Probability Calculator

Worked example

Inputs: 1 favourable outcome (rolling a 6) out of 6 total outcomes, all equally likely. Formula: P = favourable ÷ total. Substitution: P = 1 ÷ 6. Result: P = 1/6 ≈ 0.166667, or about 16.6667%. The complement, the chance of not rolling a 6, is 1 − 1/6 = 5/6.

How it works

When every outcome is equally likely, the probability of an event is the number of outcomes that count as the event divided by the number of possible outcomes: P = favourable ÷ total. It runs from 0 (impossible) to 1 (certain). The formula is only valid under that equal-likelihood assumption; it does not apply to a loaded die or to outcomes with different chances. The exact fraction is shown in lowest terms, and the decimal and percentage are exact when they end (3/10 = 0.3 = 30%) and rounded to 6 significant figures with a leading "≈" when they repeat (1/6 ≈ 0.166667). The complement 1 − P is the probability that the event does not happen.

This calculator handles a single event from counts. It does not combine events with "and" or "or", assume independence, work out conditional probabilities or Bayes' theorem, or use distributions such as the binomial or normal. To count the outcomes first, the Combination and Permutation calculators give the number of selections and arrangements.