Four calculators, one panel.
Pick a mode below — everything recalculates live as you type, and every result explains itself.
How many outcomes count as the event you want — e.g. 1 for heads on a coin.
All possible outcomes — 2 for a coin, 6 for a die, 52 for a full deck.
Example: a 50% chance of heads.
Example: a 50% chance of heads on a second, separate flip.
The chance both happen at once. It must sit between max(0, P(A)+P(B)−100%) and the smaller of P(A), P(B) — the calculator checks this for you.
How many times the experiment repeats — 5 coin flips, 10 free throws…
How many of those trials should “succeed” — 3 heads, 8 baskets…
Same chance on every trial — 50% for a fair coin, 16.67% for rolling a six.
Read together with the second number as “a to b” — like 3 to 1.
“3 to 1 in favor” = the event happens 3 times for every 1 it doesn’t — a 75% chance.
Anything strictly between 0 and 100 — 75% turns into “3 to 1 in favor”.
Two inputs to an answer.
No manual required — but if you want the full picture, here’s the entire flow in four moves.
Pick a mode
Four tabs: Single event for one experiment, Two events for a pair (independent, mutually exclusive, or a custom overlap), Repeated trials for binomial runs, and Odds converter for bookmaker-style odds.
Enter what you know
Counts for single events (3 out of 6), percentages for two events, trials + successes + success rate for repeated trials, “a to b” for odds. The example chips fill everything in with one tap.
Read the results
The main answer sits up top in large type. Related probabilities — complements, overlaps, conditionals, odds, cumulative chances — sit below, and the exact formula with your numbers substituted sits at the bottom.
Trust the checks
Impossible inputs get flagged with a plain-English reason — negative outcomes, chances over 100%, inconsistent overlaps — instead of silently wrong answers. Copy any full result set with one click.
Six rules run the whole show.
Every number this tool prints comes from one of six classic probability rules. No black boxes — here they are.
Complement rule
The chance the event doesn’t happen. Rolling something other than a six: 1 − 1/6 = 5/6.
Addition rule
The chance of either event — the overlap is subtracted so it isn’t counted twice.
Multiplication rule
The chance of both events happening, when they’re independent of each other.
Conditional probability
The chance of A once B is already known to have happened.
Binomial formula
Exactly k successes in n identical, independent trials — the engine behind the Repeated trials tab.
Odds ⇄ probability
“a to b in favor” means the event happens a times out of a + b in total.
Questions people actually ask.
The short answers — with the long ones one tap away.
How do I calculate the probability of a single event?+
Divide the number of favorable outcomes by the total number of possible outcomes: P(A) = favorable ÷ total. Rolling a 4 or more on a six-sided die has 3 favorable outcomes out of 6 total, so P = 3 ÷ 6 = 0.5 = 50%. The Single event tab also gives you the complement, the odds for and against, and the “1 in N” chance.
What’s the difference between independent and mutually exclusive events?+
Independent events don’t affect each other’s chances — knowing one happened tells you nothing about the other, like two separate coin flips. Mually exclusive events can’t happen at the same time, like one die roll being both a 2 and a 3. Independent → P(A∩B) = P(A)×P(B); exclusive → P(A∩B) = 0. Fun fact: mutually exclusive events with non-zero probabilities are never independent.
How do I find the probability of both events happening?+
If the events are independent, multiply: P(A and B) = P(A) × P(B). If they’re not independent, you need the overlap — either enter P(A and B) directly in Custom mode, or use the conditional form P(A and B) = P(B) × P(A|B).
What does conditional probability P(A|B) mean?+
It’s the probability of A happening given that B has already happened: P(A|B) = P(A∩B) ÷ P(B). Example: if 20% of days are rainy and 10% of days are rainy and cold, then P(cold | rainy) = 10% ÷ 20% = 50%.
How does the repeated-trials calculator work?+
It uses the binomial distribution: for n independent trials where each succeeds with probability p, the chance of exactly k successes is P(X = k) = C(n,k) · pk · (1−p)n−k. The panel also computes “at most” and “at least” cumulative probabilities, plus the expected value μ = np and standard deviation σ = √(np(1−p)).
How do I convert odds to probability?+
“a to b in favor” means the event happens a times out of (a + b), so P = a ÷ (a + b). “a to b against” means it fails a times out of (a + b), so P = b ÷ (a + b). For example, 3 to 1 in favor is P = 3 ÷ 4 = 75%. The converter also outputs decimal (European) odds and the American moneyline.
Can a probability be negative or over 100%?+
No — probability always sits between 0 (impossible) and 1 (certain), or 0% to 100%. The calculator validates every input: negative counts, chances above 100%, overlaps bigger than the events themselves, and P(A) + P(B) over 100% for exclusive events each get a plain-English error instead of a wrong number.
Is this tool free, and where does my data go?+
It’s completely free and runs entirely in your browser — nothing you type is uploaded, logged, or sent to any server. No account, no sign-up, no limits.