Y Plus Calculator

What Is a y+ Calculator?

y+ (y-plus) is the dimensionless distance from a wall that tells you how well a CFD mesh resolves the near-wall flow. Our y+ Calculator computes y+ from friction velocity, wall distance, and kinematic viscosity, then reports whether the first cell sits in the viscous sublayer, the buffer layer, or the log-law region.

How the Calculation Works

$$y^+ = \frac{u_\tau y}{\nu}, \qquad u_\tau = \sqrt{\frac{\tau_w}{\rho}}, \qquad \nu = \frac{\mu}{\rho}$$

Where:

• y⁺ is the dimensionless wall distance
• uτ is the friction (shear) velocity in m/s
• y is the distance from the wall to the first cell center in meters
• ν is the kinematic viscosity in m²/s
• τw is the wall shear stress and ρ is the fluid density
• μ is the dynamic viscosity, which can also be entered directly

Worked Example

With a friction velocity of 1 m/s, a first-cell distance of 0.001 m, and air at ν = 1.5 × 10⁻⁵ m²/s, y+ = (1 × 0.001) / (1.5 × 10⁻⁵) = 66.7. That value falls in the log-law region from 30 to 300, which is the usual target for wall-function turbulence models.

For other engineering calculators, see the Wavenumber Calculator, the Transmission Coefficient Calculator, and the Work and Power Calculator.