Probability Calculator
Probability is the number of ways an event can happen divided by the number of equally likely outcomes. Everything else, from complements to combined events, is built from that one fraction.
Probability
0.3
- Probability as a percent
- 30
- Complement
- 0.7
- Odds in favour
- 0.4286
- Both independent events
- 0.075
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
P = favourable outcomes / total outcomes
- P
- Probability of the event, always between 0 and 1
- n_fav
- Number of outcomes counted as the event happening
- n_total
- Total number of equally likely outcomes
- Pc
- Complement, the probability the event does not happen
How to check the result by hand
- 1
List the total number of equally likely outcomes
Count everything that could happen, not only the outcomes you care about. A single dice roll has six outcomes, and a pair of dice has thirty six.
- 2
Count the outcomes that count as the event
Rolling a seven has six ways out of thirty six, because one and six, two and five, and three and four each work in either order. Counting carefully is the whole of the method.
- 3
Divide to get the probability
Six divided by thirty six is 0.1666667. The result must lie between zero and one; anything outside that range means the counts were mixed up.
- 4
Multiply by one hundred for a percentage
A probability of 0.3 is thirty percent. Percentages are easier to compare at a glance, so it is worth writing both forms when the number will be read by someone else.
- 5
Combine events with the right rule
Multiply for independent events happening together, and use one minus the product of the complements for at least one. Adding works only for mutually exclusive outcomes.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate Probability page.