y⁺ Calculator — CFD Wall-Mesh Sizing
In CFD, y⁺ is the dimensionless wall distance that determines whether your mesh resolves or bypasses the viscous sublayer. Enter your flow conditions to find the required first cell height for a target y⁺, or supply the cell height to compute the actual y⁺ — using the Prandtl 1/7 power-law skin friction for a turbulent flat plate.
Mode
m/s
m
m²/s
kg/m³
Distance from the wall to the centre of the first mesh cell — mm
- 1
Reynolds number Re = U × L ÷ ν
10 × 1 ÷ 0.000015 = 666,667 - 2
Skin friction C_f = 0.026 × Re^(−1/7)
0.026 × 666,667^(−1/7) = 0.003828Prandtl 1/7 power-law estimate for a turbulent flat plate. - 3
Wall shear stress τ_w = C_f × ½ρU²
0.003828 × ½ × 1.225 × 10² = 0.2345 - 4
Friction velocity u_τ = √(τ_w ÷ ρ)
√(0.2345 ÷ 1.225) = 0.4375 - 5
First cell height y₁ = y⁺ × ν ÷ u_τ (in mm)
1 × 0.000015 ÷ 0.4375 × 1000 = 0.0343
How does this calculator work?
y⁺ = y·u_τ/ν, where u_τ = √(C_f·U²/2), C_f ≈ 0.026·Re^(−1/7). Target y⁺ ≤ 1 for low-Reynolds turbulence models (k-ω SST, LES); target y⁺ 30–200 for high-Reynolds wall functions (standard k-ε). Enter flow speed, length, fluid properties, and the desired y⁺ to get the required first cell height.
Formula
How this is calculated
The dimensionless wall distance y⁺ = y·u_τ/ν measures how far the first mesh cell centre sits from the wall relative to the viscous length scale ν/u_τ. The friction velocity u_τ = √(τ_w/ρ) is derived from the wall shear stress τ_w. This calculator estimates τ_w from Prandtl's 1/7 power law for turbulent boundary layers on a flat plate: C_f = 0.026·Re^(−1/7), then τ_w = C_f·½ρU². The required first-cell height is y = y⁺·ν/u_τ.
The choice of target y⁺ depends on the turbulence model. For low-Reynolds-number models (k-ω SST with enhanced wall treatment, Spalart-Allmaras in low-Re mode), y⁺ ≤ 1 is required to resolve the viscous sublayer where the velocity profile is linear. For high-Reynolds-number wall functions (standard k-ε with log-law wall functions), y⁺ should be in the fully turbulent log-law region, typically 30–200; values below 30 land in the buffer layer (y⁺ 5–30) where neither the viscous nor log-law solution applies reliably.
Limitations: Prandtl's 1/7 power law is an empirical approximation valid for fully turbulent flat-plate flow and moderate Reynolds numbers (10⁵–10⁷). Real geometries have pressure gradients, separation, curvature, and roughness that shift τ_w substantially. Treat this estimate as a starting point; always check y⁺ contours in your solver after the first run and refine the mesh if needed.
Frequently asked questions
k-ω SST with automatic wall treatment (the default in OpenFOAM, Fluent, and most modern solvers) blends low-Re and wall-function behaviour. Aim for y⁺ ≤ 1–2 when your focus is near-wall accuracy (heat transfer, separation onset, skin friction). y⁺ up to about 5 is still acceptable. Avoid y⁺ in the buffer layer (5–30) for any model.
The Prandtl 1/7 law is a widely used first estimate because it depends only on the global Reynolds number, which is always known at the start of a meshing task. Real C_f depends on local pressure gradient and surface curvature, but the flat-plate value gives a reasonable order-of-magnitude first-cell estimate. If your geometry has strong adverse pressure gradients or bluff-body wakes, you may need to reduce y₁ by 30–50% as a safety margin.
Use a geometric series: after the first layer of height y₁, subsequent layers grow by a factor r (typically 1.1–1.3). Total boundary layer thickness covered in n layers is y₁·(rⁿ−1)/(r−1). Most CFD pre-processors (Ansys Meshing, snappyHexMesh, Gmsh) accept y₁ and r directly as inflation-layer parameters.
Also known as
TG we-Calculate Editorial Team. (2026). y⁺ Calculator — CFD Wall-Mesh Sizing [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/yplus-calculator
TG we-Calculate Editorial Team. "y⁺ Calculator — CFD Wall-Mesh Sizing." TG we-Calculate. 2026. https://we-calculate.com/calculator/yplus-calculator.
TG we-Calculate Editorial Team, "y⁺ Calculator — CFD Wall-Mesh Sizing," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/yplus-calculator
@misc{wecalculate_yplus_calculator, title = {y⁺ Calculator — CFD Wall-Mesh Sizing}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/yplus-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?