Water Resources Hydrologic Curve Number

What Is Hydrologic Curve Number in Water Resources?

In water resources engineering, the Hydrologic Curve Number (CN) is one of the most widely used tools to estimate direct runoff from a rainfall event.

The Curve Number method, developed by the USDA NRCS (formerly SCS), gives a simple way to answer a fundamental question:

“If it rains this much on this type of land and soil, how much of that rain will turn into runoff?”

The CN method combines:

• Soil type (hydrologic soil group)
• Land use and land cover
• Condition or management (good, fair, poor)
• Antecedent moisture condition (AMC) – how wet or dry the soil was before the storm

All of these are wrapped up into a single dimensionless number: the Curve Number, typically ranging from about 30 to 100.

• Low CN (~30–60): High infiltration, low runoff (forest, good pasture, dry soils)
• High CN (~80–98): Low infiltration, high runoff (pavement, parking lots, compacted urban soils, saturated ground)

Your Curve Number Calculator makes this process fast, transparent, and easy to use for engineers, hydrologists, planners, and students.

Overview of the Curve Number Calculator

Your Curve Number Calculator is built around the standard NRCS CN method and allows the user to:

• Select Hydrologic Soil Group (A, B, C, D)
• Choose Land Use / Cover Type with a base CN
• Enter Rainfall depth for a single storm event (inches)
• Select Antecedent Moisture Condition (I, II, III)
• Provide Drainage area (acres)

From these inputs, the calculator computes:

• Adjusted Curve Number (CN)
• Potential maximum retention (S) in inches
• Runoff depth (Q) in inches
• Total runoff volume in acre-feet
• Runoff classification based on the CN value

The result is a compact but powerful runoff analysis that can be used for:

• Stormwater design
• Detention basin sizing
• Watershed assessments
• Urban runoff estimation

Understanding the Key Inputs in Simple Terms

Let’s walk through each input field and explain what it represents in real-world terms.

Hydrologic Soil Group (A, B, C, D)

The Hydrologic Soil Group (HSG) describes the infiltration capacity of soils when they are fully saturated.

In your calculator, the options are:

• Group A – Sand, Loamy Sand (Low Runoff)
  • High infiltration, very well-drained soils, low runoff potential.
• Group B – Silt Loam, Loam (Moderately Low Runoff)
  • Moderate infiltration, common in many agricultural and suburban areas.
• Group C – Sandy Clay Loam (Moderately High Runoff)
  • Slower infiltration, more runoff than A or B.
• Group D – Clay, Clay Loam (High Runoff Potential)
  • Very low infiltration, high runoff, often associated with clays and compacted soils.

Even though your current code doesn’t directly use the soil group to change the CN (that is baked into the selected land use options), it is still an important descriptive parameter and helps users interpret the site’s runoff behavior.

Land Use / Cover Type and Base Curve Number

The Land Use / Cover Type is where the base Curve Number really comes from in your calculator.

Each option in your dropdown menu includes a CN value. For example:

• Open Space (good condition) – 39
• Open Space (fair condition) – 61
• Open Space (poor condition) – 74
• Woods (good condition) – 57
• Pasture (poor condition) – 79
• Row Crops (good condition) – 77
• Commercial / Business – 86
• Industrial – 92
• Residential 1/4 acre – 81
• Residential townhouse – 92
• Paved parking / lot – 98

These values reflect how impervious or runoff-prone each land use is.

• Natural, vegetated areas in good condition → lower CN → more infiltration
• Urban, paved, compacted areas → higher CN → more runoff

The selected land use gives the starting CN before adjustment for moisture condition.

Rainfall Depth (inches)

The Rainfall Depth input is the total storm depth in inches (P).

• Example: A 3-inch storm means P = 3.0 in
• This is the gross rainfall, not yet reduced for initial losses or infiltration.

The calculator uses this P value in the standard NRCS runoff equation:

[
Q = \frac{(P - 0.2S)^2}{P + 0.8S}, \quad \text{for } P > 0.2S
]

Where:

• Q = runoff depth (inches)
• P = rainfall depth (inches)
• S = potential maximum retention (inches), derived from CN

Antecedent Moisture Condition (AMC I, II, III)

Antecedent Moisture Condition (AMC) describes how wet or dry the soil was before the storm:

• I – Dry (wilting point)
  • Soils are dry, plants may be stressed.
  • More capacity to absorb rainfall → lower effective CN.
• II – Normal (field capacity)
  • Average moisture conditions, typical design assumption.
  • Base CN values are usually assumed to be AMC II.
• III – Wet (saturation)
  • Soils are wet or near saturation from previous storms.
  • Less capacity to absorb rainfall → higher effective CN.

Your calculator takes the base CN from land use and adjusts it using the AMC:

• For AMC I (dry) → CN is reduced
• For AMC II (normal) → CN stays the same
• For AMC III (wet) → CN is increased

This is handled by the adjustCurveNumber function using standard NRCS-style relationships.

Drainage Area (acres)

The Drainage Area is the contributing watershed area in acres.

• The runoff depth (Q, inches) is first calculated.
• Then this depth is converted into a volume using area.

Your calculator uses:

[
\text{Runoff Volume (acre-feet)} = \frac{Q \times \text{Area (acres)}}{12}
]

Why divide by 12?

• Because 1 foot = 12 inches, so converting inches over acres to feet over acres gives acre-feet – a very common volume unit in hydrology.

How the Curve Number Calculator Works Step by Step

Let’s follow the logic your calculator uses when the user clicks “Calculate Runoff”.

Step 1 – Read Inputs

The calculator reads:

• Soil Group (A, B, C, D) – descriptive
• Land Use CN – numeric base CN from dropdown
• Rainfall depth P (inches)
• AMC condition (I, II, III)
• Drainage area (acres)

If any numeric value is missing, the script uses sensible defaults (like 3.0 inches rainfall or 1.0 acre).

Step 2 – Adjust the Curve Number for Moisture Condition

Your function adjustCurveNumber(cn, condition) does:

• If condition = I (dry) → apply formula to reduce CN
• If condition = III (wet) → apply formula to increase CN
• If condition = II (normal) → leave CN unchanged

This mirrors the NRCS approach of adjusting CN for AMC I and AMC III using conversion relationships.

The result is an Adjusted Curve Number, which represents the true runoff potential for the current soil moisture state.

This value is then:

• Rounded
• Displayed as the Curve Number in the results

Step 3 – Calculate Potential Maximum Retention (S)

Next, your calculator computes S, the potential maximum soil-water retention after runoff begins, using:

[
S = \frac{1000}{CN} - 10
]

• CN is the adjusted Curve Number
• S is in inches

Interpretation:

• Higher CN → lower S → soil can retain less → more runoff
• Lower CN → higher S → soil can retain more → less runoff

This S value is shown as Potential Maximum Retention (inches).

Step 4 – Compute Runoff Depth (Q)

Now the heart of the CN method: computing runoff depth Q.

Your calculator uses the standard NRCS runoff formula:

• If P ≤ 0.2S, then Q = 0 (no runoff; rainfall not enough to exceed initial losses)
• If P > 0.2S, then:
  [
  Q = \frac{(P - 0.2S)^2}{P + 0.8S}
  ]

Where:

• P = rainfall depth (inches)
• S = potential maximum retention (inches)
• Q = runoff depth (inches)

This formula accounts for:

• Initial abstractions (interception, depression storage, infiltration) assumed to be 0.2S
• Remaining rainfall converted to runoff after these losses are satisfied

Your Runoff Depth (Q) is displayed to two decimal places.

Step 5 – Convert Runoff Depth to Runoff Volume

After finding Q (inches), your calculator converts it to runoff volume in acre-feet:

[
\text{Runoff Volume} = \frac{Q \times \text{Area}}{12}
]

Where:

• Q = runoff depth (inches)
• Area = drainage area (acres)
• 12 = inches per foot

The result is:

• Total Runoff Volume (acre-feet)

This is a very useful quantity for:

• Detention basin sizing
• Storage requirements
• Flood volume estimation

Step 6 – Classify Runoff Potential based on CN

Your calculator then classifies the runoff potential with getRunoffClassification(cn):

• CN < 40 → Very Low Runoff Potential
• 40 ≤ CN < 60 → Low Runoff Potential
• 60 ≤ CN < 75 → Moderate Runoff Potential
• 75 ≤ CN < 85 → Moderately High Runoff Potential
• 85 ≤ CN < 95 → High Runoff Potential
• CN ≥ 95 → Very High Runoff Potential

This helps users quickly interpret whether their watershed is more infiltration-dominated or runoff-dominated.

Interpreting the Curve Number Calculator Results

Once the calculations are done, your tool shows:

1. Curve Number (Adjusted) – Composite CN Value
   • The final CN after considering land use and moisture condition.
   • Higher CN → more runoff, less infiltration.
2. Potential Maximum Retention (S, inches)
   • How much water the watershed can potentially store before runoff significantly occurs.
3. Runoff Depth (Q, inches)
   • How many inches of the rainfall become direct runoff.
4. Total Runoff Volume (acre-feet)
   • The actual runoff volume over the watershed area.
   • Useful for designing storage or hydraulic structures.
5. Runoff Classification
   • A qualitative summary of the runoff potential: very low, low, moderate, etc.

Together, this gives a complete mini-runoff analysis in just a few clicks.

Practical Uses of Hydrologic Curve Number in Design

Your Curve Number Calculator is especially useful in:

Stormwater Management Design

• Designing detention and retention basins
• Sizing storm sewers and culverts
• Estimating inflows into ponds, swales, and channels

By converting rainfall into runoff depth and volume, the CN method helps designers estimate peak flows and volumes that need to be managed.

Urban Planning and Land Development

• Comparing pre-development vs. post-development runoff
• Evaluating how much urbanization increases runoff
• Supporting low impact development (LID) strategies

By testing different land use options in your calculator, planners can see how CN and runoff change when open space is replaced with pavement or buildings.

Watershed and Flood Studies

• Assessing runoff potential at a watershed scale
• Screening basins for flood susceptibility
• Comparing different soil groups and land covers

The CN method is widely used in watershed models and flood hydrology for its simplicity and consistency.

Strengths and Limitations of the Curve Number Method

Strengths

• Simple and widely accepted in practice
• Requires a limited set of easily understandable inputs
• Integrates soil, land use, and moisture into one parameter
• Works well for design storms and planning-level analyses

Limitations

• Assumes uniform rainfall over the watershed
• Originally developed for agricultural and rural watersheds, though now commonly applied in urban areas
• Sensitive to the choice of CN and AMC
• Best suited for event-based runoff rather than continuous simulation

Your calculator is ideal for:

• Preliminary design
• Educational use
• Quick comparisons and estimates

For final designs, engineers should always:

• Cross-check with local guidelines
• Use site-specific field data where possible
• Consider more detailed hydrologic modeling when required