Phase Shift Calculator
Find the phase shift of y = A·sin(Bx + C) + D and describe the full wave.
About Phase Shift Calculator
For y = A·sin(Bx + C) + D, the phase shift (horizontal shift) is −C/B. A positive value shifts the graph right; negative shifts it left. The wave's full description includes amplitude |A|, period 2π/|B|, and vertical shift D.
Formula
Phase shift
Phase shift = −C / B
- A
- Amplitude coefficient
- B
- Frequency coefficient
- C
- Phase constant
- D
- Vertical shift
Worked example
With the default values below, Phase Shift Calculator returns Phase Shift of -0.500000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- A (amplitude coefficient)
- 1
- B (frequency coefficient)
- 2
- C (phase constant)
- 1
- D (vertical shift)
- 0
Results
- Phase Shift
- -0.500000
- Shift direction
- left
- Amplitude
- 1.000000
- Period
- 3.141593
- Frequency
- 0.318310
- Vertical shift (D)
- 0.0000
Step by step
- 1Phase shift formula= -0.5 (shift left)
- 2Amplitude= 1
- 3Period= 3.14159265
- 4Vertical shift= 0
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax or fees or charges into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What does a positive phase shift mean?
The graph is shifted to the RIGHT by that amount. A negative phase shift shifts left. It is measured in x-units (radians if the argument is in radians).
How does phase shift differ from the C value?
C is the raw constant added inside the argument. The actual shift is −C/B, because B compresses/stretches the x-axis, which affects how far the graph moves.