Probability Calculator

Probability measures how likely an event is to happen, on a scale from 0 (impossible) to 1 (certain). When every outcome is equally likely, you find it by dividing the number of favorable outcomes by the total number of outcomes. This probability calculator does that division for you and also returns the complement — the chance the event does not happen.

How to use this calculator

1. Enter the number of favorable outcomes — the outcomes that count as the event you care about.
2. Enter the total number of outcomes — every equally likely outcome that could occur.
3. Read the probability (favorable ÷ total) and its complement (1 − probability) below the tool.

The two formulas are simply:

probability = favorable outcomes / total outcomes
complement  = 1 - probability

Worked example

Suppose a bag holds 10 equally likely balls and 3 of them are red. You draw one ball at random and want the probability that it is red.

favorable outcomes = 3   (the red balls)
total outcomes     = 10  (all the balls)

probability = 3 / 10 = 0.3   (30%)
complement  = 1 - 0.3 = 0.7  (70%)

So the chance of drawing red is 0.3, and the chance of not drawing red is 0.7. The two always add up to 1, because the ball is either red or it isn’t. For a fuller treatment of how probabilities behave, see the NIST/SEMATECH e-Handbook on probability distributions.

Frequently asked questions

How do I calculate probability by hand?

To calculate probability for equally likely outcomes, count the favorable outcomes, count the total outcomes, and divide the first by the second. In the red-ball example that is 3 ÷ 10 = 0.3.

What is the probability of an event?

The probability of an event is a number between 0 and 1 that says how likely it is to occur. A value of 0 means it never happens, 1 means it always happens, and 0.5 means it is just as likely to happen as not.

What does this single event probability calculator cover?

It handles a single event with equally likely outcomes, returning a probability between 0 and 1. It is not built for combined events (such as the chance of two draws in a row) or for outcomes that are not equally likely.

Why does the complement matter?

The complement is the probability that the event does not happen, found with 1 − probability. It is often the quicker route to an answer — finding the chance of “at least one” success, for example, is usually easier through its complement.