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.
Manning's n roughness coefficient — full reference table
The roughness coefficient is the most uncertain parameter in the equation; small changes in n produce large changes in computed velocity and depth. Use the design value for the as-built condition; for natural channels, run the calculation at both endpoints of the range.
| Material / surface | n (typical) | n (range) |
|---|---|---|
| PVC, HDPE, smooth plastic pipe | 0.010 | 0.009–0.011 |
| Cast iron, coated | 0.013 | 0.011–0.014 |
| Concrete pipe, smooth wall | 0.012 | 0.011–0.013 |
| Concrete, trowel-finished | 0.013 | 0.011–0.015 |
| Concrete, float-finished | 0.015 | 0.013–0.016 |
| Concrete, unfinished (forms) | 0.017 | 0.015–0.020 |
| Corrugated metal pipe (CMP), 2⅔×½ in. corr. | 0.024 | 0.022–0.027 |
| CMP, 6×2 in. corrugations | 0.030 | 0.027–0.033 |
| Brick, mortared | 0.015 | 0.012–0.018 |
| Asphalt-lined channel | 0.014 | 0.013–0.016 |
| Channel description | n (typical) | n (range) |
|---|---|---|
| Earth, clean, recently completed | 0.018 | 0.016–0.020 |
| Earth, clean, after weathering | 0.022 | 0.020–0.025 |
| Earth, gravelly | 0.025 | 0.022–0.030 |
| Earth, with grass | 0.030 | 0.025–0.035 |
| Earth, dense weeds | 0.035 | 0.030–0.040 |
| Stony bottom, weedy banks | 0.035 | 0.030–0.040 |
| Cobble bottom, clean sides | 0.040 | 0.030–0.050 |
| Natural stream, clean & straight | 0.030 | 0.025–0.033 |
| Natural stream, sluggish, weedy pools | 0.050 | 0.040–0.080 |
| Mountain stream, gravel + cobbles | 0.040 | 0.030–0.050 |
| Mountain stream, cobbles + boulders | 0.050 | 0.040–0.070 |
| Floodplain, pasture (short grass) | 0.030 | 0.025–0.035 |
| Floodplain, dense brush | 0.070 | 0.045–0.110 |
| Floodplain, light timber | 0.080 | 0.060–0.120 |
| Floodplain, heavy timber w/ down trees | 0.120 | 0.090–0.160 |
Source: Chow, V.T. (1959). Open-Channel Hydraulics, Table 5-6. Cross-checked against USGS WSP 2339 (Arcement & Schneider, 1989) for floodplain values.
Worked examples
Example 1 — Concrete-lined trapezoidal storm channel
Example 2 — 36-inch RCP storm sewer flowing half full
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.