Permutation and Combination Calculator
nPr and nCr with the factorials shown, and the rule for choosing between them.
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Probability Calculator
Work out single and combined event probabilities.
Probability Calculator tool
A decimal, a percentage like 25%, or a fraction like 1/4.
Leave blank for a single event.
Optional. Gives the chance of at least one success.
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Both happen
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Either happens
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Neither happens
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Exactly one
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At least one in n trials
| Event | Probability | Percentage | Odds against |
|---|
These formulas assume the events are independent: one happening does not change the chance of the other. Two cards drawn without replacement are not independent, and treating them as if they were gives a wrong answer that looks reasonable.
About the Probability Calculator
Probability Calculator works out the chance of events happening, singly and in combination, and converts between probability, percentage and odds.
For a single event there is not much to it: the probability is the number of outcomes you want divided by the total number of outcomes. What the calculator adds is the conversions, because the same chance is written three ways depending on who is speaking. A probability of 0.25 is 25%, and odds of 1 to 3 against, and people routinely mistake the last of those for 1 in 3.
Combining two events is where the thinking is. If they are independent, the chance of both is the product of the two. The chance of at least one is the sum minus the product, and subtracting that product is what stops the overlap being counted twice. The chance of neither is the product of the two complements. All four are shown together, because questions usually ask for one of them and the others are the fastest way to check the answer is sensible.
Independence is the assumption underneath all of it, and it is worth stating plainly: these formulas hold when one event happening does not change the chance of the other. Two dice are independent. Two cards drawn without replacement are not, and treating them as if they were gives a wrong answer that looks perfectly reasonable.
Everything is worked out inside your browser. Nothing you enter is uploaded, logged or stored, which matters for the financial calculators in particular: the figures you put into them are nobody else's business.
Looking for something this does not cover? FreeToolsZone.org is more free browser-based tools, organised by job, and it is worth a look if probability calculator is only part of what you are working on.
How to use the Probability Calculator
- Choose single or two eventsSingle gives the conversions; two gives the combinations.
- Enter the probabilitiesAs a decimal, a percentage or a fraction; all three are accepted.
- Read the combined resultsBoth, either, neither and exactly one, all at once.
- Check the oddsShown as odds for and odds against, which are easy to confuse.
Features
- Single event probability with percentage and odds
- Both, either, neither and exactly one, for two events
- Accepts decimals, percentages or fractions
- Complement of any probability
- Repeated trials: the chance of at least one success in n attempts
- Warns when a value outside 0 to 1 is entered
- Runs in your browser
Who uses this tool
The probability calculator is used by writers, developers, students, marketers and anyone else who needs the job done once without installing software. Common cases include:
- Probability coursework and exam practice
- Working out the chance of a backup also failing
- Understanding a quoted risk figure
- Dice, cards and lottery questions
- Checking how many attempts make an outcome likely
Frequently asked questions
What does independent mean?
One event happening does not change the chance of the other. Two coin flips are independent. Drawing two cards without putting the first back is not, and these formulas do not apply to it.
Why is 'either' not just the two added together?
Because adding counts the overlap twice: the cases where both happen appear in each number. Subtracting the product of the two removes the double count.
What is the difference between odds and probability?
Probability compares favourable outcomes with all outcomes. Odds compare favourable with unfavourable. A probability of 1 in 4 is odds of 1 to 3, not 1 to 4.
How likely is at least one success in several tries?
Use the repeated trials box. It calculates one minus the chance of failing every time, which is far easier than adding up all the ways of succeeding.
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If the probability calculator is not quite what you need, these other free tools solve closely related problems, and there are 13 more in statistics calculators.
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Checked and rebuilt on 2026-10-14. The method this calculator uses is described in the section above, and corrections go through the contact page.