How to Calculate Probability (2026)
By Rui Barreira · Last updated: 18 June 2026
Probability is the measure of how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain) — or as a percentage between 0% and 100%. The basic formula is simple: divide the number of favourable outcomes by the total number of possible outcomes. Whether you are analysing dice rolls, survey results, risk scenarios, or A/B test outcomes, the same core rules apply. Use the Probability Calculator to compute single and combined probabilities instantly.
The Core Formula
For a single event where all outcomes are equally likely:
P(A) = Favourable outcomes ÷ Total outcomes
A standard six-sided die has one favourable outcome for rolling a 3, and six total outcomes, so P(3) = 1/6 ≈ 16.7%. A deck of 52 cards has four aces, so P(ace) = 4/52 = 1/13 ≈ 7.7%. The complement rule states that P(not A) = 1 − P(A), which is useful when it is easier to count what you do not want than what you do.
Combined Events: AND, OR, Independent vs. Dependent
When two events are involved, the calculation depends on their relationship.
| Scenario | Formula | Example |
|---|---|---|
| Both events occur (independent) | P(A) × P(B) | Flipping two heads: 0.5 × 0.5 = 25% |
| Either event occurs (mutually exclusive) | P(A) + P(B) | Rolling a 1 or 2: 1/6 + 1/6 ≈ 33% |
| Either event occurs (overlapping) | P(A) + P(B) − P(A and B) | Drawing a red or face card from a deck |
| A given B already occurred (conditional) | P(A and B) ÷ P(B) | Drawing a king after seeing one face card |
Two events are independent when the outcome of one does not affect the other — coin flips, dice rolls. They are dependent when the first outcome changes the remaining pool — drawing cards without replacement. Confusing the two is one of the most common probability mistakes.
Expressing and Converting Probability
Probability can be stated three ways: as a fraction (1/4), a decimal (0.25), or a percentage (25%). Odds — common in gambling and sports — are a different notation: odds of 3:1 against mean probability = 1 ÷ (3+1) = 25%. To convert odds in favour (a:b) to probability: P = a ÷ (a+b). To convert probability back to odds against: divide (1−P) by P. Keeping these distinct prevents misreading reported likelihoods, especially in medical or financial contexts where the difference between "25% chance" and "3 to 1 odds against" can matter.
Use the Probability Calculator to do this instantly.
Frequently Asked Questions
- Is this tool free?
- Yes — completely free, no signup required. All processing happens in your browser.
- Does the tool work offline?
- Once loaded, most features work without an internet connection since everything runs client-side.