Rain Probability Calculator — Stated Probability Models

Work with rain probabilities that you already have, rather than generate a weather forecast. For several periods, the calculator shows what can be concluded without knowing their dependence. You can explicitly choose an independence model, or explore the educational confidence-times-coverage calculation.

How to use this tool

1. Choose the periods model or the confidence-times-coverage example.
2. For periods, enter percentages for the same location and distinct time intervals.
3. Leave dependence unknown unless an independence assumption is justified.
4. Read the assumptions with the result; use a forecast provider for actual weather.

Formula

Bounds: max(pᵢ) ≤ P(any) ≤ min(1, Σpᵢ). Under mutual independence: P(any) = 1 − ∏(1 − pᵢ).

Probabilities pᵢ are fractions in these formulas. Confidence C times conditional coverage A gives C×A under the stated representative-point model. Expected wet-period count is Σpᵢ and does not require independence.

Example

Two periods with 40% and 30% probabilities have a combined chance somewhere from 40% to 70% without dependence information. If they are independent, the dry chance is 0.6 × 0.7 = 0.42, so the chance of at least one wet period is 58%.