What this calculator does
y+ is the dimensionless wall distance used in computational fluid dynamics to check whether a mesh resolves the boundary layer the way a chosen turbulence model expects. It compares the actual distance from the wall to the first mesh cell centre against a length scale built from the local wall shear stress, so the same physical cell height can read as a very different y+ depending on how fast the flow is moving past that wall.
Most CFD users meet y+ from the other direction: a turbulence model documentation states it needs y+ around 1 for a low-Reynolds-number approach, or y+ between roughly 30 and 300 for a wall-function approach, and the mesh has to be built to hit that target before the run even starts. This calculator works both directions: check the y+ a given first-cell height actually produces, or find the cell height needed to land on a chosen target.
The formula
Friction velocity u_τ comes from the wall shear stress τw and fluid density ρ: u_τ = √(τw/ρ). y+ is then the wall distance y, non-dimensionalised by that velocity scale and the fluid's dynamic viscosity μ: y+ = ρ·u_τ·y/μ. Running the same relationship in reverse, for a chosen target y+, gives the wall distance needed: y = y+ · μ/(ρ·u_τ).
| Term | Meaning |
|---|---|
| y+ | The dimensionless wall distance: how many viscous length scales the first mesh cell sits from the wall. |
| u_τ | Friction velocity, a velocity scale built from wall shear stress: u_τ = √(τw/ρ). |
| τw | Wall shear stress, the drag force per unit area the fluid exerts on the wall. |
| y | The actual distance from the wall to the first mesh cell centre. |
The inputs explained
| Field | What to enter |
|---|---|
| Wall shear stress (τw) (Pa) | Wall shear stress at the surface being meshed. This usually comes from a previous run, a flat-plate or pipe-flow correlation, or an estimate from the expected skin-friction coefficient. |
| Fluid density (ρ) (kg/m³) | The fluid density at the flow conditions. 1.225 kg/m³ is standard air at sea level; 998 kg/m³ is water at room temperature. |
| Dynamic viscosity (μ) (Pa·s) | The fluid's dynamic viscosity. 1.81×10⁻⁵ Pa·s is a typical value for air at 15°C; water at room temperature is about 0.001 Pa·s. |
| Wall distance to check (y, first cell height) (m) | The distance from the wall to the centre of the first mesh cell, to check what y+ that produces. |
When to use it
Checking a mesh before running a low-Reynolds-number turbulence model
Models that resolve the viscous sublayer directly, without a wall function, typically need y+ close to 1 at the wall-adjacent cells. Entering the planned first-cell height shows whether the mesh actually lands there before a lengthy solve is committed to.
Sizing the first cell for a wall-function approach
Wall functions are built to work over a target y+ band, often quoted as roughly 30 to 300. Solving for the cell height at y+ = 30 gives a starting point for the mesh generator's first layer thickness.
Diagnosing why a turbulence model gave odd results near a wall
A converged solution with unphysical near-wall behaviour is sometimes a meshing problem rather than a physics one: checking the actual y+ against what the chosen model expects is one of the first things to rule out.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How y+ changes with wall shear stress, at a fixed first-cell height
The same 0.1 mm first cell, across a range of wall shear stress values.
| Wall shear stress | y+ at 0.1 mm wall distance | Friction velocity (u_τ) |
|---|---|---|
| 0.05 Pa | 1.367 | 0.2020 m/s |
| 0.1 Pa | 1.934 | 0.2857 m/s |
| 0.5 Pa | 4.324 | 0.6389 m/s |
| 1 Pa | 6.115 | 0.9035 m/s |
| 2 Pa | 8.648 | 1.278 m/s |
| 5 Pa | 13.673 | 2.020 m/s |
What first-cell height is needed for a chosen y+ target, as wall shear stress varies
The cell height needed to hit y+ = 1, suited to a low-Reynolds-number model, and y+ = 30, a typical wall-function target, across the same range of wall shear stress values.
| Wall shear stress | Cell height needed for y+ = 1 | Cell height needed for y+ = 30 |
|---|---|---|
| 0.05 Pa | 0.00007314 m | 0.00219405 m |
| 0.1 Pa | 0.00005171 m | 0.00155143 m |
| 0.5 Pa | 0.00002313 m | 0.00069382 m |
| 1 Pa | 0.00001635 m | 0.0004906 m |
| 2 Pa | 0.00001156 m | 0.00034691 m |
| 5 Pa | 0.00000731 m | 0.00021941 m |
Questions
What is a good y+ value?
It depends entirely on the turbulence model. Models that resolve the viscous sublayer directly, without a wall function, generally need y+ around 1 at the wall. Models that rely on a wall function are usually built to work over a band, often quoted as roughly 30 to 300, and give unreliable results if y+ falls below that range.
How do I get the wall shear stress to enter here?
It usually comes from a previous CFD run on a coarser mesh, a flat-plate or pipe-flow skin-friction correlation for a first estimate, or the wall shear stress reported by the solver once a run has completed, which can then be used to refine the mesh for a follow-up run.
Why does the same first-cell height give a different y+ in water than in air?
y+ depends on density and viscosity as well as wall distance and shear stress, and water and air differ substantially in both. The same physical cell height sits at a different point in each fluid's viscous length scale, so y+ has to be checked separately for each one.
Can y+ vary across the same surface?
Yes. Wall shear stress is rarely uniform over a real geometry, so a mesh with a single fixed first-cell height typically produces a range of y+ values across the surface, higher where the local shear stress is greater. Checking y+ at the highest-shear regions is usually the more conservative approach.
For the underlying flow regime that shapes wall shear stress in a pipe or duct, see the Reynolds number calculator. For friction loss along a pipe run once the flow is characterised, see the friction loss calculator.