y+ Wall Distance Calculator

When creating a CFD mesh, getting the near-wall cell size right is critical for accurate boundary-layer resolution. The dimensionless wall distance y+ determines whether the first cell falls inside the viscous sublayer (y+ ≈ 1, required for low-Re turbulence models and wall-resolved LES) or in the log-law region (30 < y+ < 300, used with wall functions). This page provides the formulas behind the y+ wall-distance estimation and a calculator that returns the required first-cell height for any combination of flow conditions and desired y+.

Formulas for Estimating First-Cell Height from y+

The Reynolds number for a given free-stream velocity \(U_\infty\) and reference length \(L\) is:

$$Re = \frac{\rho \cdot U_{\infty} \cdot L}{\mu}$$

The Schlichting skin-friction correlation is used to estimate the friction coefficient \(C_f\). It is valid for \(Re_x < 10^9\):

$$C_f = \left[ 2 \cdot \log_{10}(Re_x) - 0.65 \right]^{-2.3} \quad \text{for} \quad Re_x < 10^9$$

The wall shear stress follows from the skin-friction coefficient:

$$\tau_w = C_f \cdot \tfrac{1}{2} \, \rho \, U_{\infty}^2$$

The friction velocity \(u^*\) is derived from the wall shear stress and the fluid density:

$$u^* = \sqrt{\frac{\tau_w}{\rho}}$$

Finally, the wall distance (first-cell height) for a desired y+ is:

$$y = \frac{y^+ \cdot \mu}{\rho \cdot u^*}$$

The calculator below evaluates all of these equations and returns the intermediate results (Re, Cf, τw, u*) as well as the wall distance in millimetres.

y+ Wall Distance Calculator

The default values for density and dynamic viscosity are for air at 1 atm and 20 °C. For water at the same conditions, use ρ = 998.21 kg/m3 and μ = 1.002×10−3 Pa·s.

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Disclaimer: The tools, calculators and formulas provided on this website are intended for educational and informational purposes only. While we strive to ensure accuracy, we cannot guarantee that the results will be applicable to your specific circumstances. Users are encouraged to verify results independently and consult a qualified professional if necessary. By using these tools, you acknowledge that the use of any information obtained from this site is at your own risk.

For complex geometries where a flat-plate estimate is not sufficient, our CFD team can run preliminary simulations to verify the near-wall mesh resolution and adjust the boundary-layer prism layers accordingly. To learn more about the fundamentals, see our course Introduction to Computational Fluid Dynamics.

Frequently asked questions

Common questions about y⁺ and near-wall meshing.

It depends on the turbulence model. Low-Reynolds-number models (e.g. SST k-ω without wall functions) and wall-resolved LES require y+ ≈ 1, meaning the first cell must lie within the viscous sublayer. Standard wall-function approaches (e.g. standard k-ε) work best with 30 < y+ < 300, placing the first cell in the log-law region. Values in the buffer layer (5 < y+ < 30) should be avoided, as neither the viscous sublayer model nor the wall-function model is valid there.

The reference length is the characteristic length of the surface over which the boundary layer develops. For external aerodynamics this is typically the chord length (airfoil) or the body length (vehicle). For internal flows it is usually the hydraulic diameter of the duct. The choice of reference length affects the Reynolds number and therefore the estimated skin-friction coefficient — use the length that best represents the boundary-layer development in your application.

The Schlichting formula provides a quick empirical estimate of the skin-friction coefficient for a flat-plate turbulent boundary layer, valid up to Re ≈ 109. It is accurate enough for the purpose of mesh sizing, where the goal is an order-of-magnitude estimate of the first-cell height. For geometries with strong pressure gradients, separation or curvature the actual wall shear stress will differ from the flat-plate estimate, so the calculated y value should be treated as a starting point and verified after running the simulation.