About the Probability Calculator
Probability Calculator answers the four questions people ask most about chance. One event: what is the probability when there are some ways it can happen out of a total number of outcomes, such as rolling a 6 on a die. Two events: for two independent events, what is the chance that both happen, that at least one happens, that neither happens, or that exactly one happens. At least once: the chance of one or more successes in a number of tries. Exactly k times: the binomial probability of exactly, at most, at least, fewer than or more than k successes, with the expected number and standard deviation. Chances can be typed as decimals, percentages or fractions such as 1/6, and results are shown as percentages and decimals.
Updated September 2026
How to use the Probability Calculator
- 1Choose the type of question: one event, two events, at least once or exactly k times.
- 2Enter the numbers. Chances can be typed as 0.25, 25% or 1/4.
- 3Read the main result in the big box.
- 4Look at the smaller boxes for related chances, such as at most or neither.
- 5Change any number to try a different situation.
Reading a probability
Probability can be written as a fraction, a decimal or a percentage, and this tool shows the decimal and the percentage. A probability of 0.25 is 25 percent, or one chance in four. Where it helps, the result also says 1 in N, which is easier to picture: a probability of 0.0167 is about 1 in 60.
A high probability does not guarantee an outcome, and a low one does not rule it out. Chance describes what happens over many repeats, not what will happen next time. A coin that has landed on heads five times is still 50 percent likely to land on heads on the next flip.
Which mode should I use?
- One event: dice, cards, lucky draws and any case of favourable outcomes out of a total.
- Two events: separate things that do not influence each other, such as weather on two days.
- At least once: the chance that something happens at least one time over many tries, such as a defect in a batch.
- Exactly k times: a count of successes over repeated tries with the same chance each time, such as free throws or survey answers.
Worked examples
A bag has 3 red and 7 blue marbles. The chance of pulling a red one is 3 out of 10, which is 30 percent. If a machine makes parts with a 2 percent defect rate, the chance that a box of 20 has at least one bad part is 1 − 0.98^20, about 33.2 percent. A basketball player who makes 70 percent of free throws will make exactly 8 of 10 shots about 23.3 percent of the time, and at least 8 about 38.3 percent of the time.
The expected successes figure shown in the binomial mode is n × p, the average count you would see over many rounds, and the standard deviation shows how much the count typically varies around it.
Limits and related tools
The tool assumes independence and equal chance on each try. Dependent situations such as drawing cards without replacement, or events where knowing one outcome changes the other, need other formulas. For the number of possible arrangements, Permutation and Combination Calculator gives nPr and nCr, and Random Number Generator or Dice Roller can be used to test a chance by simulation.
For results expressed as percentages of an amount use Percentage Calculator. To see how far a measurement is from the average, use Z-Score Calculator, and for the spread of your own data, Standard Deviation Calculator.
Features
- Probability from favourable outcomes and total outcomes
- Two independent events: and, or, neither, exactly one
- At least one success in n tries
- Binomial: exactly, at most, at least, fewer and more than
- Accepts decimals, percentages and fractions
- Shows percentage, decimal and 1 in N
- Runs in your browser
Frequently asked questions
How do you calculate probability?
Divide the number of ways the event can happen by the total number of equally likely outcomes. The chance of rolling an even number on a fair die is 3 ÷ 6 = 0.5, or 50 percent. A probability is always between 0, which means impossible, and 1, which means certain.
How do I find the probability of A and B?
If the two events do not affect each other, multiply their probabilities. For a 50 percent chance of rain on Saturday and a 30 percent chance of rain on Sunday, and assuming they are independent, the chance of rain on both days is 0.5 × 0.3 = 0.15, or 15 percent.
How do I find the probability of A or B?
Add the two probabilities and subtract the chance that both happen, so you do not count it twice: P(A or B) = P(A) + P(B) − P(A and B). With 50 percent and 30 percent, that is 0.5 + 0.3 − 0.15 = 0.65, or 65 percent.
How do I find the chance of getting at least one success?
It is easier to work out the chance of no success and subtract it from 1. If each try has a chance p, then the chance of at least one success in n tries is 1 − (1 − p)^n. Rolling at least one 6 in four rolls of a die is 1 − (5/6)^4, about 51.8 percent.
What is binomial probability?
It is the chance of getting exactly k successes in n independent tries where each try has the same chance of success. Coin flips are the classic case: the chance of exactly 3 heads in 5 flips is 10 × 0.5^5 = 31.25 percent. The tool also gives at most and at least figures.
What does independent mean?
Two events are independent when one happening does not change the chance of the other. Successive coin flips are independent. Drawing cards from a deck without putting them back is not, because each draw changes what is left, so the two events mode does not apply to it.