Screen 2- through 500-year flood estimates from a complete record of positive annual peaks. This tool fits the Log-Pearson Type III and Gumbel distributions to your data using basic systematic-record statistics. It does not perform a complete USGS Bulletin 17C analysis.
Bulletin 17C and Log-Pearson Type III, in brief
USGS Bulletin 17C flood-frequency analysis fits a Log-Pearson Type III (LP3) distribution to the base-10 logarithms of annual peak discharges. The full federal procedure also uses the Expected Moments Algorithm, weighted regional skew, and the Multiple Grubbs-Beck test to incorporate historical or censored information and identify potentially influential low floods.
This calculator implements only the basic systematic-record LP3 frequency-factor calculation and optional regional-skew weighting. It omits EMA, MGBT, historical information, censored or interval data, and zero-flow handling. Its optional confidence bounds are a central-t/delta-method approximation, not the Bulletin 17C noncentral-t/EMA interval. Use USGS PeakFQ or an agency-approved workflow for regulatory, floodplain-mapping, or final-design work.
Source: USGS Bulletin 17C, Guidelines for Determining Flood Flow Frequency
Systematic-record screening only
This calculator fits basic LP3 or Gumbel distributions to complete, positive annual peaks. It is not a complete Bulletin 17C analysis: EMA, MGBT, historical information, censored or interval data, and zero-flow handling are not implemented. Use USGS PeakFQ or an agency-approved workflow for regulatory or design work.
About this screening fit
A simple flood-frequency fit uses systematic annual peak flow data to estimate the magnitude of floods for various return periods (recurrence intervals). The analysis fits a probability distribution to the observed data and extrapolates to estimate flows with lower probabilities of occurrence.
Log-Pearson Type III is the reference distribution in US federal guidance, but the full Bulletin 17C procedure includes data treatment that this tool omits. The Gumbel distribution is included only as a simpler comparison.
Distribution Comparison
| Aspect | Log-Pearson Type III | Gumbel (EV1) |
|---|---|---|
| Parameters | 3 (mean, std dev, skew) | 2 (location, scale) |
| Skewness | Variable (data-driven) | Fixed (1.14) |
| Standard | Reference distribution in US guidance; this fit is not full B17C | International |
| Best for | Screening complete, positive systematic records | Method comparison and sensitivity screening |
Data Requirements
Required:
- Minimum 10 positive annual peak flow values
- Annual maximum instantaneous peaks
- No zero, censored, or interval-valued records
- Consistent measurement method
- Representative of current conditions
Recommended:
- 20+ years for reliable skew estimate
- Regional skew for weighted analysis
- PeakFQ/EMA and MGBT review before design use
- Verification with nearby gages
Data Source: Annual peak flow data can be obtained from the USGS National Water Information System (NWIS).
For educational purposes only. Not a substitute for professional engineering judgment.
How flood frequency analysis works
The Log-Pearson Type III (LP3) method works in log space. The annual peak flows Qi are transformed to base-10 logarithms, and the mean, standard deviation and skew of those logs are computed. The discharge for a given return period T is then:
log₁₀(QT) = ȳ + KT · sy ⟶ QT = 10(ȳ + KT · sy)
- ȳ — mean of the log-transformed peaks, ȳ = (1/n)·Σ log₁₀(Qi)
- sy — standard deviation of the logs, sy = √[ Σ(yi − ȳ)² / (n − 1) ]
- Gs — station skew of the logs, Gs = n·Σ(yi − ȳ)³ / [ (n − 1)(n − 2)·sy³ ]
- KT — the Pearson III frequency factor, read from the table below for the skew and the exceedance probability P = 1/T
- T — return period in years; exceedance probability P = 1/T
When a regional skew is supplied, the calculator computes a weighted skew Gw by blending station and regional skew in inverse proportion to their mean square errors (Bulletin 17C):
Gw = (MSEGr·Gs + MSEGs·Gr) / (MSEGs + MSEGr)
The Gumbel (Extreme Value Type I) alternative works directly on the untransformed flows. Its scale and location parameters are α = s·√6/π and μ = x̄ − 0.5772·α (0.5772 is the Euler–Mascheroni constant), and the design flow is QT = μ + α·y, where the reduced variate y = −ln(−ln(1 − 1/T)). Gumbel has a fixed skew of about 1.14.
Log-Pearson III frequency factors (KT)
Selected KT values from the classic Pearson Type III table (USGS Bulletin 17B, Appendix 3) for positive-skew watersheds. The calculator computes each factor exactly from the Pearson Type III quantile function, which reproduces the printed table to within 0.001. The full table it interpolates runs from skew −3.0 to +3.0 in steps of 0.1 and ends at the 500-year (0.2% chance) column. Negative skews reduce the upper-tail factors, raise the lower tail, and a skew of exactly 0 reproduces the standard-normal Z values.
| Skew (G) | 2-yr (P=0.50) | 10-yr (P=0.10) | 25-yr (P=0.04) | 50-yr (P=0.02) | 100-yr (P=0.01) | 500-yr (P=0.002) |
|---|---|---|---|---|---|---|
| 0.0 | 0.000 | 1.282 | 1.751 | 2.054 | 2.326 | 2.878 |
| 0.2 | −0.033 | 1.301 | 1.818 | 2.159 | 2.472 | 3.122 |
| 0.4 | −0.067 | 1.317 | 1.880 | 2.261 | 2.615 | 3.366 |
| 0.6 | −0.099 | 1.329 | 1.939 | 2.359 | 2.755 | 3.609 |
| 0.8 | −0.132 | 1.336 | 1.993 | 2.453 | 2.891 | 3.850 |
| 1.0 | −0.164 | 1.340 | 2.043 | 2.542 | 3.023 | 4.088 |
KT is dimensionless. For example, with a log mean ȳ = 3.05, log standard deviation sy = 0.20 and skew G = 0.4, the 100-year factor is 2.615, so log₁₀(Q₁₀₀) = 3.05 + 2.615 × 0.20 = 3.573 and Q₁₀₀ ≈ 3,740 cfs.
Return periods and exceedance probability
Return period vs annual chance
A T-year flood has an annual exceedance probability of 1/T. The 100-year flood is the flow with a 1% chance of being equalled or exceeded in any single year — not an event that happens only once per century. Over a 30-year period the chance of seeing at least one 100-year flood is about 26%.
Default return periods
This calculator reports the 2-, 5-, 10-, 25-, 50-, 100-, 200- and 500-year screening estimates. Regulatory floodplain, critical-facility, and dam-safety studies require a complete agency-approved analysis such as PeakFQ, not these screening values. When enabled, this tool's approximate sensitivity intervals widen sharply for rarer events; they are not regulatory confidence limits.
Key assumptions and limitations
Screening-fit assumptions
- Annual peaks are independent and identically distributed
- The record is stationary and representative of future conditions
- The fitted distribution represents the population of annual peaks
- No significant flow regulation or watershed change during the record
- Every record is a complete positive value, not censored or interval data
Limitations
- Extrapolation beyond about 2× the record length is highly uncertain
- Records under 20 years give unreliable skew estimates
- Does not account for non-stationarity from climate or land-use change
- No EMA, MGBT, historical-data, censored-data, or zero-flow procedures
- Optional intervals are only a central-t/delta-method approximation
Annual peak-flow records for US streams are published by the USGS National Water Information System (NWIS). Do not use this screening output for regulatory or final-design work. Analyze the complete record with USGS PeakFQ or another agency-approved Bulletin 17C workflow.
Frequently asked questions
What is flood frequency analysis?
Flood frequency analysis is a statistical method that uses a record of annual peak flows (the single largest instantaneous discharge each year) to estimate the magnitude of floods for a range of return periods, such as the 2-, 10-, 50-, 100- and 500-year flood. A probability distribution is fitted to the observed peaks and then used to extrapolate to the rarer, larger events used in design.
How many years of data do I need?
This screening calculator requires at least 10 complete, positive annual peaks, and 20 or more years generally gives a more stable station-skew estimate. A short record makes rare-event extrapolation highly uncertain. A complete Bulletin 17C analysis may also incorporate historical and censored information that this tool cannot accept.
Why is the Log-Pearson Type III distribution used in the US?
Log-Pearson Type III (LP3) is the reference distribution in US federal flood-frequency guidance. Its three parameters are the mean, standard deviation and skew of the log-transformed flows. Using the LP3 distribution alone does not make a calculation Bulletin 17C compliant; the complete procedure also addresses censored, historical, zero-flow and potentially influential low-flow data.
What is the difference between Log-Pearson III and Gumbel?
LP3 fits three parameters, including skew, to the base-10 logarithms of the flows. Gumbel (Extreme Value Type I) is a simpler two-parameter distribution with fixed shape. This tool can report both as a screening comparison; neither output is a regulatory analysis by itself.
What is regional (weighted) skew and when should I use it?
The station skew from a short record is statistically noisy. This tool can apply a simple inverse-MSE blend of station and regional skew. Use it only with an applicable published regional-skew value and its MSE. This optional weighting does not add the EMA, MGBT and data-treatment procedures needed for a complete Bulletin 17C analysis.
Is this a complete Bulletin 17C analysis?
No. This is a basic systematic-record LP3 screening fit. It does not implement the Expected Moments Algorithm (EMA), Multiple Grubbs-Beck Test (MGBT), historical flood information, censored or interval data, or zero-flow conditional-probability handling. Its optional confidence bounds use a central-t/delta approximation, not the Bulletin 17C noncentral-t/EMA procedure. Use PeakFQ or an agency-approved workflow for design and regulatory work.
Standards & related tools
What This Solves
Fits basic Log-Pearson Type III and Gumbel distributions to complete positive systematic annual peaks for preliminary screening.
Best Used When
- You have a simple record of complete positive annual peaks and need an educational screening fit
- You want to compare basic LP3 and Gumbel method-of-moments estimates
- You are checking a hand calculation before using a complete agency-approved workflow
Do NOT Use When
- You are estimating peak flows at an ungauged site without stream gauge data — Use USGS Regression & StreamStats Guide
- You need a design flow for a small urban drainage area (not a gauged stream) — Use Rational Method Calculator
Key Assumptions
- Annual peak flows are independent and identically distributed random variables
- The record is stationary (no significant trends from land use change, climate change, or regulation)
- Every input is a complete, positive systematic annual peak
- No historical, censored, interval, or zero-flow observations are present
- Optional regional-skew weighting uses an applicable published skew and MSE
Input Quality Notes
Screening only: EMA, MGBT, historical/censored data treatment, and zero-flow procedures are not implemented. Optional intervals are a central-t/delta approximation, not Bulletin 17C noncentral-t/EMA confidence limits. Use USGS PeakFQ or an agency-approved workflow for regulatory or final-design work.
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Last verified: February 2026