Home › Calculators › Likelihood Calculator

Likelihood Calculator

Work out how likely an event is, the chance of it happening at least once, combined and/or probabilities, binomial and Poisson probabilities, and conditional probability with Bayes' theorem.

Updated November 4, 2026. Free, no sign-up; everything runs in your browser and nothing you type is stored.

Likelihood calculator: probability of an event

Favorable outcomesTotal equally likely outcomesNumber of tries

Probability

–

–Odds

–Chance of at least once in the tries

Two events: and, or, not

P(A) (0 to 1)P(B) (0 to 1)

–P(A and B), independent

–P(A or B)

–P(not A)

Probability of binomial distribution calculator

Trials nSuccesses kProbability of success p

–P(X = k)

–P(X ≤ k)

–P(X ≥ k)

–Mean n·p

Poisson distribution probability calculator

Average rate λ (events per interval)Number of events k

–P(X = k)

–P(X ≤ k)

–P(X ≥ k)

Conditional probability (Bayes' theorem)

Base rate P(A)P(B given A), e.g. test sensitivityP(B given not A), e.g. false positive rate

–P(A given B)

–P(B) overall

Probability formula

P(event) = favorable outcomes ÷ total equally likely outcomes. Rolling a 6 on a fair die is 1 ÷ 6 = 0.1667 (16.67%). The chance of at least one 6 in four rolls is 1 − (5/6)⁴ = 51.77%. This calculating probability calculator (and compute probability calculator) also handles combined events: for independent events P(A and B) = P(A) × P(B), and P(A or B) = P(A) + P(B) − P(A and B). A probability is between 0 (impossible) and 1 (certain); a "possibility calculator" search usually means this same thing: how likely something is.

Binomial and Poisson probabilities

Binomial: P(X = k) = C(n, k) · p^k · (1 − p)^{n − k}, for a fixed number of independent yes/no trials. Exactly 3 heads in 10 fair coin flips: 120 × 0.5¹⁰ = 11.72%; 3 or fewer: 17.19%.

Poisson: P(X = k) = e^−λ λ^k ÷ k!, for counts of events at an average rate λ (calls per hour, defects per batch). With λ = 3, exactly 2 events has probability 22.40%.

Probability given formula: conditional probability

P(A given B) = P(A and B) ÷ P(B). Bayes' theorem turns it around: P(A | B) = P(B | A) × P(A) ÷ P(B). For a condition that affects 1% of people and a test that's 95% sensitive with a 5% false positive rate, a positive result means only a 16.1% chance of having the condition, because false positives from the 99% who don't have it outnumber the true positives.

Common questions

What is the probability formula?

Favorable outcomes ÷ total equally likely outcomes.

What are the chances of rolling at least one 6 in 4 rolls?

1 − (5/6)⁴ = 51.77%.

How do I calculate a binomial probability?

C(n, k) × p^k × (1 − p)^(n − k). Exactly 3 heads in 10 flips is 11.72%.

When do I use the Poisson distribution?

For counts of independent events happening at a known average rate, such as calls per hour.

What is conditional probability?

The probability of A given that B happened: P(A and B) ÷ P(B).

Sources

General information, not financial, tax or legal advice. Check important numbers with the official source before acting on them.