Flood Return Period Calculator
Flood frequency analysis determines how often floods of different sizes occur by fitting statistical distributions to annual maximum peak flow records. The Weibull plotting position is the simplest method: T = (n+1)/m, where T is the return period in years, n is the length of the record in years, and m is the rank of the event in descending order (1 = largest). The corresponding exceedance probability is P = 1/T. Enter the total years of record and the rank of the flood event to calculate its return period and annual exceedance probability.
Flood return period formula (Weibull)
T (years) = (n + 1) / m
AEP (%) = 1 / T * 100 = m / (n + 1) * 100
P(at least once in N years) = 1 - (1 - AEP/100)^N * 100
The Weibull plotting position T = (n+1)/m is the standard formula in US hydrology education (USGS, ASCE). For a 50-year record, the largest observed flood (m=1) has T = 51 years. The USGS uses the more sophisticated Log-Pearson Type III distribution (Bulletin 17C) for engineering design, but Weibull is standard for visual plotting and education.
Flood frequency concepts
- A 100-year flood (AEP = 1%) has a 26 percent chance of occurring at least once in a 30-year mortgage period.
- FEMA's National Flood Insurance Program (NFIP) uses the 1% annual chance (100-year) flood as the base flood elevation standard.
- USGS maintains over 8,000 stream gauges providing peak flow records used for flood frequency analysis.
- Climate change is altering flood frequencies: studies show the 100-year flood is becoming more frequent in many eastern US watersheds (USGS).
- USGS Bulletin 17C (2019) is the current federal standard for flood frequency analysis in the US, replacing Bulletin 17B from 1982.
Frequently asked questions
What is a flood return period?
A flood return period (also called recurrence interval) is the average number of years between floods that equal or exceed a given discharge. A 100-year flood has a return period of 100 years, meaning there is a 1 percent probability of it occurring in any given year. It does NOT mean it occurs exactly once per century.
What is the Weibull plotting position formula?
The Weibull formula T = (n+1)/m estimates the return period for ranked flood data, where n is the total number of years of record and m is the rank of the event (1 = largest). The exceedance probability is P = m/(n+1) = 1/T. The Weibull formula is one of several plotting positions; others include Cunnane (m-0.4)/(n+0.2) and Hazen.
What is a 100-year flood?
A 100-year flood (also called the 1% annual chance flood) is the flow that has a 1 percent probability of being exceeded in any given year. It is the standard FEMA flood insurance and regulatory baseline for the Special Flood Hazard Area (SFHA). Despite its name, it is a statistical concept, not a guarantee of periodicity.
What is the annual exceedance probability?
Annual exceedance probability (AEP) is the probability that a flood of a given magnitude will be equaled or exceeded in any single year. AEP = 1/T, where T is the return period. A 100-year flood has AEP = 1/100 = 1%. The probability of at least one occurrence in 30 years is 1 - (1-0.01)^30 = 26 percent.
How is flood frequency analysis done in practice?
USGS uses Log-Pearson Type III frequency analysis (Bulletin 17C) as the national standard for flood frequency analysis in the US. This fits a statistical distribution to annual maximum peak flows from a stream gauge record to estimate return period flows. USGS StreamStats automates this for gaged sites.
Official sources
- USGS: Bulletin 17C: Guidelines for Determining Flood Flow Frequency (2019).
- USGS: USGS Peak Streamflow Data.
- FEMA: FEMA Flood Maps and Flood Zones.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.