Formula sheet

Stormwater and Urban Flood Resilience Formula Sheet

Stormwater formulas for runoff, peak flow, detention routing, outlet control, freeboard, inlet blockage, overland flow, pollutant load, reliability, and validation.

Branch: Environmental Engineering
Content: Formula sheet
Updated: Jun 24, 2026
Revision: v1.0.0 · reviewed

This formula sheet collects first-pass calculations used in stormwater and urban flood resilience engineering. Use it to screen runoff volume, rational-method peak flow, detention routing, outlet controls, freeboard, inlet blockage, overland flow, infiltration drawdown, water-quality load, pump reliability, maintenance risk, and validation evidence.

The equations are screening tools. They do not replace local rainfall data, intensity-duration-frequency analysis, hydrologic and hydraulic modelling, surveyed topography, inlet hydraulic methods, geotechnical review, tailwater analysis, public-safety review, water-quality design, emergency planning, permitting, or professional engineering judgement.

Before calculating, state the design boundary: catchment, drainage asset, detention basin, street low point, overland route, pump station, green-infrastructure cell, critical doorway, treatment device, or receiving water. Stormwater calculations are useful only when tied to a storm basis, unit convention, asset condition, exceedance path, uncertainty, and validation record.

Symbols and Basis

Symbol	Meaning	Common unit
$A$	catchment or facility area	$\text{ha}$ or $\text{m}^2$
$P_d$	rainfall depth	$\text{mm}$ or $\text{m}$
$C_r$	runoff coefficient	dimensionless
$Q$	flow rate	$\text{m}^3/\text{s}$
$Q_p$	peak runoff flow	$\text{m}^3/\text{s}$
$i$	rainfall intensity	$\text{mm/h}$
$S$	stored water volume	$\text{m}^3$
$\Delta t$	routing time step	$\text{s}$
$C_d$	orifice discharge coefficient	dimensionless
$A_o$	orifice opening area	$\text{m}^2$
$h$	hydraulic head	$\text{m}$
$C_w$	broad-crested or sharp-crested weir coefficient by convention	varies
$L_w$	weir length	$\text{m}$
$F$	freeboard	$\text{m}$
$B$	blockage factor	dimensionless
$f$	infiltration rate	$\text{m/h}$
$C$	concentration	$\text{mg/L}$
$L_m$	pollutant mass load	$\text{kg/h}$
$A_{pump}$	availability of a pump or component	dimensionless

Use units deliberately. The rational-method coefficient shown below assumes $i$ in $\text{mm/h}$ and $A$ in hectares. If local practice uses different units, use the local conversion.

Runoff Volume

A common runoff-volume screen is:

V_{runoff}=C_rP_dA

where $P_d$ is in metres and $A$ is in square metres.

Mini-Check

A commercial catchment has:

A=12\ \text{ha}=120000\ \text{m}^2

Rainfall depth:

P_d=45\ \text{mm}=0.045\ \text{m}

Runoff coefficient:

C_r=0.72

Runoff volume:

V_{runoff}=0.72(0.045)(120000)=3888\ \text{m}^3

Engineering Comment

The runoff coefficient compresses imperviousness, connection, slope, storage, antecedent moisture, soil and drainage condition into one number. Use the result as a volume screen, not as final proof that a basin, pipe or overflow route is acceptable.

Composite Runoff Coefficient

For subareas:

\displaystyle C_{r,comp}=\frac{\sum C_{r,j}A_j}{\sum A_j}

Mini-Check

Use:

Surface	Area $(\text{ha})$	Runoff coefficient
roofs	$4$	$0.95$
pavement	$6$	$0.85$
landscaped area	$2$	$0.25$

Composite coefficient:

\displaystyle C_{r,comp}=\frac{0.95(4)+0.85(6)+0.25(2)}{4+6+2}

\displaystyle C_{r,comp}=\frac{9.4}{12}=0.783

Engineering Comment

Composite coefficients should distinguish directly connected impervious area from disconnected surfaces. A landscaped strip that drains to soil before reaching an inlet does not behave the same as a roof leader connected directly to a pipe.

Rational-Method Peak Flow

For small catchments using the metric rational-method convention:

Q_p=0.00278C_riA

where $Q_p$ is in $\text{m}^3/\text{s}$ , $i$ is in $\text{mm/h}$ and $A$ is in hectares.

Mini-Check

Use:

C_r=0.65

i=75\ \text{mm/h}

A=18\ \text{ha}

Peak flow:

Q_p=0.00278(0.65)(75)(18)=2.44\ \text{m}^3/\text{s}

Engineering Comment

The method assumes a duration at least as long as the time of concentration and a catchment small enough for the approximation. It is often useful for inlet, local pipe and screening checks, but not for every storage, river, coastal, or large urban catchment problem.

Detention Storage Routing

For a time step:

\Delta S=(Q_{in}-Q_{out})\Delta t

Cumulative storage is:

S_k=\max(0,S_{k-1}+\Delta S_k)

The required storage is the maximum cumulative value during the design event:

S_{req}=\max(S_k)

Mini-Check

Use five intervals of:

\Delta t=900\ \text{s}

with average inflows:

1.2,\ 2.5,\ 3.0,\ 1.4,\ 0.7\ \text{m}^3/\text{s}

and controlled outflow:

Q_{out}=1.0\ \text{m}^3/\text{s}

The net storage increments are:

180,\ 1350,\ 1800,\ 360,\ -270\ \text{m}^3

Cumulative storage values are:

180,\ 1530,\ 3330,\ 3690,\ 3420\ \text{m}^3

Therefore:

S_{req}=3690\ \text{m}^3

Engineering Comment

Storage depends on timing, not only total runoff volume. A basin can receive a large event volume but need less active storage if outflow occurs throughout the event. Conversely, a short high peak can require significant storage even when total rainfall depth is moderate.

Orifice Outlet Control

A first-pass orifice equation is:

Q=C_dA_o\sqrt{2gh}

Solving for area:

\displaystyle A_o=\frac{Q}{C_d\sqrt{2gh}}

Equivalent circular diameter:

\displaystyle D_o=\sqrt{\frac{4A_o}{\pi}}

Mini-Check

Use:

Q=0.90\ \text{m}^3/\text{s}

C_d=0.62

h=1.20\ \text{m}

Area:

\displaystyle A_o=\frac{0.90}{0.62\sqrt{2(9.81)(1.20)}}=0.299\ \text{m}^2

Equivalent diameter:

\displaystyle D_o=\sqrt{\frac{4(0.299)}{\pi}}=0.617\ \text{m}

Engineering Comment

Outlet sizing must check clogging, trash rack behavior, head variation, tailwater, safety, maintenance, sediment, fish or ecological constraints where relevant, and emergency overflow. A single orifice equation is not an operating plan.

Weir Overflow

A common screen for overflow is:

Q=C_wL_wH^{3/2}

where $H$ is head over the weir crest and $C_w$ depends on weir type and units.

Mini-Check

Use:

C_w=1.7

L_w=4.0\ \text{m}

H=0.25\ \text{m}

Then:

Q=1.7(4.0)(0.25)^{3/2}=0.85\ \text{m}^3/\text{s}

Engineering Comment

Overflow should be intentional. The question is not only whether water leaves the basin, but where it goes, whether velocities erode the route, whether people are exposed, and whether the overflow protects embankment integrity.

Freeboard and Uncertainty

Freeboard is:

F=z_{crest}-z_{peak}

Guarded freeboard with water-level uncertainty $U_h$ is:

F_g=F-U_h

Mini-Check

Basin crest elevation:

z_{crest}=102.50\ \text{m}

Modelled peak water level:

z_{peak}=101.65\ \text{m}

Freeboard:

F=102.50-101.65=0.85\ \text{m}

If water-level uncertainty is:

U_h=0.15\ \text{m}

guarded freeboard is:

F_g=0.85-0.15=0.70\ \text{m}

Engineering Comment

Freeboard should be checked after uncertainty, blockage, tailwater, wind setup, settlement, survey error, debris and emergency spillway performance are considered. A small nominal freeboard can disappear in the field.

Inlet Capture With Blockage

For inlets with clean capacity $Q_{clean,j}$ and blockage factor $B_j$ :

Q_{cap,total}=\sum_j Q_{clean,j}(1-B_j)

Bypass flow:

Q_{bypass}=Q_p-Q_{cap,total}

Mini-Check

Four inlets have clean capacity:

Q_{clean}=0.38\ \text{m}^3/\text{s}

Blockage factors are:

0.65,\ 0.45,\ 0.25,\ 0.10

Captured flow:

Q_{cap,total}=0.38(0.35)+0.38(0.55)+0.38(0.75)+0.38(0.90)

Q_{cap,total}=0.969\ \text{m}^3/\text{s}

If peak runoff is:

Q_p=1.40\ \text{m}^3/\text{s}

bypass flow is:

Q_{bypass}=1.40-0.969=0.431\ \text{m}^3/\text{s}

Engineering Comment

Clean inlet capacity is often not the capacity available during a storm. Leaves, sediment, trash, snow, construction debris, ponding geometry, and local grading can reduce capture. Maintenance condition is part of hydraulic capacity.

Overland Ponding Volume

For an excess surface flow lasting $t_p$ :

V_{pond}=Q_{excess}t_p

Excess beyond street storage:

V_{excess}=V_{pond}-S_{street}

Mini-Check

Bypass flow:

Q_{excess}=0.431\ \text{m}^3/\text{s}

Duration:

t_p=18\ \text{min}=1080\ \text{s}

Potential ponding volume:

V_{pond}=0.431(1080)=465\ \text{m}^3

Street storage before a critical flow path activates:

S_{street}=240\ \text{m}^3

Excess volume:

V_{excess}=465-240=225\ \text{m}^3

Engineering Comment

This screen explains whether nuisance water can become critical flooding. If street storage fills, water follows the next low path. That path should be a planned overflow route, not a loading dock, basement, electrical room, transit entrance, or hospital access.

Infiltration Drawdown

If stored volume $V$ drains through infiltration area $A_i$ at rate $f$ :

\displaystyle t_{drawdown}=\frac{V}{fA_i}

where $f$ is in $\text{m/h}$ .

Mini-Check

Stored volume:

V=450\ \text{m}^3

Infiltration rate:

f=12\ \text{mm/h}=0.012\ \text{m/h}

Infiltration area:

A_i=2500\ \text{m}^2

Drawdown time:

\displaystyle t_{drawdown}=\frac{450}{0.012(2500)}=15.0\ \text{h}

Engineering Comment

Infiltration drawdown depends on soil testing, clogging, groundwater separation, underdrains, seasonal conditions, compaction, pretreatment and maintenance. Do not use infiltration where it threatens basements, contaminated soils, unstable slopes, karst, utilities, or high groundwater.

Water-Quality Volume and Pollutant Load

Water-quality runoff volume can be screened as:

V_{wq}=C_rP_{wq}A

For concentration $C$ in $\text{mg/L}$ and flow or volume in $\text{m}^3$ :

\displaystyle M=\frac{CV}{1000}

where $M$ is in kilograms.

Mini-Check

Directly connected impervious area:

A=22\ \text{ha}=220000\ \text{m}^2

Water-quality rainfall depth:

P_{wq}=25\ \text{mm}=0.025\ \text{m}

Runoff coefficient:

C_r=0.85

Water-quality volume:

V_{wq}=0.85(0.025)(220000)=4675\ \text{m}^3

If event mean TSS concentration is:

C=180\ \text{mg/L}

mass load is:

\displaystyle M=\frac{180(4675)}{1000}=841.5\ \text{kg}

Engineering Comment

Water-quality design is not only a concentration target. The mass load depends on volume. A larger runoff volume at moderate concentration can carry more pollutant mass than a small first-flush sample with high concentration.

Pump Availability for Flood Systems

For one repairable pump:

\displaystyle A_{pump}=\frac{MTBF}{MTBF+MTTR}

For two independent parallel pumps where either one can serve:

A_{parallel}=1-(1-A_{pump})^2

Mini-Check

Use:

MTBF=2000\ \text{h}

MTTR=8\ \text{h}

Single-pump availability:

\displaystyle A_{pump}=\frac{2000}{2000+8}=0.9960

Parallel availability:

A_{parallel}=1-(1-0.9960)^2=0.999984

Engineering Comment

Independence is the fragile assumption. Flood pumps often share power, wet well, controls, debris exposure, access, maintenance staff, telemetry and discharge route. Common-cause failure can dominate the real risk.

Maintenance Risk Priority

A simple risk priority number is:

RPN=SOD

where $S$ is severity, $O$ is occurrence, and $D$ is detection rating.

Mini-Check

Before inlet-cleaning and inspection controls:

S=8,\quad O=5,\quad D=4

Then:

RPN=8(5)(4)=160

After added maintenance and sensor review:

S=8,\quad O=2,\quad D=3

Then:

RPN=8(2)(3)=48

Engineering Comment

Severity stays high because flooding a critical opening remains serious. Controls reduce occurrence and improve detection. A lower RPN does not remove the need for planned overland flow and emergency response.

Validation Gates

Use formula results as gates for evidence.

Calculation	Required validation evidence
Runoff volume	catchment boundary, imperviousness, storm basis, rainfall record and coefficient basis
Rational-method peak flow	time of concentration, local intensity data, catchment scale and unit convention
Storage routing	inflow hydrograph, outlet rating, tailwater condition, basin survey and event telemetry
Orifice or weir capacity	measured dimensions, head range, debris protection, tailwater and overflow route
Freeboard	survey datum, peak water level, uncertainty, settlement, wind, blockage and spillway condition
Inlet capture	grate condition, gutter spread, blockage allowance, approach flow and maintenance record
Overland ponding	surveyed low paths, critical openings, street storage, safe overflow route and high-water marks
Infiltration drawdown	field infiltration tests, groundwater separation, clogging control and underdrain configuration
Pollutant load	paired flow and concentration data, event sampling, treatment capacity and receiving-water objective
Pump availability	proof test, backup power, common-cause review, alarm response and maintenance records

Common Mistakes

Common mistakes include:

using total rainfall volume as storage volume without routing outflow;
using the rational method outside its scale and duration assumptions;
sizing only the pipe network while ignoring inlet capture and overland paths;
assuming clean inlet capacity during leaf, sediment, snow or trash loading;
checking freeboard without uncertainty, blockage, tailwater or emergency overflow;
treating green infrastructure as decorative landscaping rather than hydraulic infrastructure;
using infiltration where groundwater, contamination, basements, karst or slope stability make it unsafe;
reporting pollutant concentration without event volume or mass load;
trusting pump redundancy without checking common power, controls, access and debris exposure;
failing to update models after observed flood events.

Engineering Takeaway

Stormwater resilience calculations should answer where water goes when the normal system is exceeded. Runoff and peak flow estimate the demand. Routing and outlet formulas estimate storage behavior. Freeboard, inlet capture and overland-flow checks reveal whether exceedance remains controlled. Water-quality and reliability checks connect flood protection to environmental and operational performance. The engineering result is a validated flood pathway, not just a pipe size.

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