Y+ Calculator

Calculate CFD y+ and first-cell wall distance from flow speed, viscosity, wall shear stress, or skin friction coefficient inputs for meshes.

Choose the starting point that matches the values you have.

First layer

Check y+

Known shear/Cf

Target y+

Flow speed

Characteristic length

Fluid

Kinematic viscosity, ν

Skin-friction model

Wall distance to first cell center

Friction velocity, uτ

Fluid

Kinematic viscosity, ν

Target y+

Friction velocity from

Fluid

Kinematic viscosity, ν

Wall shear stress, τw

Density, ρ

Skin friction coefficient, Cf

Flow speed

Related Calculators

Y+ Formula

y+ = y * u_tau / nu

Where the friction velocity is:

u_tau = sqrt(tau_w / rho) = U * sqrt(Cf / 2)

And the first cell-center distance for a target y+ is:

y = y+ * nu / u_tau

y+ — dimensionless wall distance
y — distance from the wall to the first cell center (m)
u_tau — friction velocity (m/s)
tau_w — wall shear stress (Pa)
rho — fluid density (kg/m³)
nu — kinematic viscosity (m²/s)
U — freestream or reference flow speed (m/s)
Cf — local skin friction coefficient

For the first-layer estimate, Cf comes from smooth flat-plate correlations: Cf = 1.328/√Re for laminar flow and Cf ≈ 0.0592/Re^0.2 for turbulent flow, with Re = UL/ν. These are first-cell estimates only. After running the simulation, recompute y+ from the solved wall shear stress and refine the mesh if needed.

Reference Values

Typical y+ ranges by near-wall treatment:

Approach	Target y+	Notes
Wall-resolved (low-Re, SST k-ω, Spalart-Allmaras)	y+ < 1	Resolves the viscous sublayer.
Enhanced / blended wall treatment	y+ < 5 or y+ > 30	Avoid the buffer zone.
Standard wall functions	30 ≤ y+ ≤ 300	Log-law region.
Buffer layer	5 < y+ < 30	Avoid placing the first cell here.

Common fluid properties at 20°C used by the calculator:

Fluid	ν (m²/s)	ρ (kg/m³)
Air	1.5 × 10⁻⁵	1.225
Water	1.004 × 10⁻⁶	998
Seawater	1.05 × 10⁻⁶	1025
Light oil	1.0 × 10⁻⁴	870

Example and FAQ

Example. A 1 m chord airfoil in air at 30 m/s, target y+ = 1. Re = 30 × 1 / 1.5e-5 = 2.0 × 10⁶. Cf ≈ 0.0592 / (2.0e6)^0.2 ≈ 0.00328. u_tau = 30 × √(0.00328/2) ≈ 1.22 m/s. y = 1 × 1.5e-5 / 1.22 ≈ 1.23 × 10⁻⁵ m, or about 0.012 mm.

Is y the first cell height or the cell-center distance? y is the distance from the wall to the first cell center. With a typical near-wall prism, the full first-layer thickness is about 2y.

Should I divide by 2 for a half-channel? No. y is measured from the wall, regardless of channel symmetry.

My solved y+ differs from the estimate. Expected. Flat-plate Cf is a starting point. Use the Check y+ tab with the solved wall shear stress (u_tau = √(τw/ρ)) and adjust the mesh.

What about pipe flow? Use hydraulic diameter as the characteristic length and the bulk velocity as U. For a more accurate first guess, substitute a pipe Cf correlation such as Cf = 0.079·Re^-0.25 and use the Known shear/Cf tab.