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Probability
Calculator.

Modify the values in any of the four calculators below and the results update live. Find the union, intersection and complement of two independent events, solve for the missing probabilities from any two, compute repeated trials, or measure the area under a normal distribution between two bounds.

// Probability of Two Events

Probability of A: P(A) Values between 0 and 1. Probability of B: P(B) Values between 0 and 1.

P(A')—

P(B')—

P(A ∩ B)—

P(A ∪ B)—

P(A Δ B)—

P((A ∪ B)')—

// Probability Solver for Two Events Fill any 2 — the rest are derived

P(A) P(B) P(A') P(B') P(A ∩ B) P(A ∪ B) P(A Δ B) P((A ∪ B)')

Values must be between 0 and 1. Highlighted fields are computed.

// Probability of a Series of Independent Events

Event A — Probability Event A — Repeat Times Event B — Probability Event B — Repeat Times

P(A all n times)—

P(A never)—

P(A at least once)—

P(B all m times)—

P(B never)—

P(B at least once)—

P(A all AND B all)—

P(A ≥1 AND B ≥1)—

// Probability of a Normal Distribution P(Lb ≤ X ≤ Rb)

Mean (µ) Standard Deviation (σ) Left Bound (Lb) Use -inf for negative infinity. Right Bound (Rb) Use inf for positive infinity.

// Area P

—

Enter μ, σ and the two bounds.

50% CI—

80% CI—

90% CI—

95% CI—

99% CI—

99.9% CI—

// Related

Probability of two events

Probability is the measure of the likelihood of an event occurring, quantified as a number between 0 and 1, with 1 meaning certainty and 0 meaning impossibility. In its most general form, probability equals desired outcomes ÷ total outcomes. The formulas below assume two events A and B are independent.

Complement of A and B

P(A') = 1 − P(A)
P(B') = 1 − P(B)

Intersection · Union · XOR

P(A ∩ B) = P(A) × P(B)                ; independent
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
P(A Δ B) = P(A) + P(B) − 2·P(A ∩ B)
P((A ∪ B)') = 1 − P(A ∪ B)

Series of independent events

If P(A) is the probability of event A in one trial and it is repeated n independent times:

P(A all n times)     = P(A)^n
P(A never)           = (1 − P(A))^n
P(A at least once)   = 1 − (1 − P(A))^n

Normal distribution

For a normal distribution with mean μ and standard deviation σ, the probability that Lb ≤ X ≤ Rb is given by:

P(Lb ≤ X ≤ Rb) = Φ((Rb − μ) / σ) − Φ((Lb − μ) / σ)

Frequently asked questions

What does Probability Calculator do?

Joint, conditional and complementary probability. The whole thing runs in your browser tab, so it is ready the moment the page finishes loading.

Is Probability Calculator free to use?

Yes. Probability Calculator is completely free on ToolMunch — no trial, no premium tier holding back the main feature, and no daily or hourly cap on how many times you can use it.

Do I need to create an account or sign up?

No. There is no account, no email address, and no login. Open Probability Calculator, do the job, and take the result — nothing is gated behind a signup form.

Are the numbers I enter sent to a server?

No. Probability Calculator runs entirely inside your browser tab, so what you type never leaves your own device. Nothing is uploaded, which means there is no copy of it on a server to worry about.

Does Probability Calculator work on Mac, Windows, and phones?

Yes. Probability Calculator runs in any modern web browser on Windows, macOS, Linux, Chromebook, Android, and iOS. There is nothing to download or install.

Can I use it as many times as I want?

Yes. There is no queue, no per-hour quota, and no counter that runs out — run Probability Calculator as often as the work needs.