What This Solves
Generates the SCS/NRCS dimensionless curvilinear unit hydrograph for a watershed, providing a detailed runoff response to a unit of rainfall excess.
Best Used When
- You need a detailed runoff hydrograph for medium-scale watershed analysis
- You are developing inputs for detention basin routing or downstream flood analysis
- You want the standard NRCS curvilinear hydrograph shape rather than the simplified triangular version
Do NOT Use When
- You only need the peak flow rate and a simplified triangular shape — Use SCS Triangular Hydrograph Calculator
- The drainage area is under 200 acres and you only need peak flow — Use Rational Method Calculator
Key Assumptions
- The dimensionless unit hydrograph shape follows NRCS NEH Part 630 Chapter 16 ratios
- Peak flow occurs at the dimensionless time ratio t/Tp = 1.0
- The hydrograph shape is fixed — only the peak magnitude and timing scale with watershed characteristics
- Watershed lag time is 0.6 * time of concentration
- The peak rate factor (PRF) of 484 applies (standard for average conditions)
Input Quality Notes
Watershed area, time of concentration, and curve number are the key inputs. Ensure Tc is computed with methods appropriate for the watershed size. For urban watersheds, consider reduced Tc due to improved channels and storm sewers.
The SCS (NRCS) unit hydrograph calculator generates a synthetic storm runoff hydrograph and its peak discharge from a watershed's drainage area, time of concentration and excess rainfall — using the dimensionless unit hydrograph method from TR-55 and the NRCS National Engineering Handbook.
Calculate Storm Hydrograph
For educational purposes only. Not a substitute for professional engineering judgment.
SCS Unit Hydrograph Method Overview
The SCS (NRCS) Dimensionless Unit Hydrograph method generates synthetic hydrographs for storm runoff analysis. Key equations:
- Peak discharge: qp = K x A x Q / Tp
- Time to peak: Tp = D/2 + Tlag
- Lag time: Tlag = 0.6 x Tc
- Time base: Tb = 5 x Tp
Where:
- K = Peak rate factor (484 for US units)
- A = Drainage area (mi²)
- Q = Excess rainfall depth (in)
- D = Unit hydrograph duration (hours)
- Tc = Time of concentration (hours)
Peak Rate Factor Guidelines
| Watershed Condition | K (US) | K (SI) |
|---|---|---|
| Flat/Swampy terrain | 300 | 1.29 |
| Standard conditions | 484 | 2.08 |
| Steep terrain | 600 | 2.58 |
Source: TR-55 (1986), Chapter 3. The standard peak rate factor of 484 applies to average watershed conditions. Adjust for terrain and storage effects.
How the SCS unit hydrograph method works
The SCS dimensionless unit hydrograph is a curve-fit of the average runoff response from many natural watersheds, expressed as discharge ratio (q/qp) against time ratio (t/Tp). To apply it to a specific site you compute the peak discharge and the time to peak, then scale the standard shape. The governing relationships are:
- Lag time: Tlag = 0.6 × Tc
- Time to peak: Tp = D / 2 + Tlag
- Peak discharge: qp = K × A × Q / Tp
- Time base: Tb = 5 × Tp
Where:
- K = peak rate factor — 484 (US, qp in cfs) or 2.08 (SI, qp in m³/s) for average watershed conditions
- A = drainage area (mi² for US, km² for SI)
- Q = excess rainfall / runoff depth (in for US, mm for SI)
- Tc = time of concentration (hours)
- D = unit (excess-rainfall) duration in hours; this calculator defaults to Tc/5 when not specified
The full storm hydrograph is built by multiplying the peak discharge by the dimensionless q/qp ordinate at each time step. By definition a unit hydrograph represents one unit (1 in or 1 mm) of runoff; scaling its ordinates by the actual excess rainfall depth Q gives the storm hydrograph used for design.
Sources: USDA-SCS, TR-55: Urban Hydrology for Small Watersheds (1986), Chapter 3; NRCS National Engineering Handbook, Part 630, Chapter 16.
SCS dimensionless unit hydrograph ordinates
The standard curve that gives the SCS unit hydrograph its shape. Discharge ratio (q/qp) peaks at a time ratio of 1.0 and the curve effectively ends near t/Tp = 5, where the cumulative runoff (Qa/Q) reaches 1.0.
| t / Tp | q / qp | Qa / Q (cumulative) |
|---|---|---|
| 0.0 | 0.000 | 0.000 |
| 0.2 | 0.100 | 0.006 |
| 0.4 | 0.310 | 0.035 |
| 0.6 | 0.660 | 0.107 |
| 0.8 | 0.930 | 0.228 |
| 1.0 | 1.000 | 0.375 |
| 1.2 | 0.930 | 0.522 |
| 1.5 | 0.680 | 0.700 |
| 2.0 | 0.280 | 0.871 |
| 2.6 | 0.107 | 0.953 |
| 3.0 | 0.055 | 0.977 |
| 4.0 | 0.011 | 0.997 |
| 5.0 | 0.000 | 1.000 |
Abridged from the full 32-point table. Source: TR-55 (1986), Exhibit 3-1, and NRCS National Engineering Handbook, Part 630, Chapter 16. About 37.5% of the total runoff volume has passed by the time the peak occurs (t/Tp = 1.0).
Peak rate factor (K) by watershed condition
The peak rate factor controls how sharp the computed peak is. Use 484 (US) / 2.08 (SI) for average conditions and adjust for terrain and storage.
| Watershed condition | K (US, cfs) | K (SI, m³/s) | Effect on peak |
|---|---|---|---|
| Flat / swampy terrain | ~300 | ~1.29 | Lower, broader peak |
| Standard / average conditions | 484 | 2.08 | Reference value |
| Steep terrain | ~600 | ~2.58 | Higher, sharper peak |
Source: TR-55 (1986), Chapter 3. The standard K = 484 corresponds to a time base of about 5 × Tp; the factor decreases for flatter, storage-heavy watersheds and increases for steep, fast-responding ones.
Worked example
A 1.0 mi² watershed with a time of concentration of 1.0 hour and 2.0 inches of excess rainfall (US units, standard K = 484):
- Lag time = 0.6 × Tc = 0.6 × 1.0 = 0.6 hr
- Unit duration = Tc / 5 = 1.0 / 5 = 0.2 hr
- Time to peak = D/2 + Tlag = 0.2/2 + 0.6 = 0.7 hr
- Peak discharge = 484 × 1.0 × 2.0 / 0.7 ≈ 1,383 cfs
- Time base = 5 × Tp = 5 × 0.7 = 3.5 hr
- Runoff volume = 2.0 in × 1.0 mi² × 53.33 ≈ 107 acre-ft
Matches the TR-55 Chapter 3 verification case used by this calculator.
Frequently asked questions
What is the SCS (NRCS) dimensionless unit hydrograph?
It is a synthetic unit hydrograph developed by the Soil Conservation Service (now NRCS) from averaging the hydrographs of many natural watersheds. The shape is expressed in dimensionless form as discharge ratio (q/qp) versus time ratio (t/Tp), so it can be scaled by the peak discharge and time to peak of any watershed. Scaling it by the storm runoff depth produces the storm runoff hydrograph. The method is documented in TR-55 (1986), Chapter 3 and the NRCS National Engineering Handbook, Part 630, Chapter 16.
How is peak discharge calculated?
Peak discharge uses qp = K × A × Q / Tp. In US customary units qp is in cfs with A in square miles, Q (excess rainfall/runoff depth) in inches, Tp in hours, and the peak rate factor K = 484 for average watersheds. In SI units qp is in m³/s with A in km², Q in mm, and K = 2.08. For example, a 1 mi² watershed with Tc = 1.0 hr produces Tlag = 0.6 hr, D = Tc/5 = 0.2 hr, Tp = D/2 + Tlag = 0.7 hr, so for Q = 2 in: qp = 484 × 1.0 × 2.0 / 0.7 ≈ 1,383 cfs.
What is the peak rate factor (K) and when should I change it?
The peak rate factor (also called the unit-hydrograph constant) reflects how quickly a watershed concentrates runoff. The standard value is K = 484 (US) or 2.08 (SI), which corresponds to a time base of about 5 times the time to peak. Use a lower value — around 300 (US) for very flat, swampy, or heavily storage-attenuated watersheds, and a higher value — around 600 (US) for steep terrain that produces a sharper, faster peak. Lowering K reduces the computed peak discharge and broadens the hydrograph.
What are the limits of the SCS unit hydrograph method?
The method is best suited to watersheds up to about 2,000 mi² (5,000 km²). It assumes a single-peaked response, a hydrograph shape that stays similar across storm magnitudes, uniform excess rainfall over the watershed, and no baseflow. It can under-represent watersheds with significant internal storage, highly variable land use or soils, extensive storm-sewer networks, or snowmelt-driven runoff, and it cannot produce multi-peaked hydrographs. Treat results as planning-level estimates and verify against local design standards.
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Last verified: February 2026