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Phase Shift Calculator.

Find phase shift and period for A·sin(Bx − C) + D.

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01

Set your values

Results update as you type.

Phase shift: 0.5

Phase shift

0.000000
Period: 3.141593

Period

0.000000

Results update automatically as you type.

Use Cases

Graphing Sinusoidal Functions

Quickly find the phase shift and period to accurately plot sine or cosine waves, especially useful for students and educators.

Example: For y = sin(2x - π/3), enter B=2 and C=-π/3 to get phase shift = π/6 and period = π.

Analyzing Wave Properties

In physics or engineering, determine the horizontal displacement and cycle length of a wave from its equation.

Example: For a wave described by y = cos(0.5x + 1), enter B=0.5 and C=1 to find phase shift = -2 and period = 4π.

Frequently Asked Questions

What does the phase shift calculator compute?
This calculator determines the phase shift and period of a sinusoidal function based on the coefficients B and C. The phase shift is calculated as -C/B, and the period is 2π divided by the absolute value of B.
How do I use the B and C fields?
Enter the coefficient B (which affects the period) and the constant C (which affects the horizontal shift) of your sinusoid. The calculator then outputs the phase shift and period, assuming the function is in the form y = sin(Bx + C) or y = cos(Bx + C).
What is the meaning of a negative phase shift?
A negative phase shift indicates that the graph of the sinusoid is shifted to the left on the x-axis, while a positive phase shift shifts it to the right. The calculator provides the signed value directly.

Tips & Common Mistakes

Tips

  • Ensure B is not zero, as the period formula requires division by B.
  • Use consistent units (radians or degrees) for C, but the calculator assumes radians for the period calculation.
  • Double-check the sign of C: in the standard form y = sin(Bx + C), a positive C shifts left, negative shifts right.
  • For a quick check, remember that the period is always positive, while the phase shift can be positive or negative.

Common Mistakes to Avoid

  • Forgetting to include the negative sign in the phase shift formula: phase shift = -C/B, not C/B.
  • Using the absolute value of B for the phase shift, which is incorrect; only the period uses |B|.
  • Entering C in degrees when the calculator expects radians, leading to incorrect phase shift values.

Last updated: August 13, 2026