Phase Shift Calculator

Math

Phase Shift Calculator determines horizontal displacement of sinusoidal functions. For y = A·sin(Bx - C) + D, phase shift = C/B.

Formula

Phase Shift = C/B (for y = A·sin(Bx - C) + D)
  • Phase shift = horizontal displacement of wave
  • Positive: shift right; Negative: shift left
  • Period = 2π/B; Phase shift = C/B

Example

Inputs
  • Phase Constant (C): 0.7853981633974483
  • Frequency Factor (B): 2
  • Direction: right

y = sin(2x - π/4): phase shift = (π/4)/2 = π/8 ≈ 0.3927 units right

Frequently asked questions

What is phase shift?
Horizontal displacement of a sinusoidal wave left or right
How to find phase shift?
For y = sin(Bx - C), phase shift = C/B; for y = sin(B(x - h)), phase shift = h