Enter the wavelength and the distance to calculate the phase change (phase shift) of a wave over that distance. The phase constant (also called the wavenumber) is β = 2π/λ in rad/m, and the total phase change over distance d is Δφ = βd in radians.

Phase Change (Δφ) Calculator

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By Frequency & Material (β)

Enter any 2 values to calculate the missing variable using Δφ = (2π/λ)·d

Phase Change / Phase Constant Formulas

The following formulas are used for a sinusoidal wave:

β = \frac{2\pi}{\lambda}
\quad,\quad
\Delta\phi = βd = \left(\frac{2\pi}{\lambda}\right)d

Variables:

  • β is the phase constant (wavenumber) (rad/m)
  • Δφ is the phase change (phase shift) over distance d (radians)
  • λ is the wavelength of the wave (meters)
  • d is the distance traveled (meters)

To calculate the phase change over a distance, compute β = 2π/λ and then multiply by the distance traveled: Δφ = βd.

What is a Phase Constant?

The phase constant (often written as β or k) is the rate at which a wave’s phase changes with position. For a lossless, single-frequency wave, it is related to wavelength by β = 2π/λ and has units of rad/m. The total phase change (phase shift) after traveling a distance d is Δφ = βd in radians.

How to Calculate Phase Change (Phase Shift)?

The following steps outline how to calculate the phase change of a wave over a distance:

  1. First, determine the wavelength (λ) of the wave in meters.
  2. Next, determine the distance (d) the wave has traveled in meters.
  3. Use the formula Δφ = (2π / λ) · d to calculate the phase change (Δφ).
  4. Finally, report the phase change (Δφ) in radians (or convert to degrees if needed).
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

wavelength (λ) = 0.5 meters

distance (d) = 2 meters

Phase change: Δφ = (2π/0.5)·2 = 8π ≈ 25.133 radians (which is equivalent to 1440°).