Hydraulic Radius Calculator — Manning's Equation
The hydraulic radius R_h = A/P (flow area ÷ wetted perimeter) governs friction losses in open channels and full pipes. Enter the channel geometry (rectangular, circular or trapezoidal), then add Manning's roughness coefficient and bed slope to get mean velocity and discharge via Manning's equation.
Channel cross-section shape
m
m
m/m
R_h = Flow area / Wetted perimeter
- 1
Flow area
A = 4.5 m² = 4.5 - 2
Wetted perimeter
P = 6 m = 6 - 3
Hydraulic radius
R_h = 4.5 ÷ 6 = 0.7500Ratio of flow area to wetted perimeter — governs friction in Manning's equation.
How does this calculator work?
Hydraulic radius R_h = A/P_w measures flow efficiency. For a rectangle, R_h = by/(b+2y); for a full circle, R_h = D/4. Manning's equation V = (1/n)R_h^(2/3)S^(1/2) then gives mean channel velocity and discharge Q = VA. Enter geometry, roughness (n) and slope (S) for results.
Formula
How this is calculated
The hydraulic radius summarises a cross-section's flow efficiency: more area relative to wetted perimeter means less friction and faster flow. For a full circular pipe, R_h = D/4; for a wide rectangular channel (b >> y), R_h ≈ y — the flow depth.
Manning's equation V = (1/n) R_h^(2/3) S^(1/2) is an empirical formula for the mean velocity in a uniform open-channel flow. The Manning roughness coefficient n characterises the channel lining (e.g. smooth concrete 0.011–0.013, excavated earth 0.022–0.030, natural river 0.030–0.070). S is the longitudinal bed slope. Multiplying by area gives discharge Q = V × A.
Manning's formula is accurate for fully turbulent, uniform, steady flow in the units used here (SI: metres and seconds). It should not be used for laminar flow (Re < ~2000) or rapidly varying flows. The formula assumes a constant cross-section and roughness along the reach.
Frequently asked questions
The semicircle (half-pipe) is the hydraulically most efficient shape — it maximises R_h for a given cross-sectional area, meaning less wetted perimeter and less friction. Practically, trapezoidal channels with a 60° bank angle closely approximate this.
Common values: smooth PVC pipe 0.009, precast concrete 0.013, rough concrete 0.017, gravel lining 0.025–0.030, earth channel 0.022–0.030, natural stream 0.030–0.050. Published tables (Chow, 1959) list over 100 lining types.
Hydraulic radius R_h = A/P_w is used in friction formulas (Manning's, Chezy). Hydraulic depth D_h = A/T (area / top width) is used in wave-speed and Froude-number calculations for non-rectangular channels.
Also known as
TG we-Calculate Editorial Team. (2026). Hydraulic Radius Calculator — Manning's Equation [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/hydraulic-radius-calculator
TG we-Calculate Editorial Team. "Hydraulic Radius Calculator — Manning's Equation." TG we-Calculate. 2026. https://we-calculate.com/calculator/hydraulic-radius-calculator.
TG we-Calculate Editorial Team, "Hydraulic Radius Calculator — Manning's Equation," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/hydraulic-radius-calculator
@misc{wecalculate_hydraulic_radius_calculator, title = {Hydraulic Radius Calculator — Manning's Equation}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/hydraulic-radius-calculator}}, year = {2026}, note = {TG we-Calculate} }
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