Math

Phase Shift Calculator

Find amplitude, period, phase and vertical shift of A·sin(Bx − C) + D.

Calculated Output

Phase shift 0.3333

Period 2.094

Amplitude 2

Formula: phase = C/B, period = 2π/|B|

Step-by-Step Breakdown

1. Values used:

2. Amplitude A = 2

3. B = 3

4. C = 1

5. Vertical shift D = 0

7. Phase shift = 0.3333

8. Period = 2.094

9. Amplitude = 2

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The math behind it

Amplitude is |A|, period is 2π/|B|, the phase shift is C/B (right if positive), and D shifts the graph vertically.

y = 2·sin(3x − 1) → amplitude 2, period 2π/3 ≈ 2.094, phase shift 1/3.

Which way does a positive phase shift move?

To the right along the x-axis.