Calculator Inputs
Use one method at a time. Enter only the values needed for your selected mode.
Phase Shift Plot
The graph compares a reference sine wave with a phase-shifted wave.
Example Data Table
| Case | Known Inputs | Formula | Phase (rad) | Phase (deg) | Meaning |
|---|---|---|---|---|---|
| 1 | f = 50 Hz, Δt = 0.002 s | φ = 2πfΔt | 0.6283 | 36.00° | Small lead or lag. |
| 2 | T = 0.02 s, Δt = 0.005 s | φ = 2π(Δt/T) | 1.5708 | 90.00° | Quarter-cycle difference. |
| 3 | Δx = 0.15 m, λ = 0.60 m | φ = 2π(Δx/λ) | 1.5708 | 90.00° | Useful in interference problems. |
| 4 | ω = 40 rad/s, Δt = 0.03 s | φ = ωΔt | 1.2000 | 68.75° | Direct angular method. |
Formula Used
φ = 2πfΔt
φ = 2π(Δt/T)
φ = 2π(Δx/λ)
φ = ωΔt
Here, φ is phase difference, f is frequency, Δt is time delay, T is period, Δx is path difference, λ is wavelength, and ω is angular frequency.
Phase difference is often shown in radians or degrees. One full cycle equals 2π radians, or 360 degrees.
How to Use This Calculator
- Select the calculation mode that matches your known inputs.
- Enter only the required values for that method.
- Keep all units consistent before calculating.
- Choose graph amplitude and sample points if needed.
- Press the calculate button to see results above the form.
- Review phase difference, normalized phase, and cycle shift.
- Use the graph to compare the reference and shifted waves.
- Download the results as CSV or PDF when needed.
Frequently Asked Questions
1. What is phase difference in physics?
Phase difference shows how far two periodic waves are shifted relative to each other. It measures angular separation within a cycle. The value explains whether one wave leads, lags, or matches another wave exactly.
2. Why can phase difference be negative?
A negative value means the second wave lags the reference wave under your sign convention. The normalized angle may still be written between 0° and 360° for easier interpretation.
3. When should I use radians instead of degrees?
Use radians in formulas, derivations, and most advanced physics work. Use degrees for quick interpretation or classroom discussion. Both units describe the same phase shift.
4. How does path difference create phase difference?
If two waves travel different distances, they reach a point at different cycle positions. That travel difference becomes a phase difference, based on what fraction of the wavelength the path difference represents.
5. What does a 90° phase difference mean?
A 90° phase difference equals one quarter of a cycle. For sine waves, one signal reaches its peak one quarter-cycle earlier or later than the other.
6. What does a 180° phase difference mean?
A 180° phase difference means the waves are half a cycle apart. When one wave is at a positive peak, the other is at a negative peak.
7. Can this calculator help with interference problems?
Yes. Phase difference is central to interference analysis. Constructive and destructive interference depend on whether the phase shift aligns the waves or places them out of step.
8. Why is normalized phase useful?
Normalized phase converts large angles into one standard cycle range. This makes comparisons easier, especially when several whole cycles are included in the raw phase value.