Manning Open-Channel Discharge Calculator

It applies the SI form of Manning's equation and returns both discharge in cubic meters per second and mean velocity in meters per second. Use it for a quick engineering check, comparison of channel alternatives, or repeatable automated calculations when the channel geometry and resistance have already been established.

Prepare hydraulic inputs that describe the same flow section

Start with a cross section and flow condition that can reasonably be treated as steady and uniform. Enter the wetted flow area in square meters, not the total excavated area above the water surface. Hydraulic radius is the wetted area divided by wetted perimeter; it is not generally the same as water depth, although the two can become close in a very wide rectangular channel. Enter bed slope as a dimensionless ratio, such as 0.002 for a drop of two meters over one thousand horizontal meters. The Manning coefficient must represent the channel material, vegetation, irregularity, alignment, and flow condition being evaluated. All four values must describe the same water level and channel reach. Mixing an area from one stage with a hydraulic radius from another produces a numerical answer that has no consistent physical section behind it. This calculator uses SI units throughout, so convert dimensions before calculating rather than attempting to correct the final discharge afterward.

Understand how Manning's equation produces discharge

The calculation uses Q = (1/n) A R^(2/3) S^(1/2), where Q is discharge, n is Manning roughness, A is wetted cross-sectional area, R is hydraulic radius, and S is bed slope. The velocity form is V = (1/n) R^(2/3) S^(1/2), and multiplying that velocity by area gives discharge. Because roughness is in the denominator, a larger coefficient reduces the predicted velocity and flow for otherwise identical geometry. Hydraulic radius has a two-thirds exponent, while slope enters through its square root, so doubling either input does not double discharge. A zero slope produces zero velocity and discharge in this idealized uniform-flow equation. A zero roughness coefficient is mathematically undefined because it would require division by zero, so the calculator returns an input error instead of infinity. Results are rounded to a stable precision for repeatable API and browser output, but that numerical precision should not be mistaken for equal precision in field measurements or the selected roughness coefficient.

Interpret the result and check whether the model applies

Treat the returned discharge as an estimate conditioned on Manning's assumptions, not as a substitute for hydraulic judgment. The equation is commonly used for gravity-driven open-channel flow that is approximately uniform, with a representative energy slope often approximated by the bed slope. It may be unsuitable near controls, transitions, culverts, gates, hydraulic jumps, backwater zones, rapidly varied reaches, or locations where the water surface changes substantially along the reach. Compare the returned mean velocity with acceptable erosion, sedimentation, lining, and safety criteria for the specific channel. Sensitivity checks are especially valuable because Manning roughness is selected rather than measured exactly: run plausible low and high coefficients, and consider alternate stages when area and hydraulic radius vary with depth. Document the geometry source, roughness basis, survey datum, and slope calculation so another reviewer can reproduce the result. The API price is $0.002 per calculation, while the browser version can be used for quick interactive checks with the same deterministic calculation logic.