Phase Shift Calculator
Find the phase shift of y = A·sin(Bx + C) + D and describe the full wave.
Inputs
Phase Shift
-0.500000
Shift direction
left
Amplitude
1.000000
Period
3.141593
Frequency
0.318310
Vertical shift (D)
0.0000
Step by step
Phase shift formula
−C/B = −(1)/(2)
= -0.5 (shift left)
Amplitude
|A| = |1|
= 1
Period
2π/|B| = 2π/|2|
= 3.14159265
Vertical shift
= 0
How it works
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
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.