Manning's equation gives the flow rate in an open channel — a river, canal, gutter or part-full pipe — from the channel roughness, cross-section area, hydraulic radius and bed slope: Q = (1/n)·A·R2/3·S1/2. This free calculator solves for the flow, area, slope or roughness, and reports the mean velocity too.
Manning's equation (metric form) is Q = (1/n)·A·R2/3·S1/2, where n is the Manning roughness coefficient, A the flow cross-section area, R the hydraulic radius (area divided by wetted perimeter) and S the bed slope. Enter these values and read the discharge Q; the mean velocity follows from v = Q/A. The calculator can also rearrange the formula to solve for the area, the slope or the roughness when the discharge is known.
The roughness coefficient sets the scale of the answer, so choosing it well matters. Typical n values are about 0.013 for a concrete channel and 0.035 for a natural stream, with smoother surfaces giving faster flow. The hydraulic radius captures the channel shape: it is the wetted area divided by the wetted perimeter, and for a wide, shallow flow it is close to the water depth. Keep every quantity in SI units — square metres, metres and a dimensionless slope — and the discharge comes out in cubic metres per second.
Manning's equation assumes steady, uniform flow, meaning the depth and velocity do not change along the reach. For pressurised or energy-based flow problems, reach instead for the Bernoulli equation calculator or the pressure calculator. For definitions of the terms used here, the physics glossary explains hydraulic radius, discharge and slope.
A concrete channel (n = 0.013) has a flow area A = 1 m2, a hydraulic radius R = 0.5 m and a slope S = 0.001. Its discharge is Q = (1/0.013)·1·0.52/3·(0.001)1/2, which works out to about 1.53 m3/s. Dividing by the area gives a mean velocity of about 1.53 m/s. Halving the slope would drop the flow by a factor of the square root of two, showing how gently the discharge responds to bed gradient.
Manning's equation is the workhorse of hydraulic engineering for sizing storm drains, culverts, irrigation canals and river channels, and for flood modelling. Because it is empirical and metric here, the roughness coefficient n carries hidden units, so keep everything in SI to avoid errors. For pressurised pipe flow rather than open channels, see the friction factor calculator.
Manning’s equation is an empirical formula for steady uniform open-channel flow: Q = (1/n) A R^(2/3) S^(1/2), giving discharge from roughness, area, hydraulic radius and slope.
The hydraulic radius is the flow cross-section area divided by the wetted perimeter (the length of channel boundary in contact with the water); for a wide shallow flow it approaches the depth.
A typical Manning roughness n is about 0.011 to 0.013 for smooth concrete, 0.024 for gravel, and 0.03 to 0.05 for natural streams with vegetation.
This calculator uses the SI (metric) form with the 1/n coefficient; the US customary form multiplies by 1.49 and uses feet.
Manning’s equation is for open-channel (gravity) flow, while the Darcy friction factor handles pressurised pipe flow; both estimate flow resistance.