Hydraulic Radius Calculator

R_h = A/P — cross-section area divided by wetted perimeter. Computes R_h, hydraulic diameter D_h = 4R_h, and hydraulic depth D = A/T for rectangular, trapezoidal, full-pipe, and partially-filled circular sections.

Open Channel Flow · Pipe Flow

Inputs

Cross-section shape:

Length units:

Bottom width b (m)

Flow depth y (m)

Theory

Definitions:

R_h = A / P [m] hydraulic radius (Manning, Chézy)

D_h = 4A / P = 4R_h [m] hydraulic diameter (pipe-flow Re)

D = A / T [m] hydraulic depth (Froude number)

T = dA/dy [m] top width (free surface width)

Channel geometry formulas:

Shape	A	P	T
Rectangular	b × y	b + 2y	b
Trapezoidal	(b + zy)y	b + 2y√(1+z²)	b + 2zy
Circular (full)	πD²/4	πD	0 (closed)
Circular (partial)	(D²/8)(θ−sinθ)	Dθ/2	D sin(θ/2)
Wide/shallow (b >> y)	≈ b × y	≈ b	b

θ = 2 × arccos(1 − 2y/D) for circular partial fill.

Where R_h and D_h appear:

Manning: V = (1/n) × R_h^2/3 × S^1/2

Chézy: V = C × √(R_h × S)

Pipe Re: Re = ρ V D_h / μ (uses D_h not R_h)

Froude: Fr = V / √(g × D) (uses hydraulic depth D)