Manning's Equation Calculator

V = (1/n) × R_h^2/3 × S^1/2 — uniform open-channel flow. Solve for velocity, slope, roughness, or hydraulic radius with built-in channel geometry presets and Manning's n tables.

Open Channel Flow · Hydraulics

Inputs

Solve for:

Channel cross-section:

Bottom width b (m)

Flow depth y (m)

Computed geometry:

A [m²]

3.6

P [m]

5.4

R_h [m]

0.6667

Manning's roughness coefficient n (dimensionless)

Channel slope S (m/m)

Theory

Manning's equation and derived forms:

V = (1/n) × R_h^2/3 × S^1/2 [m/s]

Q = V × A = (A/n) × R_h^2/3 × S^1/2 [m³/s]

S = (n × V / R_h^2/3)² [m/m]

n = R_h^2/3 × S^1/2 / V [dimensionless]

Hydraulic radius for common cross-sections:

Shape	Area A	R_h = A/P
Rectangular	b × y	by / (b + 2y)
Trapezoidal	(b + zy) × y	(b+zy)y / (b + 2y√(1+z²))
Circular (full)	πD²/4	D/4
Wide channel	b × y (b >> y)	≈ y (depth)

Froude number and flow regime:

Fr = V / √(g × y) [dimensionless, y = flow depth]

Fr < 1 subcritical — tranquil, controlled from downstream

Fr = 1 critical — maximum discharge for given energy

Fr > 1 supercritical — rapid, controlled from upstream