What This Solves
Estimates peak flood flows at ungauged sites using USGS regional regression equations based on drainage area and basin characteristics.
Best Used When
- You need a peak flow estimate at a location without a stream gauge
- You want a quick screening-level estimate of flood flows for planning or preliminary design
- You are comparing regression-based estimates with other hydrologic methods as a reasonableness check
Do NOT Use When
- A stream gauge with adequate record length exists at or near the site — Use Flood Frequency Analysis Calculator
- The drainage area is small enough for the Rational Method and you have IDF data — Use Rational Method Calculator
Key Assumptions
- Regional regression equations are valid within the hydrologic region where they were developed
- Basin characteristics (area, slope, precipitation) are within the range of the calibration dataset
- The regression equations account for average regional conditions and may not capture site-specific factors
- Standard errors of prediction are inherent in regression estimates (typically 30-60%)
- Urbanization adjustments may be needed if the regression equations were developed for rural basins
Input Quality Notes
Drainage area is typically the most important predictor variable. Measure it from the best available topographic data (USGS maps or LiDAR-based DEMs). Check that you are using the correct regional equation set for your state and hydrologic region.
Estimate the peak flood discharge at an ungauged stream site using USGS regional regression equations. Select a hydrologic region, enter the drainage area and return period, and get a screening-level peak flow with a 90% prediction interval — useful for planning, preliminary culvert and bridge sizing, and cross-checking other methods.
Screening-Level Tool
This calculator provides preliminary estimates only. Regional regression equations give approximate peak flows for ungauged sites. For final design, use state-specific USGS publications or USGS StreamStats.
About USGS Regional Regression
Regional regression equations estimate peak streamflow at ungauged sites based on statistical relationships developed from streamgage data. The USGS has developed equations for all 50 states based on regional hydrologic characteristics.
The general equation form is:
Q = a × DAb × Sc × Pd × ...
Where Q is peak discharge, DA is drainage area, and other variables may include channel slope (S), mean annual precipitation (P), basin storage, impervious area, and forested area.
Hydrologic Regions Overview
| Region | Description | DA Range (sq mi) |
|---|---|---|
| Northeast Highlands | Mountainous terrain with moderate precipitation, mixed forest cover | 0.1 - 1000 |
| Coastal Plain | Low-gradient terrain with sandy soils, higher water table | 0.05 - 500 |
| Piedmont | Rolling hills with clay soils, moderate forest cover | 0.1 - 800 |
| Appalachian Plateau | Mountainous terrain with high precipitation, steep valleys | 0.2 - 1500 |
| Great Lakes / Upper Midwest | Glaciated terrain with moderate topography, abundant lakes | 0.1 - 2000 |
| Central Plains | Low relief agricultural land, seasonal precipitation | 0.5 - 5000 |
| Southwest Semi-Arid | Arid to semi-arid terrain with ephemeral streams | 0.1 - 3000 |
| Pacific Northwest | High precipitation coastal and mountain terrain | 0.1 - 2500 |
Note: These are generalized regions for educational purposes. For actual design, use state-specific USGS publications or StreamStats.
When to Use This Calculator
Appropriate Uses:
- • Preliminary/screening estimates
- • Planning-level studies
- • Ungauged site analysis
- • Comparison with other methods
- • Educational purposes
Not Appropriate For:
- • Final engineering design
- • Heavily regulated streams
- • Highly urbanized areas (>50%)
- • Areas outside DA limits
- • Critical infrastructure
For educational purposes only. Not a substitute for professional engineering judgment.
How regional regression works
The USGS analyzes annual peak-flow records from many streamgages within a hydrologically similar region and fits a power-law relationship between peak discharge and basin characteristics. The general form of a regional regression equation is:
QT = a × DAb × Sc × Pd × (ST + 1)e × (IMP + 1)f × (FOR/100 + 1)g
Not every term appears in every region — most regions use only drainage area plus one or two extra variables. The variables are:
- QT — peak discharge for return period T, in cubic feet per second (cfs); metric output is converted to m³/s
- DA — contributing drainage area (square miles)
- S — main channel slope (feet per mile)
- P — mean annual precipitation (inches)
- ST — basin storage: percent of area in lakes, ponds and wetlands
- IMP — percent impervious cover
- FOR — percent forested cover
- a, b, c, d, e, f, g — region- and return-period-specific regression coefficients/exponents
The reported uncertainty comes from the standard error of estimate (SE), expressed in base-10 log units. The 90% prediction interval is found in log space:
Qbounds = 10(log10(Q) ± 1.645 × SE)
Each region also reports an equivalent years of record — a measure of how much streamgage data the regression statistically represents at your site.
Hydrologic region reference
Generalized regions used by this screening calculator, showing each region's equation form, the basin variables it can use, the applicable drainage-area range and the standard error range across return periods. For actual design, substitute the published equations for your specific state and study area.
| Region | Equation form | Optional variables | DA range (sq mi) | SE (log10) |
|---|---|---|---|---|
| 1 — Northeast Highlands | Q = a·DAb·Sc | Channel slope, precipitation | 0.1 – 1,000 | 0.20 – 0.25 |
| 2 — Coastal Plain | Q = a·DAb·(ST+1)e | Basin storage, impervious | 0.05 – 500 | 0.24 – 0.28 |
| 3 — Piedmont | Q = a·DAb·Sc·(FOR/100+1)g | Channel slope, forested | 0.1 – 800 | 0.21 – 0.25 |
| 4 — Appalachian Plateau | Q = a·DAb·Sc·Pd | Channel slope, precipitation | 0.2 – 1,500 | 0.18 – 0.22 |
| 5 — Great Lakes / Upper Midwest | Q = a·DAb·Pd·(ST+1)e | Basin storage, precipitation | 0.1 – 2,000 | 0.23 – 0.27 |
| 6 — Central Plains | Q = a·DAb·Sc·Pd | Channel slope, precipitation | 0.5 – 5,000 | 0.27 – 0.32 |
| 7 — Southwest Semi-Arid | Q = a·DAb·Sc·Pd·(IMP+1)f | Slope, precipitation, impervious | 0.1 – 3,000 | 0.29 – 0.38 |
| 8 — Pacific Northwest | Q = a·DAb·Pd·(FOR/100+1)g | Precipitation, forested | 0.1 – 2,500 | 0.20 – 0.24 |
These are generalized, representative regions and coefficients for screening and educational use. They are not a substitute for the official, state-specific USGS regression equations or USGS StreamStats, which you should use for engineering design.
Worked example
Region 1 (Northeast Highlands), 100-year flood, 10 sq mi drainage area, 50 ft/mi channel slope. The equation form is Q = a · DAb · Sc, with 100-year coefficients a = 65.2, b = 0.794, c = 0.180:
- DAb = 100.794 = 6.22
- Sc = 500.180 = 2.02
- Q100 = 65.2 × 6.22 × 2.02 ≈ 820 cfs
- With SE = 0.22, the 90% interval is 10(log10(820) ± 1.645 × 0.22) ≈ 350 to 1,930 cfs
The wide interval illustrates the inherent uncertainty of regression-based peak-flow estimates at ungauged sites.
Frequently asked questions
What are USGS regional regression equations?
They are statistical equations the U.S. Geological Survey develops by relating annual peak-flow records from streamgages to measurable basin characteristics — primarily drainage area, and sometimes channel slope, mean annual precipitation, basin storage, impervious cover or forest cover. Within a hydrologically similar region, the resulting equation (Q = a × DA^b × S^c × P^d × …) lets you estimate a peak discharge of a given return period at an ungauged site without any flow records of your own.
How accurate are regional regression peak-flow estimates?
Accuracy is limited. The standard error of estimate for these equations is typically in the range of about 0.20 to 0.38 log10 units, which corresponds to roughly a 20% to 50% spread on the discharge. That is why the result is reported with a 90% prediction interval rather than a single number, and why this is a screening-level tool. For final design, use the published state-specific USGS equations or USGS StreamStats.
What is the 90% prediction interval and why is it so wide?
The prediction interval is the band within which the true peak discharge is expected to fall 90% of the time. It is computed in log space from the standard error: Q_bounds = 10^(log10(Q) ± 1.645 × SE). Because regression scatter is large, the interval can easily span a factor of two or more around the point estimate. Treat the upper bound as a reminder of how much real uncertainty exists in ungauged peak-flow estimation.
When should I NOT use this calculator?
Regional regression is inappropriate for final engineering design, for streams significantly regulated by dams or diversions, for heavily urbanized watersheds (more than about 50% impervious), and for drainage areas outside the equation's applicable range. It also assumes stationary (non-changing) flood frequency, so it does not capture recent land-use change. Where streamgage data exists at or near the site, use that data directly instead.
Standards & related tools
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Last verified: February 2026