What This Solves
Generates a simplified triangular unit hydrograph based on SCS/NRCS methodology, providing peak flow rate, time to peak, and recession time for a watershed.
Best Used When
- You need a quick estimate of peak flow and hydrograph shape for a small to medium watershed
- You want a simplified hydrograph for preliminary detention sizing without full curvilinear analysis
- You are performing hand calculations or need a simple hydrograph shape for routing
Do NOT Use When
- You need the more detailed curvilinear SCS dimensionless unit hydrograph — Use SCS Unit Hydrograph Calculator
- You need to convolve the unit hydrograph with a rainfall distribution — Use Hydrograph Convolution Calculator
Key Assumptions
- The hydrograph is approximated as a triangle with a rising limb, peak, and falling limb
- Time to peak equals 0.5 * storm duration + 0.6 * time of concentration
- The recession limb duration is 1.67 times the time to peak
- Total volume under the triangle equals the runoff depth times the drainage area
- The peak rate factor is 484 (standard SCS assumption for average watershed conditions)
Input Quality Notes
Time of concentration has the largest effect on peak flow. Verify Tc using appropriate methods for your watershed size and land use. The peak rate factor of 484 can be adjusted for flat or steep terrain.
Generate a simplified SCS (NRCS) triangular unit hydrograph from a watershed's drainage area, time of concentration and runoff depth. The calculator returns the peak discharge, time to peak, time base and runoff volume, plus the full set of hydrograph ordinates for quick runoff and detention analysis.
How the SCS triangular hydrograph works
The triangular unit hydrograph replaces the curved NRCS dimensionless unit hydrograph with a single triangle that has the same peak, timing and volume. The geometry is built from the watershed's time of concentration (Tc) using a fixed set of timing ratios, then the peak discharge is scaled to the runoff volume.
The governing relationships (per TR-55 and NEH Part 630, Chapter 16) are:
- Lag time: Tlag = 0.6 × Tc
- Unit (excess) rainfall duration: D ≈ Tc / 5 (default)
- Time to peak: Tp = D / 2 + Tlag
- Recession time: Tr = 1.67 × Tp
- Time base: Tb = Tp + Tr = 2.67 × Tp
- Peak discharge: qp = (K × A × Q) / Tp
- Runoff volume (triangle area): V = ½ × qp × Tb
The discharge at any time on the triangle is found by linear interpolation:
- Rising limb (0 ≤ t ≤ Tp): q = qp × (t / Tp)
- Falling limb (Tp < t ≤ Tb): q = qp × (Tb − t) / Tr
| Symbol | Variable | US units | SI units |
|---|---|---|---|
| A | Drainage (watershed) area | mi² | km² |
| Q | Excess rainfall (runoff depth) | in | mm |
| Tc | Time of concentration | hr | hr |
| Tp | Time to peak | hr | hr |
| Tb | Time base (duration) | hr | hr |
| qp | Peak discharge | cfs | m³/s |
| K | Peak rate factor (shape constant) | 484 | 2.08 |
Methodology: USDA NRCS TR-55 (1986), Urban Hydrology for Small Watersheds, and NEH Part 630 Hydrology, Chapter 16 (2004). K bundles the hydrograph shape and a unit conversion, so its value differs between US customary and SI units.
SCS triangular hydrograph constants
Fixed geometry ratios and peak rate factors used by the triangular unit hydrograph. These are the standard NRCS values applied by this calculator.
| Parameter | Relationship / value | Notes |
|---|---|---|
| Lag ratio | Tlag = 0.6 × Tc | Watershed lag from time of concentration |
| Recession ratio | Tr / Tp = 1.67 | Falling limb is longer than the rising limb |
| Time base ratio | Tb / Tp = 2.67 | Tb = Tp + Tr |
| Peak rate factor K (US) | 484 | A in mi², Q in in → qp in cfs |
| Peak rate factor K (SI) | 2.08 | A in km², Q in mm → qp in m³/s |
| Default unit duration D | ≈ Tc / 5 | Override in advanced parameters if needed |
K = 484 is the standard value for average watersheds. Flat or storaged basins use lower factors (roughly 100–300); steep, well-drained basins can justify higher factors (up to about 600).
Worked example
A 1 mi² watershed with a time of concentration Tc = 1.0 hr and 1.0 inch of excess rainfall (runoff), US customary units:
- Lag time = 0.6 × 1.0 = 0.6 hr
- Unit duration D ≈ Tc / 5 = 0.2 hr
- Time to peak Tp = 0.2 / 2 + 0.6 = 0.7 hr
- Time base Tb = 2.67 × 0.7 ≈ 1.87 hr
- Peak discharge qp = 484 × 1.0 × 1.0 / 0.7 ≈ 691 cfs
This matches the calculator's built-in verification case (≈691 cfs). Adjusting D, K or Tc changes Tp and therefore the peak.
Frequently asked questions
What is the SCS triangular unit hydrograph?
It is a simplified, straight-sided approximation of the NRCS (SCS) dimensionless unit hydrograph. The runoff response is represented as a triangle: a linear rising limb from zero to the peak discharge at the time to peak (Tp), then a linear falling limb back to zero at the time base (Tb = 2.67 × Tp). It preserves the same peak discharge, time to peak and total runoff volume as the curved dimensionless hydrograph, which makes it convenient for hand calculations and quick estimates.
How is the peak discharge calculated?
Peak discharge uses qp = K × A × Q / Tp. In US customary units K = 484 with drainage area A in square miles and excess rainfall (runoff depth) Q in inches, giving qp in cubic feet per second (cfs). In SI units K = 2.08 with A in square kilometres and Q in millimetres, giving qp in cubic metres per second (m³/s). The peak rate factor K embeds the assumed hydrograph shape and a unit conversion, so it changes with the unit system.
What does the peak rate factor (K = 484) mean, and can I change it?
The peak rate factor reflects how quickly runoff concentrates and is tied to the shape of the dimensionless unit hydrograph (the standard ratio of 37.5% of volume under the rising limb). K = 484 is the standard NRCS value for average watersheds. Flat, swampy, or heavily-storaged basins use lower values (down to roughly 100–300), while steep, well-drained basins can justify higher values (up to about 600). This calculator lets you override K in the advanced parameters when local guidance calls for it.
How are time to peak and time base determined?
Lag time is estimated as Tlag = 0.6 × Tc, where Tc is the time of concentration. The unit (excess rainfall) duration D defaults to about Tc/5. Time to peak is Tp = D/2 + Tlag. The triangular geometry then fixes the recession time as Tr = 1.67 × Tp and the time base as Tb = Tp + Tr = 2.67 × Tp.
When should I use the triangular hydrograph instead of the full curvilinear one?
Use the triangular form for preliminary peak-flow estimates, simple detention sizing, teaching, and situations where computational simplicity matters. Switch to the full SCS dimensionless (curvilinear) unit hydrograph or a model such as HEC-HMS when the detailed hydrograph shape, early recession flows, storage routing, or multi-peaked responses are important.
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Last verified: February 2026