Phase Shift Calculator
The phase shift calculator is here to find the amplitude, period, phase shift, and vertical shift of an arbitrarily changed sine or cosine function.
Amplitude2peak height above the midline
Period2.0943951120° — one full cycle
Phase shift0.5shifted right
Vertical shift (midline)y = 1
Range-1 to 3
Frequency0.47746483cycles per unit of x
The formula
y = A·sin(B(x − C)) + D
Reading the four parameters
A stretches vertically — the amplitude is |A|, and a negative A flips the wave. B squeezes horizontally: the period is 2π/|B|, so larger B means faster oscillation. C slides it right, and D slides it up.
Watch the form: sin(3x − 1.5) is sin(3(x − 0.5)), so the phase shift is 0.5, not 1.5. Factoring B out first is the step people skip.