Prandtl–Meyer Expansion Calculator
Get the expansion angle ν(M, γ) in degrees.
How to Use This Calculator
1
Enter M > 1
Prandtl–Meyer function is defined for supersonic Mach numbers.
2
Choose γ
Use 1.4 for air at standard conditions.
3
Calculate ν
The result is in degrees.
Formula
ν(M) = √((γ+1)/(γ−1)) · arctan(√(((γ−1)/(γ+1))(M² − 1))) − arctan(√(M² − 1))
This formula gives ν in radians; the calculator reports degrees.
Example: M=2, γ=1.4 ⇒ ν ≈ 26.38°.
Frequently Asked Questions
Can I get M from ν?
This tool outputs ν from M. Inverting requires iteration; a future update can add ν→M.
Units?
Angles shown are in degrees. γ is dimensionless; M is unitless.