Phase Shift Calculator
Calculate phase shift of sinusoidal functions
Must be greater than 0
How to Use This Calculator
Enter Amplitude
Input the amplitude (A) of your sinusoidal function. This is the maximum displacement.
Enter Frequency
Input the frequency (f) of the wave. This must be greater than 0.
Enter Phase Constant
Input the phase constant (c) from your function y = A·sin(2πft + c) or y = A·cos(2πft + c).
Select Unit
Choose whether your phase constant is in degrees or radians, then calculate.
Formula
Phase Shift = -c / (2πf)
For y = A·sin(2πft + c) or y = A·cos(2πft + c)
Where:
- c = phase constant (the horizontal shift parameter)
- f = frequency (cycles per unit time)
- 2πf = angular frequency (radians per unit time)
- Phase shift has units of time (seconds, etc.)
General Form:
y = A·sin(ωt + φ) or y = A·cos(ωt + φ)
where ω = 2πf (angular frequency) and φ is the phase constant
About Phase Shift Calculator
The Phase Shift Calculator calculates the phase shift of sinusoidal functions like sine and cosine waves. Phase shift represents the horizontal displacement of a wave along the time axis. It's crucial in signal processing, electronics, physics, and any field dealing with periodic phenomena.
What is Phase Shift?
Phase shift is the horizontal displacement of a sinusoidal function. For a function y = A·sin(2πft + c), the phase shift is -c/(2πf), measured in time units. A positive phase shift means the wave is shifted to the left (starts earlier), while a negative phase shift means it's shifted to the right (starts later).
When to Use This Calculator
- Signal Processing: Analyze phase relationships in signals
- Electronics: Calculate phase differences in AC circuits
- Physics: Study wave interference and standing waves
- Mathematics: Transform and analyze sinusoidal functions
- Engineering: Design filters and oscillators
Why Use Our Calculator?
- ✅ Instant Results: Get phase shift values immediately
- ✅ Multiple Units: Supports degrees and radians for phase constant
- ✅ Complete Analysis: Shows period and angular frequency
- ✅ 100% Free: No registration required
- ✅ Educational: Helps understand wave properties
Frequently Asked Questions
What is phase shift in simple terms?
Phase shift is how much a wave is shifted horizontally along the time axis. Think of it as starting the wave at a different time - positive phase shift means starting earlier, negative means starting later.
How does phase shift differ from phase constant?
Phase constant (c or φ) is the parameter in the function y = A·sin(2πft + c). Phase shift is the calculated time displacement: -c/(2πf). Phase constant is in radians/degrees, while phase shift is in time units.
What does a negative phase shift mean?
A negative phase shift means the wave is shifted to the right (delayed) along the time axis. The wave reaches its peak later than the unshifted version.
Can phase shift be greater than the period?
Yes, but phase shifts that are multiples of the period represent the same wave (due to periodicity). Phase shifts are often considered modulo the period.