relationship was designed for.
Is the answer exact?
It is as exact as the formula and the inputs allow. The method itself is the standard one for this problem, so the only sources of error are the figures you enter and the precision you ask for.