Phase difference to path difference calculator

Enter the phase difference and a positive wavelength, using any length unit for the wavelength. The result uses that same unit. The calculation applies the standard relation ΔL = Δφλ/(2π), so a full 2π-radian cycle corresponds to one wavelength and a half-cycle corresponds to half a wavelength.

Relate angular phase to a physical distance

Phase describes position within a repeating wave cycle, while path difference describes how much farther one wave has traveled than another. The bridge between them is the wavelength. One complete cycle is 2π radians and spans exactly one wavelength, so the fraction Δφ/(2π) tells you how many cycles separate the waves. Multiplying that fraction by λ gives ΔL = Δφλ/(2π). For example, π/2 radians is one quarter of a cycle, which produces a path difference of one quarter wavelength. The calculator keeps this relationship explicit by returning the entered phase difference, the wavelength, the phase difference expressed in cycles, and the resulting path difference. It accepts signed phase values rather than silently reducing them modulo 2π. That choice preserves direction: a negative phase offset produces a negative path difference, while a positive offset produces a positive one. If your application cares only about magnitude, take the absolute value of the returned path difference after deciding that direction is irrelevant to your convention.

Choose wavelength units and interpret the sign

The wavelength may be entered in metres, nanometres, micrometres, millimetres, or another length unit, provided you understand that the output remains in exactly the same unit. Entering 632.8 as a wavelength measured in nanometres returns the path difference in nanometres; entering 6.328 × 10⁻⁷ in metres returns the equivalent distance in metres. No unit conversion is performed or guessed. This unit-preserving design avoids ambiguity and works equally well for visible light, infrared radiation, microwaves, or any coherent wave for which a wavelength is known. The wavelength must be positive because it represents a physical spatial period. Phase difference is signed because sign conventions differ between instruments and derivations. Before comparing the result with laboratory data, confirm which beam is subtracted from which and whether your instrument reports wrapped phase in a principal interval such as −π to π. A wrapped reading identifies an equivalent path difference within one wavelength but does not reveal an unknown whole-number multiple of the wavelength.

Apply the result to interference measurements

In interferometry, phase is often the directly observed quantity, while displacement, thickness, or optical path length is the quantity of interest. This calculator performs only the core phase-to-path conversion. It does not automatically account for a double-pass reflection, refractive index, incidence angle, or the geometry of a particular instrument. Those factors belong in the model that connects optical path difference to the physical dimension being measured. For a mirror displacement in a simple Michelson interferometer, for instance, moving the mirror changes the round-trip path, so the physical mirror motion can be half the optical path difference under the usual normal-incidence arrangement. Similarly, propagation through material involves optical path length nL, not merely geometric length L, and a phase measurement can combine thickness and refractive-index effects. Use the returned ΔL as the equivalent path difference at the supplied wavelength, then apply the appropriate experimental geometry separately. Keeping these steps distinct makes assumptions visible, reduces factor-of-two mistakes, and lets the same conversion serve many optical setups without pretending they share one geometry.