Set catchment inputs for the Rational method and conveyance geometry — circular pipe, rectangular, triangular or trapezoidal channel — to calculate peak runoff, flow velocity and capacity via Manning's equation, and check conveyance capacity against design-storm demand, in metric or US customary units.
Choose metric or US customary — all fields and formulas below update to match
Peak runoff discharge feeding the pipe or channel
Pipe or open channel — choose a cross-section
Tap to browse roughness values
Circular pipe
Rational-method design-storm check
This tool does the two calculations that sit at the heart of gravity drainage design, one after the other: it works out how much stormwater a catchment will deliver, then works out whether the pipe or channel you propose can carry it. It is built for highway, drainage and civil engineers sizing culverts, roadside ditches, storm sewers and outfall channels.
Peak flow is estimated as Q = C × I × A, where C is the
runoff coefficient, I the design rainfall intensity and A the catchment area. In
metric working the result is divided by 360 so that mm/hr and hectares yield
m³/s. The runoff coefficient runs from about 0.10 for flat woodland to 0.95 for
asphalt and roofs; the terrain presets set a representative value if you do not have
a measured one. The Rational method is intended for small catchments, broadly under
80 hectares.
Velocity follows V = (k/n) × R^(2/3) × S^(1/2), with
k = 1 in metric and k = 1.49 in US customary units.
Hydraulic radius is R = A / P — flow area divided by wetted perimeter —
and capacity is then Q = V × A. Manning's n describes boundary
roughness, and because velocity is inversely proportional to it, the value you pick
moves the answer directly. The built-in reference table lists typical values.
The tool compares conveyance capacity against peak runoff and tells you whether the section works for that design storm. If it does not, the levers are a larger diameter or channel, a steeper bed slope, or a smoother lining.
The depth slider sets water depth as a percentage of pipe diameter or channel height, and every hydraulic property is recalculated for that partial depth. This matters in practice: a circular pipe does not reach its maximum discharge when flowing completely full, and gravity drainage is normally designed part-full anyway.
These are steady, uniform-flow screening calculations. They do not model backwater, surcharging, inlet control at culverts, or unsteady hydrographs. Verify against project-specific data and the governing local design standard before relying on the output. For culvert quantities and cost once the size is fixed, see the box culvert quantities calculator.
Manning's equation gives the average velocity of water flowing in a pipe or open
channel under gravity. In metric units it is
V = (1/n) × R^(2/3) × S^(1/2), where V is velocity in m/s,
n is the Manning roughness coefficient, R is the hydraulic radius in metres and S
is the bed slope. In US customary units the constant 1.49 replaces the 1.
Multiplying the velocity by the flow area gives the discharge.
Discharge is velocity multiplied by flow area, Q = V × A. Work
out the flow area and wetted perimeter for the geometry, divide area by wetted
perimeter to get the hydraulic radius, use Manning's equation for velocity, then
multiply back by the area. This calculator does all four steps and shows every
intermediate value.
Hydraulic radius is flow area divided by wetted perimeter, R = A / P.
It represents how efficiently a cross-section carries water: a shape with a large
area relative to the surface in contact with the water has less friction per unit
of flow and therefore a higher velocity. For a circular pipe flowing full, the
hydraulic radius equals one quarter of the diameter.
The Rational method estimates peak flow from a small catchment as
Q = C × I × A, where C is the runoff coefficient, I the
design rainfall intensity and A the catchment area. In metric working the result is
divided by 360 so that mm/hr and hectares give m³/s. It is intended for small
catchments, generally under about 80 hectares.
The runoff coefficient is the proportion of rainfall that becomes surface runoff rather than infiltrating or being intercepted. It ranges from near 0.10 for flat woodland and sandy soils to about 0.95 for asphalt, concrete and roofs. Mixed catchments are handled by area-weighting the individual coefficients, and this tool includes terrain presets that set a representative value.
Manning's n is a roughness coefficient describing how much the boundary resists flow. Typical values are around 0.011–0.013 for smooth concrete and PVC pipe, 0.013–0.017 for corrugated or rough concrete, 0.025–0.035 for earth channels, and 0.05 or more for heavily vegetated watercourses. Because velocity is inversely proportional to n, the value chosen has a direct effect on computed capacity.
Compare the conveyance capacity from Manning's equation against the peak runoff from the Rational method. If capacity exceeds peak runoff the section is adequate for that design storm; if not, increase the diameter or channel dimensions, steepen the slope, or use a smoother lining. This calculator performs the comparison and reports the result directly.
Yes. The water depth slider sets the depth as a percentage of the pipe diameter or channel height, and the flow area, wetted perimeter and hydraulic radius are recalculated for that partial depth. This matters because a circular pipe does not carry its maximum discharge when flowing completely full, and part-full conditions are the normal design case for gravity drainage.
Designing and costing the rest of the same drainage scheme: