TR-55 Calculator

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Estimate peak runoff from small urban and suburban watersheds using the USDA/NRCS Technical Release 55 graphical peak discharge method. This guide covers the Curve Number runoff foundation, hydrologic soil groups, SCS rainfall distributions, and the step-by-step peak discharge calculation — with a worked suburban example.

Overview

The TR-55 Calculator implements the USDA/NRCS Technical Release 55 graphical peak discharge method for estimating peak runoff from small watersheds. Originally published in 1986 (second edition) by the Natural Resources Conservation Service (formerly the Soil Conservation Service), TR-55 remains one of the most widely used methods for peak discharge estimation worldwide, particularly in stormwater and small-structure design.

The method combines the SCS Curve Number runoff equation with unit peak discharge data derived from TR-20 (Computer Program for Project Formulation Hydrology) to produce peak discharge estimates for ungauged watersheds. It is applicable to watersheds where the time of concentration ($T_c$) is between 0.1 and 10 hours and the drainage area is small enough that a single, uniform rainfall distribution can be assumed.

When to use TR-55

TR-55 is best suited for estimating peak discharges from small, ungauged watersheds where a full hydrograph is not required. It is commonly used in preliminary stormwater management design, culvert sizing, minor bridge hydrology, and small dam spillway design.

Getting started

To estimate peak discharge using the TR-55 method, follow these steps:

1. Navigate to the TR-55 Calculator from the Tools menu or dashboard.
2. Enter your watershed parameters: drainage area, curve number, time of concentration, 24-hour rainfall depth, rainfall distribution type, and pond/swamp adjustment (if applicable).
3. Click Calculate to generate the peak discharge estimate.
4. Review the results including peak discharge, runoff depth, and intermediate values (S, $I_a$, $I_a/P$, $q_u$).

Quick start

If you are unsure about the curve number for your watershed, refer to the CN reference table in the Curve Number section below. For most general-purpose international applications — including South Africa — use the Type II rainfall distribution.

NRCS Curve Number foundations

The TR-55 method rests on the NRCS (SCS) Curve Number rainfall-runoff relation, one of the most widely used empirical models in applied hydrology. It assumes that for a given storm, the ratio of actual retention to potential maximum retention equals the ratio of actual runoff to maximum potential runoff after the initial abstraction. This yields the familiar rainfall-runoff equation:

$$Q \;=\; \frac{(P - I_a)^2}{P - I_a + S} \qquad \text{for } P > I_a$$

NRCS rainfall-runoff relation

where $Q$ is the direct runoff depth, $P$ is the 24-hour rainfall depth, $I_a$ is the initial abstraction, and $S$ is the potential maximum retention. If $P \leq I_a$, then $Q = 0$ (no runoff).

The initial abstraction is taken as a fixed fraction of $S$ — the NRCS standard assumption is:

$$I_a \;=\; 0.2 \, S$$

Initial abstraction relation

The potential maximum retention $S$ is related to the dimensionless Curve Number $CN$ by:

$$S \;=\; \frac{1000}{CN} - 10$$

Retention-to-Curve-Number relation (S in inches)

For $S$ in millimetres, the equivalent form is $S = 25400/CN - 254$. The Curve Number itself ranges from 30 (very low runoff potential) to 98 (nearly impervious) and encapsulates the combined effect of soil type, land cover, land treatment, hydrologic condition, and antecedent moisture.

See the full SCS Method guide for the theoretical development of the curve number, including the dimensional assumptions and empirical basis for the $I_a = 0.2S$ relationship.

Hydrologic soil groups

The NRCS classifies soils into four Hydrologic Soil Groups (HSG) based on infiltration capacity under bare-soil, fully-wetted conditions. The HSG largely controls the CN value for a given land cover.

HSG	Infiltration when wet	Typical soils
A	High (> 7.6 mm/hr)	Deep well-drained sands, gravels, loamy sands
B	Moderate (3.8 – 7.6 mm/hr)	Shallow loess, sandy loams, fine-textured sands
C	Slow (1.3 – 3.8 mm/hr)	Clay loams, shallow sandy loams, soils with high clay content
D	Very slow (< 1.3 mm/hr)	Clays, soils with permanent high water table, shallow soils over bedrock

Group A has the highest infiltration capacity (lowest runoff potential) and Group D the lowest (highest runoff potential). For a fixed land use, moving from HSG A to HSG D can increase the CN by 30 – 40 points.

Finding HSG values

In South Africa, hydrologic soil group mapping is available from the Agricultural Research Council’s soil database and the Terrain Morphological Unit Data (TMU) series. For US sites, the USDA Web Soil Survey returns HSG directly for any polygon. When in doubt on a mixed profile, assign the more conservative (higher-CN) group for design.

Antecedent runoff condition (ARC)

The standard tabulated CN values assume Antecedent Runoff Condition II (ARC II) — an average moisture state representative of annual floods. In real storms, the wetness of the catchment at the onset of rainfall can shift the effective CN significantly. The NRCS recognises three conditions:

• ARC I (dry): 5-day antecedent rainfall < 35 mm (growing season) or < 12 mm (dormant). Reduces effective CN.
• ARC II (average): 5-day antecedent rainfall 35 – 53 mm (growing) or 12 – 28 mm (dormant). This is the standard tabulated value.
• ARC III (wet): 5-day antecedent rainfall > 53 mm (growing) or > 28 mm (dormant). Increases effective CN — near-saturated soils.

Approximate conversions between conditions (in terms of CN):

$$CN_{\mathrm{I}} \;=\; \frac{4.2 \, CN_{\mathrm{II}}}{10 - 0.058 \, CN_{\mathrm{II}}} \qquad CN_{\mathrm{III}} \;=\; \frac{23 \, CN_{\mathrm{II}}}{10 + 0.13 \, CN_{\mathrm{II}}}$$

ARC conversions (Chow, Maidment & Mays, 1988)

For most design applications — including TR-55 itself — the ARC II value is used directly. Converting to ARC I or III is reserved for event-based hydrograph simulation or for calibrating against measured events of known antecedent state.

Input parameters

The TR-55 method requires six input parameters. Each is described in detail below.

Drainage area

The drainage area ($A_m$) is the total contributing area of the watershed upstream of the point where peak discharge is being estimated, typically in km² (SI) or mi² (US customary). It can be determined from topographic maps, GIS analysis, or the HydroDesign Watershed Delineation tool.

Curve Number (CN)

The Curve Number (CN) is a dimensionless parameter that represents the runoff potential of a watershed based on its soil type, land use, land treatment, hydrologic condition, and antecedent moisture. Values range from 30 (very low runoff potential) to 98 (nearly impervious), with higher values producing more runoff.

The following reference table gives representative CN values (ARC II) for common urban and rural land uses across the four hydrologic soil groups. Values are taken from TR-55 Tables 2-2a/b (1986 second edition).

Land use / cover description	HSG A	HSG B	HSG C	HSG D
Open space (lawns, parks) — poor condition	68	79	86	89
Open space (lawns, parks) — fair condition	49	69	79	84
Open space (lawns, parks) — good condition	39	61	74	80
Impervious: paved parking, rooftops, driveways	98	98	98	98
Paved streets with curbs and storm sewers	98	98	98	98
Gravel roads / unpaved surfaces	76	85	89	91
Residential — 1/8 acre lots (65% impervious)	77	85	90	92
Residential — 1/4 acre lots (38% impervious)	61	75	83	87
Residential — 1/2 acre lots (25% impervious)	54	70	80	85
Residential — 1 acre lots (20% impervious)	51	68	79	84
Residential — 2 acre lots (12% impervious)	46	65	77	82
Commercial / business (85% impervious)	89	92	94	95
Industrial (72% impervious)	81	88	91	93
Row crops — straight row, good condition	67	78	85	89
Small grain — straight row, good condition	63	75	83	87
Pasture / range — good condition (> 75% cover)	39	61	74	80
Pasture / range — fair condition (50 – 75%)	49	69	79	84
Meadow — continuous grass, not grazed	30	58	71	78
Woods — good condition (dense cover, deep litter)	30	55	70	77
Woods — fair condition	36	60	73	79
Farmsteads — buildings, lanes, surrounds	59	74	82	86

Composite Curve Number

For watersheds with mixed land uses, compute a weighted (composite) CN as the area-weighted average of the individual CN values: $CN_{\text{comp}} = \sum(CN_i \cdot A_i) / \sum A_i$. Caution is warranted if the watershed contains a large fraction of connected impervious area (DCIA) — TR-55 Figure 2-3/2-4 provides adjusted composite CN procedures in that case.

Time of concentration ($T_c$)

The time of concentration ($T_c$) is the time required for runoff to travel from the hydraulically most distant point in the watershed to the outlet. It is measured in hours and must lie between 0.1 and 10 hours for the TR-55 graphical method to be valid.

$T_c$ is typically computed as the sum of travel times for three flow segments — sheet flow, shallow concentrated flow, and channel flow — following the procedures in TR-55 Chapter 3. The HydroDesign Tc Calculator supports six methods including the NRCS lag equation, Kirpich, FAA, Kerby, the SA SCS (SANRAL) method, and the FHWA 3-component segmented approach.

Tc limits

If your computed $T_c$ falls outside 0.1 – 10 hours, the TR-55 graphical method does not apply. Use the SCS Unit Hydrograph method, TR-20, or a continuous hydrologic model (e.g. HEC-HMS) instead.

24-hour rainfall depth

The 24-hour rainfall depth ($P$) is the design storm depth in inches or millimetres for the desired return period (e.g. 1:10, 1:25, 1:50, 1:100 year). This value comes from local rainfall frequency atlases, IDF curves, or the HydroDesign Design Rainfall tool, which provides point rainfall depths for 23 durations and 7 return periods across South Africa.

Units

The original TR-55 formulation uses inches for rainfall and square miles for area. Ensure inputs are consistent with the unit system selected in the calculator — the tool handles conversions automatically when metric inputs are supplied.

Rainfall distribution type

The NRCS defines four standard 24-hour synthetic rainfall distributions that describe how rainfall intensity is distributed in time within a 24-hour design storm. Each distribution was derived to envelope the sub-daily intensities (5 min to 24 hr) implied by NOAA Atlas 2 / TP-40 IDF curves in the respective climate region.

Type	Regional applicability (US)	Shape / character
I	Hawaii, coastal Alaska, coastal California	Gentle; lower peak, spread over longer period
IA	Pacific Northwest (coastal OR, WA)	Lowest peak — rainfall nearly uniform over 24 hr
II	Most of the continental United States; general international use	Sharp, high-intensity burst near the middle of the storm
III	Gulf of Mexico and Atlantic coastal areas	Broader peak than Type II; higher early- and late-storm fractions

Regional map (US): TR-55 Figure B-2 shows Type IA covering coastal WA/OR, Type I a narrow Pacific corridor, Type III along the Gulf and South Atlantic coasts (FL, coastal LA, MS, AL, GA, SC, NC), and Type II covering the remainder of the continental US — the Midwest, Plains, Rockies, Southwest, and Northeast.

Type II for South Africa and most international use

For most South African watersheds — and for general international application where no local synthetic distribution is available — Type II is the default recommendation. It best represents the convective thunderstorm pattern that dominates the summer rainfall region and matches the intensity envelope of local IDF curves.

Pond and swamp adjustment ($F_p$)

The pond and swamp adjustment factor ($F_p$) accounts for the attenuation effect of ponds, wetlands, and swamps scattered throughout the watershed. It is expressed as the percentage of the watershed area covered by ponds or swamps, ranging from 0 % to 5 %. $F_p$ reduces the peak discharge to reflect temporary storage.

Pond / swamp area (% of watershed)	$F_p$ factor
0.0	1.00
0.2	0.97
1.0	0.87
3.0	0.75
5.0	0.72

Ponds at the outlet do not count

Only apply $F_p$ when ponds or swamps are distributed throughout the watershed, not concentrated at or near the outlet. Ponds located entirely at the outlet should be analysed separately by reservoir routing, not lumped into $F_p$.

Calculation method

The TR-55 graphical peak discharge method follows a step-by-step procedure to convert 24-hour rainfall into a peak discharge. The six computational steps are outlined below.

Step 1 — Potential maximum retention (S)

$$S \;=\; \frac{1000}{CN} - 10$$

Retention from Curve Number (S in inches)

$S$ represents the maximum depth of rainfall the watershed can absorb after runoff begins.

Step 2 — Initial abstraction ($I_a$)

$$I_a \;=\; 0.2 \, S$$

Initial abstraction

$I_a$ accounts for all rainfall losses before runoff begins — interception, infiltration, and surface depression storage. The standard NRCS assumption is $I_a = 0.2\,S$.

Step 3 — Runoff depth (Q)

$$Q \;=\; \frac{(P - I_a)^2}{P - I_a + S}$$

NRCS runoff equation

Where $P$ is the 24-hour design rainfall depth. If $P \leq I_a$, then $Q = 0$ (no runoff).

Step 4 — Unit peak discharge ($q_u$)

$q_u$ is the unit peak discharge — the peak flow per unit area per unit runoff depth, in csm/in (cubic feet per second per square mile per inch of runoff). It is read from TR-55 Exhibit 4 (one chart per rainfall type) as a function of $T_c$ and the ratio $I_a/P$:

$$\log_{10}(q_u) \;=\; C_0 + C_1 \log_{10}(T_c) + C_2 \, [\log_{10}(T_c)]^2$$

Unit peak discharge (polynomial fit to TR-55 Exhibit 4)

The coefficients $C_0$, $C_1$, $C_2$ depend on the rainfall distribution type and the $I_a/P$ ratio. The following table reproduces the TR-55 Table 4-1 coefficients for Type II at representative $I_a/P$ values; the calculator interpolates between adjacent rows.

$I_a/P$	$C_0$	$C_1$	$C_2$
0.10	2.55323	-0.61512	-0.16403
0.30	2.46532	-0.62257	-0.11657
0.35	2.41896	-0.61594	-0.08820
0.40	2.36409	-0.59857	-0.05621
0.45	2.29238	-0.57005	-0.02281
0.50	2.20282	-0.51599	-0.01259

$I_a/P$ limits

Table 4-1 is defined for $0.10 \leq I_a/P \leq 0.50$. If your computed $I_a/P$ falls outside this range, use the limiting value (0.10 or 0.50) with a cautionary note — results become less reliable at the extremes.

Step 5 — Pond / swamp adjustment ($F_p$)

$F_p$ is read from the pond-and-swamp adjustment table (see Pond/swamp adjustment) based on the percentage of watershed area covered by ponds or swamps distributed through the catchment. If none are present, $F_p = 1.00$.

Step 6 — Peak discharge ($q_p$)

$$q_p \;=\; q_u \cdot A_m \cdot Q \cdot F_p$$

TR-55 peak discharge equation

where $q_p$ is the peak discharge (cfs or m³/s), $q_u$ is the unit peak discharge from Step 4, $A_m$ is the drainage area, $Q$ is the runoff depth from Step 3, and $F_p$ is the pond/swamp adjustment from Step 5.

Interpreting results

The calculator produces the following outputs:

• Peak discharge $q_p$ (m³/s or cfs): The estimated peak flow rate at the watershed outlet for the given design storm. Primary output used for infrastructure sizing.
• Runoff depth $Q$ (mm or in): Depth of direct runoff generated by the design storm. Typical values range from a few mm for low-CN watersheds with small storms to values approaching the rainfall depth for highly impervious areas.
• Initial abstraction $I_a$: The rainfall captured before runoff begins.
• $I_a/P$ ratio: Check that this lies within 0.10 – 0.50 (Table 4-1 applicability range).
• Potential maximum retention $S$: Indicates overall catchment absorption capacity.
• Unit peak discharge $q_u$: Useful intermediate for verification.

Verify reasonableness

Always compare TR-55 results with independent methods (Rational, SCS Unit Hydrograph, regional regression) for critical designs. If $Q < 0.5$ in (about 13 mm), or if $I_a/P$ falls outside 0.10 – 0.50, the results are less reliable.

Worked example — small suburban catchment

A complete TR-55 calculation for a small suburban watershed draining to a proposed culvert crossing.

Given information

• Drainage area: $A_m = 0.60$ km² (0.2317 mi²)
• Land use: Residential, 1/4-acre lots on Hydrologic Soil Group B → $CN = 75$
• Time of concentration: $T_c = 0.5$ hr (computed using the NRCS lag method)
• Design return period: 1:25 year
• 24-hour rainfall depth: $P = 95$ mm (3.74 in) from the local IDF atlas
• Rainfall distribution: Type II
• Pond / swamp area: 0 % → $F_p = 1.00$

Step 1 — Potential maximum retention

$$S = \frac{1000}{75} - 10 = 13.33 - 10 = 3.33 \text{ in} = 84.7 \text{ mm}$$

Step 2 — Initial abstraction

$$I_a = 0.2 \times 3.33 = 0.667 \text{ in} = 16.9 \text{ mm}$$

Step 3 — Runoff depth

$$Q = \frac{(3.74 - 0.667)^2}{3.74 - 0.667 + 3.33} = \frac{(3.073)^2}{6.40} = \frac{9.44}{6.40} = 1.476 \text{ in} = 37.5 \text{ mm}$$

Step 4 — Unit peak discharge

$I_a / P = 0.667 / 3.74 = 0.178$. From Table 4-1 (Type II, interpolating between the 0.10 and 0.30 rows):

• At $I_a/P = 0.178$: $C_0 \approx 2.52$, $C_1 \approx -0.618$, $C_2 \approx -0.146$
• $\log_{10}(T_c) = \log_{10}(0.5) = -0.301$
• $\log_{10}(q_u) = 2.52 + (-0.618)(-0.301) + (-0.146)(-0.301)^2 = 2.52 + 0.186 - 0.0132 = 2.693$
• $q_u = 10^{2.693} \approx 493$ csm/in

Step 5 — Pond / swamp adjustment

$F_p = 1.00$ (no ponds or swamps).

Step 6 — Peak discharge

In US customary units:

$$q_p = q_u \cdot A_m \cdot Q \cdot F_p = 493 \times 0.2317 \times 1.476 \times 1.00 \approx 168.6 \text{ cfs}$$

Converting to SI (1 cfs = 0.02832 m³/s):

$$q_p \approx 168.6 \times 0.02832 \approx \boxed{4.77 \ \mathrm{m^3/s}}$$

Interpretation. The estimated 1:25 year peak discharge at the proposed culvert is ~4.8 m³/s. This value would be used to size the culvert opening together with an appropriate headwater allowance and freeboard per the applicable road drainage standard.

Sensitivity check

Increasing the CN from 75 to 80 (HSG B → borderline C) raises $Q$ from 37.5 to 49.0 mm — a 31 % increase in runoff depth, which flows directly through to the peak. CN uncertainty is typically the dominant source of error in TR-55; always check sensitivity for critical designs.

Limitations

TR-55 is a widely accepted, practical method — but it has important limitations:

• Peak discharge only: The graphical method yields only the peak, not a full hydrograph. For pond routing or flood-inundation mapping, use the SCS Unit Hydrograph method or TR-20 instead.
• $T_c$ range: Must lie between 0.1 and 10 hours. Shorter or longer $T_c$ values fall outside the unit-peak tabulation.
• Catchment area: Generally applicable to watersheds smaller than ~25 km² (~10 mi²). Larger basins violate the uniform-rainfall assumption.
• Low runoff depth: Results degrade when $Q < 0.5$ in (~13 mm); small CN errors are amplified at low runoff depths.
• Extreme CN values: The CN method is least reliable for $CN < 40$ and $CN > 95$. The $I_a = 0.2\,S$ relation has been shown to overestimate initial losses at low CN and underestimate them at very high CN.
• $I_a/P$ range: Table 4-1 coefficients are defined only for $0.10 \leq I_a/P \leq 0.50$.
• Uniform rainfall: Rainfall assumed spatially uniform. Not valid for elongated or very large catchments.
• Single sub-area only: The graphical method assumes a single homogeneous watershed. For heterogeneous basins, consider the TR-55 tabular method (Chapter 5), the SCS Unit Hydrograph, or a full hydrologic model.

Not for channel routing

The graphical method (TR-55 Chapter 4, implemented here) does not account for channel or reservoir routing. If in-stream storage or routing effects are significant, use the tabular method (TR-55 Chapter 5) or a hydrologic model such as HEC-HMS.

See also

• SCS Method — Full SCS Unit Hydrograph approach, including hydrograph generation
• Tc Calculator — Compute time of concentration with six supported methods
• Design Rainfall — 24-hour rainfall depths by return period
• Rational Method — Alternative peak-only method for very small urban catchments
• Watershed Delineation — Automated drainage area extraction

References

• USDA Natural Resources Conservation Service. (1986). Urban Hydrology for Small Watersheds — Technical Release 55 (TR-55), 2nd Edition. United States Department of Agriculture, Washington D.C., June 1986.
• USDA Natural Resources Conservation Service. National Engineering Handbook, Part 630 — Hydrology, Chapter 9: Hydrologic Soil-Cover Complexes. United States Department of Agriculture.
• USDA Natural Resources Conservation Service. National Engineering Handbook, Part 630 — Hydrology, Chapter 10: Estimation of Direct Runoff from Storm Rainfall. United States Department of Agriculture.
• Chow, V.T., Maidment, D.R. & Mays, L.W. (1988). Applied Hydrology. McGraw-Hill, New York. Chapter 5 — Hydrologic Processes; Chapter 15 — Hydrologic Statistics.
• SANRAL. (2013). Drainage Manual (6th ed.). South African National Roads Agency, Pretoria. Chapter 3 — Hydrology.

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