Return Period Calculator (100-Year Flood Probability)

How it works

Annual exceedance probability p = 1 ÷ T · P(at least one in n years) = 1 − (1 − 1/T)ⁿ · P(exactly one) = n p (1 − p)ⁿ⁻¹ · design return period for risk R over n years: T = 1 ÷ [1 − (1 − R)^(1/n)]

A "100-year flood" is not one that happens once a century: it is a flood with a 1% chance of being equalled or exceeded in any year. Treating years as independent trials, the chance of at least one such event in n years follows from the binomial distribution. The USGS points out that over a 30-year mortgage a 100-year flood has about a 26% chance of occurring. Engineers turn the formula around to choose a design return period — building codes, for example, design for earthquake shaking with a 10% chance of exceedance in 50 years, which is a 475-year return period.

Worked example

For a 100-year flood over 30 years: P = 1 − (1 − 0.01)³⁰ = 1 − 0.99³⁰ = 26.0%. The chance of exactly one is 30 × 0.01 × 0.99²⁹ = 22.4%, of two or more 3.6%, and the expected number of floods is 0.30.

Sources: USGS — The 100-year flood · Wikipedia — Return period

Frequently asked questions