Manning's Equation Calculator
Open-channel discharge from Manning's roughness, cross-section area, hydraulic radius, and channel slope. Used for natural channels, lined channels, storm sewers flowing partial, and open conduits in general.
Defaults shown are a typical concrete-lined trapezoidal storm channel. Adjust to match your section.
How to use this calculator
Manning's equation is the standard for steady, uniform flow in an open channel. Enter the channel's roughness coefficient, the cross-sectional area of flow, the hydraulic radius, and the friction slope. The calculator returns the mean velocity and total discharge.
For uniform flow, the friction slope equals the channel bed slope. For gradually varied flow, the friction slope is approximated by the bed slope but the depth varies — use a step method (standard step or HEC-RAS) for a real solution. This calculator is for the uniform-flow case only.
Choosing Manning's n
The roughness coefficient is the most uncertain parameter in the equation. Common values:
- Smooth concrete or PVC: 0.011–0.013
- Trowel-finished concrete: 0.013
- Corrugated metal pipe: 0.024
- Earth, clean and straight: 0.022–0.030
- Earth, weedy with stones: 0.030–0.040
- Mountain stream with cobbles: 0.040–0.070
Chow's Open-Channel Hydraulics (1959) Table 5-6 has the canonical reference list. For natural channels, allow a range and run the calculation at both endpoints to see how sensitive your design is.
Hydraulic radius
The hydraulic radius is the cross-sectional area of flow divided by the wetted perimeter. For a wide rectangular channel where width ≫ depth, R ≈ depth. For a circular pipe flowing full, R = D/4. For partial-flow circular pipes, R varies with depth — see Brater & King's tables or compute geometrically.
Why the 1.486 factor?
Manning's original equation is dimensionally non-homogeneous. The coefficient k = 1.486 in US customary units (= 1 m¹ᐟ³/s converted to ft¹ᐟ³/s) preserves the SI form. In SI units, k = 1 and the equation reads V = (1/n)R^(2/3)S^(1/2). Different texts use different presentations; the math is the same.
Reference: Chow, V.T. (1959). Open-Channel Hydraulics. McGraw-Hill. The original publication is Manning, R. (1891). "On the flow of water in open channels and pipes." Trans. Inst. Civil Engrs. Ireland, 20, 161–207.