Manning's Equation Calculator

Manning's equation is an empirical formula for uniform, steady, open-channel flow. It assumes the flow is fully developed and the depth, velocity, and cross-section remain constant along the channel (normal flow).

Velocity: $$v = \frac{1}{n} R_h^{2/3} S^{1/2}$$

Hydraulic radius: $$R_h = \frac{A}{P}$$ where A is the cross-sectional flow area and P is the wetted perimeter. For a wide, shallow channel, R_h ≈ depth.

Common n values: Smooth concrete: 0.012 | Clean earth: 0.022 | Gravel: 0.025 | Natural stream (clean): 0.030 | Natural stream (weeds): 0.050 | Floodplain (heavy brush): 0.10–0.15

The slope S is the energy grade line slope, which equals the bed slope for uniform flow (normal depth). For gradually varied flow, the actual energy slope differs from the bed slope.

A smaller n value (smoother channel) yields higher velocity for the same geometry and slope. Velocity increases with hydraulic radius (larger or more efficient cross-section) and with steeper slope. The 2/3 exponent on R_h means that velocity is less sensitive to changes in depth than to changes in roughness. The discharge Q = vA combines velocity and area effects — doubling the area more than doubles discharge because the larger area also increases R_h.