Phase Shift Calculator

Enter the parameters A, B, C, and D from a sinusoidal function of the form f(x) = A·sin(Bx − C) + D or its cosine equivalent, and this Phase Shift Calculator returns the amplitude, period, phase shift, and vertical shift. You can also input a time delay and frequency to calculate the phase shift in degrees between two signals.

The coefficient multiplying the trig function. Determines the amplitude. Can be negative.

The coefficient of x inside the trig function. Affects the period.

The constant subtracted from Bx. Phase shift = C/B.

The constant added to the function. Shifts the graph up or down.

Hz

Signal frequency — used to calculate phase shift from time delay.

s

Time difference between two signals. Enter frequency and Δt to calculate phase angle.

Results

Phase Shift

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Amplitude |A|

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Period (2π / |B|)

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Vertical Shift (D)

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Phase Shift (degrees)

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Phase Angle from Time Delay

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Function

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Sinusoidal Function Plot (one period)

Frequently Asked Questions

How do I calculate the phase shift?

For a function of the form f(x) = A·sin(Bx − C) + D, the phase shift is C divided by B (i.e., C/B). A positive result means the graph shifts to the right; a negative result means it shifts to the left. For example, in 3·sin(2x − 1), the phase shift is 1/2 = 0.5 units to the right.

How do I find the phase shift from a graph?

Identify a reference point on the base sine or cosine wave (such as a peak or zero crossing) and compare it to the same point on the shifted wave. The horizontal distance between these points is the phase shift. If the shifted wave appears to the right, the phase shift is positive; to the left means it is negative.

How do I find the amplitude, period, and phase shift?

Given f(x) = A·sin(Bx − C) + D: the amplitude is |A|, the period is 2π/|B|, the phase shift is C/B, and the vertical shift is D. Simply read off the coefficients A, B, C, and D from the function and apply these formulas.

Are horizontal shift and phase shift the same thing?

Yes, in the context of trigonometric functions, the phase shift is the horizontal (left or right) translation of the graph. It describes how many units the graph has been moved along the x-axis relative to the standard sine or cosine function.

How do I calculate phase shift from time delay and frequency?

The phase angle φ (in degrees) between two signals is calculated as φ = 360° × frequency × time delay (Δt). For example, two signals at 440 Hz with a 1 ms delay have a phase difference of 360 × 440 × 0.001 = 158.4°.

What is the period of a sinusoidal function?

The period is the length of one complete cycle of the wave. For f(x) = A·sin(Bx − C) + D, the period is 2π divided by the absolute value of B. A larger |B| compresses the wave (shorter period), while a smaller |B| stretches it (longer period).

How do I graph trig functions with a phase shift?

Start by plotting the standard sine or cosine curve. Then shift every point horizontally by the phase shift value (C/B): right if positive, left if negative. Scale the y-axis by the amplitude |A|, stretch or compress the x-axis according to the period 2π/|B|, and shift everything vertically by D.

Can the amplitude be negative?

The amplitude is always a non-negative value, defined as |A|. However, if the coefficient A is negative in the function, this reflects the graph across the x-axis (flips it upside down) in addition to scaling it. The amplitude still equals the absolute value of A.

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