Birthday Collision Probability

Formula

Use P = 1−∏ᵢ₌₀ⁿ⁻¹(1−i/d). n is people and d is equally likely days; the product is the no-match probability. If people outnumber days, a match is certain. The result assumes independent birthdays.

Find the chance that at least two people share a birthday.

Worked example

Scope and limitations

Assumes independent and equally likely birthdays; actual birth dates are not uniform.

Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.

Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.

Formula version: 3152b69c6ae2 · Example checked: 2026-10-30

Methodology

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