The Rational Method Explained: A Complete Guide

The Rational Method is the most widely used technique for estimating peak stormwater runoff from small watersheds. Despite being over 150 years old, it remains the standard for sizing drainage infrastructure for small urban areas.

History and Development

The Rational Method was first introduced by Emil Kuichling in 1889, though similar concepts had been developed earlier by Thomas Mulvaney in Ireland (1851). The method emerged from observations of urban drainage systems in Rochester, New York.

The “rational” name comes from the rational relationship between rainfall and runoff—a direct proportionality that made intuitive sense to early engineers before computational hydrology existed.

The Fundamental Equation

The Rational Method equation is elegantly simple:

Where:

• Q = Peak discharge (cfs in U.S. customary units, or m³/s in SI)
• C = Runoff coefficient (dimensionless, 0 to 1)
• i = Rainfall intensity (inches/hour or mm/hour)
• A = Drainage area (acres or hectares)

Unit Conversion Factor

In U.S. customary units, the equation is dimensionally consistent when using:

• Q in cubic feet per second (cfs)
• i in inches per hour
• A in acres

The dimensional analysis:

The factor 1.008 is close enough to 1.0 that it’s typically ignored—a convenient coincidence that makes the equation easy to remember.

Understanding Each Variable

Runoff Coefficient (C)

The runoff coefficient represents the fraction of rainfall that becomes direct runoff. It accounts for:

• Infiltration losses
• Depression storage
• Surface roughness effects
• Initial abstraction

Factors affecting C:

• Soil permeability (sandy vs. clay)
• Slope (steeper = higher C)
• Storm intensity (C increases for larger storms)
• Surface characteristics

See complete tables: Runoff Coefficients Guide →

Rainfall Intensity (i)

Rainfall intensity is determined from Intensity-Duration-Frequency (IDF) curves for your location. The key relationship is:

Storm duration = Time of concentration (Tc)

This is the critical duration assumption. When storm duration equals Tc:

• The entire watershed is contributing to runoff
• Maximum discharge occurs
• Using a shorter duration would give higher intensity but incomplete watershed contribution

Drainage Area (A)

The drainage area includes all land that contributes runoff to your design point. Determining this requires:

1. Topographic analysis (reading contour maps)
2. Identifying drainage divides (ridgelines)
3. Accounting for constructed drainage features (curbs, pipes)

Key Assumptions

The Rational Method is based on several important assumptions:

1. Uniform Rainfall Distribution

Rainfall intensity is constant over the entire drainage area. This assumption becomes less valid as watershed size increases.

2. Rainfall Duration ≥ Tc

The design storm lasts at least as long as the time of concentration, ensuring the entire watershed contributes to peak flow.

3. Peak Flow Timing

Peak runoff occurs when the storm duration equals Tc. At this moment, the entire drainage area is contributing.

4. Constant Runoff Coefficient

C doesn’t change during the storm. In reality, C tends to increase as soils become saturated, but the method uses a single representative value.

5. No Storage Effects

The method doesn’t account for channel or pond storage that would attenuate the peak. The calculated Q is the peak that would occur without any attenuation.

Calculating Composite Runoff Coefficient

For drainage areas with multiple surface types, calculate a weighted average:

Worked Example

A 10-acre site contains:

• 3 acres of pavement (C = 0.90)
• 5 acres of lawn on clay soil (C = 0.25)
• 2 acres of rooftops (C = 0.90)

Try the Runoff Coefficient Calculator →

Step-by-Step Application

Step 1: Determine the Drainage Area

Delineate the watershed boundary and measure the area contributing to your design point.

Step 2: Characterize Land Use

Identify surface types and their areas. Select appropriate runoff coefficients. Calculate composite C if multiple surfaces exist.

Step 3: Calculate Time of Concentration

Trace the longest flow path and calculate Tc using appropriate methods (sheet flow, shallow concentrated flow, channel flow).

Learn more: Time of Concentration Explained →

Step 4: Select Design Storm Frequency

Common choices:

• Minor drainage (pipes, inlets): 10-year
• Major drainage (channels, roadways): 25-year or 100-year
• Check your local requirements!

Step 5: Find Rainfall Intensity

Using local IDF curves, find intensity for:

• Duration = Tc
• Frequency = design storm return period

Step 6: Calculate Peak Flow

Apply the Rational Method equation:

Complete Worked Example

Given:

• Drainage area: 5 acres
• Land use: Commercial parking lot
• Composite C: 0.85
• Tc: 10 minutes
• Location: Example City
• Design storm: 10-year

Solution:

1. From Example City’s IDF curve, 10-year, 10-minute intensity = 5.8 in/hr

2. Apply the equation:

3. This is the peak flow for sizing the drainage system.

Try the Rational Method Calculator →

When NOT to Use the Rational Method

The Rational Method has significant limitations. Don’t use it for:

Large Watersheds

General rule: Maximum 200 acres (80 hectares)

As watersheds get larger:

• Rainfall becomes non-uniform
• Travel time assumptions break down
• Storage effects become significant
• The SCS method or hydrograph analysis is more appropriate

Volume Calculations

The Rational Method calculates peak flow only, not volume. Don’t use it for:

• Detention pond sizing (need total volume)
• Flood storage calculations
• Water quality volume
• Infiltration system design

Complex Watersheds

Avoid the Rational Method when:

• Multiple distinct sub-watersheds exist
• Significant storage (ponds, wetlands) affects flow
• Timing of tributary flows matters
• Back-to-back storms need to be analyzed

Non-Urban Areas

The method was developed for urban drainage. For:

• Agricultural watersheds: Use SCS/NRCS method
• Large natural watersheds: Use hydrograph methods
• Forested areas: Consider infiltration-excess vs. saturation-excess runoff

Modifications and Variations

Modified Rational Method

For detention basin preliminary sizing, some jurisdictions use a “Modified Rational Method” that creates a simplified hydrograph:

1. Rising limb from 0 to Tc
2. Constant Q for storm duration
3. Falling limb from end of storm to end of storm + Tc

This provides a rough volume estimate but is still an approximation.

C Adjustment for Storm Intensity

Some agencies adjust C for larger storms to account for:

• Soil saturation
• Reduced infiltration at high intensities

Where Ff is a frequency factor (e.g., 0.1 for 25-year, 0.25 for 100-year).

Common Mistakes and How to Avoid Them

Mistake 1: Using Wrong Duration

Error: Using a standard storm duration (e.g., 1-hour) instead of Tc

Consequence: If duration > Tc, you underestimate intensity and peak flow If duration < Tc, not all area is contributing

Solution: Always use duration = Tc for the Rational Method

Mistake 2: Applying to Large Areas

Error: Using Rational Method for 500+ acre watershed

Consequence: Results become unreliable; may significantly over- or under-estimate

Solution: Switch to SCS method or detailed hydrograph analysis for large watersheds

Mistake 3: Summing Flows Incorrectly

Error: Adding peak flows from sub-areas without considering timing

Consequence: Overestimated combined flow (peaks don’t occur simultaneously)

Solution: For complex systems, use hydrograph methods to properly combine flows

Mistake 4: Confusing C Determination

Error: Using the wrong C for conditions (e.g., using saturated soil C for normal conditions)

Consequence: Over- or under-design

Solution: Select C appropriate for design conditions; document your assumptions

Mistake 5: Ignoring Local Requirements

Error: Using generic C values or IDF data without checking local standards

Consequence: Design may not meet local approval requirements

Solution: Always obtain local IDF data and check for jurisdiction-specific C tables

Summary

The Rational Method remains valuable because it:

• Is simple and quick to apply
• Requires minimal data
• Works well for small urban watersheds
• Is universally understood by reviewers

But remember its limitations:

• Peak flow only (not volume)
• Small watersheds only (≤200 acres)
• Assumes uniform rainfall and constant C
• No storage effects

For applications beyond these limitations, learn the SCS/NRCS Method or hydrograph techniques.

References

1. Kuichling, E. (1889). The relation between the rainfall and the discharge of sewers in populous districts. Transactions of the American Society of Civil Engineers, 20, 1-56.

2. Federal Highway Administration. (2013). Urban drainage design manual (3rd ed., Hydraulic Engineering Circular No. 22). U.S. Department of Transportation.

3. American Society of Civil Engineers. (2017). Design and construction of urban stormwater management systems (ASCE Manual of Practice No. 77). ASCE Press.

4. Chow, V. T., Maidment, D. R., & Mays, L. W. (1988). Applied hydrology. McGraw-Hill.

5. McCuen, R. H. (2016). Hydrologic analysis and design (4th ed.). Pearson.

6. Mulvaney, T. J. (1851). On the use of self-registering rain and flood gauges in making observations of the relations of rainfall and flood discharges in a given catchment. Proceedings of the Institution of Civil Engineers of Ireland, 4, 18-33.