Probability Calculator
Turn a count of outcomes into a probability.
Probability Calculator
P = favourable outcomes / total outcomes
Calculated instantly
Embed this calculator
Put this calculator on your own site with the snippet below. The frame contains the tool only, reports its own height, and carries a visible link back to the full page. Embedding is free; keep the attribution link as it is, and do not wrap the frame in a way that hides it.
Preparing the embed code for this page...
What This Calculator Does
The Probability Calculator converts a count of favourable outcomes and total possible outcomes into a probability, a decimal, and odds in favour and against. It is the single-event case behind dice, cards, raffles, and simple quality checks.
How It Works
Classical probability is the number of favourable outcomes divided by the number of equally likely outcomes. Multiply by 100 for a percentage. Odds compare favourable to unfavourable outcomes instead of favourable to total, which is why a probability of 1/6 is stated as 1:5 odds, not 1:6.
Example
Rolling a single six-sided die and wanting a 4: one favourable outcome out of six gives a probability of 1/6 = 16.67%. The odds in favour are 1:5, and the odds against are 5:1.
Formula
P(A) = favourable outcomes / total outcomesRequires equally likely outcomes and no overlap between them.
Odds = favourable : unfavourable = f : (n − f)P(not A) = 1 − P(A)Reading the Results
Probability
The chance of the event as a percentage, assuming every listed outcome is equally likely and mutually exclusive.
Odds in favour
The ratio of favourable to unfavourable outcomes. Odds of 1:5 correspond to a probability of 1/6, not 1/5.
Sources and References
NIST/SEMATECH e-Handbook of Statistical Methods
Probability, odds, and equally likely outcomes
The handbook distinguishes classical probability from frequency-based estimates.
References identify the method or data behind this calculator. Where a standard or tariff changes, the current edition applies, and the assumptions stated above take precedence over a remembered figure.
Frequently Asked Questions
What is the difference between probability and odds?
Probability compares favourable outcomes with all outcomes. Odds compare favourable outcomes with unfavourable ones. A 25% probability is 1:3 odds in favour, because there is one success for every three failures.
Can probability be greater than 1?
No. A probability runs from 0 (impossible) to 1 (certain). If your calculation exceeds 1, you have counted more favourable outcomes than total outcomes, or an outcome is being counted twice.
Does this work for two events at once?
No. This is a single-event calculator. For independent events multiply their probabilities; for either of two mutually exclusive events add them. For overlapping events subtract the overlap.
What does it mean for outcomes to be equally likely?
Each outcome must have the same chance — true for a fair die or a well-shuffled deck, false for a biased coin or a rigged draw. When outcomes are not equally likely, use observed frequencies instead.