Statistics

Conditional Probability Calculator

Compute the conditional probability P(A given B) from the joint probability P(A and B) and P(B). The tool divides the two inputs and shows the result as both a decimal and a percentage.

What this calculator does

The Conditional Probability Calculator estimates your result instantly from the values you enter, using standard statistics formulas. Compute the conditional probability P(A given B) from the joint probability P(A and B) and P(B). The tool divides the two inputs and shows the result as both a decimal and a percentage. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.

Conditional Probability Calculator

Result

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P(A | B)

About Conditional Probability Calculator

Conditional probability answers how likely A is once B is known to have happened. This calculator uses the definition P(A | B) = P(A ∩ B) / P(B), taking your joint probability P(A and B) and dividing by P(B).

Both inputs must lie between 0 and 1, P(B) must be greater than 0, and P(A and B) cannot exceed P(B). The result appears as a decimal with its percentage in parentheses.

Formula & Mathematical Calculation

P(A | B) = f(P(A and B), P(B))

Calculated according to standard stats formulas implemented in the calculator core.

Calculation Example

With P(A and B) = 0.2 and P(B) = 0.5:

  • P(A | B) = 0.2 / 0.5 = 0.4

The P(A | B) box shows 0.4 (40%).

Key Benefits

  • Applies the definition P(A|B) = P(A and B) / P(B) directly, so you only supply two probabilities
  • Shows the answer as both a decimal and a percentage in one box
  • Enforces that inputs stay between 0 and 1 and that P(B) is greater than zero
  • Catches the impossible case where P(A and B) exceeds P(B); free and in-browser

How to Use this Calculator

  1. Enter the joint probability
    Type P(A and B), the probability that both events occur, into the first field; use a value between 0 and 1.
  2. Enter P(B)
    Type P(B), the probability of the conditioning event, into the second field; it must be greater than 0.
  3. Calculate
    Press Calculate to read the conditional probability P(A | B).

Assumptions & Limitations

What the calculation assumes

  • Every value you enter is treated as an exact, known amount.
  • Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
  • Results use standard published formulas and account only for the values entered above.
  • Rounding is applied for display; the underlying calculation uses your full precision.
  • Results are returned in the same units you enter, unless the tool states the output unit.

What it does not cover

  • Conditional Probability Calculator produces a calculated result for reference and learning, not a certified or official measurement.
  • Real-world outcomes differ when tolerances, rounding rules or local standards apply.
  • Definitions and standards vary by region and change over time; verify the convention that applies to your case.
  • Figures are only as accurate as the inputs you supply — check them before acting on the result.
  • For work where the result carries real consequences, confirm it against an authoritative source.

Frequently Asked Questions

The joint event A and B is contained within B, so its probability can never exceed P(B); the tool flags any entry that breaks this rule.

It uses the standard definition of conditional probability, P(A | B) = P(A intersect B) / P(B).

Conditioning on an event of probability zero would divide by zero, which is undefined, so the tool requires P(B) to be positive.

Yes, enter each as a decimal between 0 and 1; the result is then shown as a decimal with the equivalent percentage beside it.

Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.