Phase Shift Calculator
Use one page, several physics modes, and consistent sign handling. Results appear above this form after each submission.
Calculation History
Export your recent results as CSV or PDF.
| Timestamp | Mode | Direction | Phase (°) | Phase (rad) | Cycles | Frequency (Hz) | Delay (ms) | Type |
|---|---|---|---|---|---|---|---|---|
| No saved results yet. Run a calculation to populate this table. | ||||||||
Example Data Table
Use these sample cases to test the calculator quickly.
| Mode | Input A | Input B | Direction | Phase (°) | Phase (rad) | Cycles |
|---|---|---|---|---|---|---|
| Time Delay + Frequency | 50 Hz | 5 ms | Lagging | 90 | 1.570796 | 0.25 |
| Path Difference + Wavelength | 0.25 m | 1 m | Leading | 90 | 1.570796 | 0.25 |
| Angular Frequency + Delay | 314.159 rad/s | 2.5 ms | Lagging | 45 | 0.785398 | 0.125 |
| Phase Angle + Frequency | 120° | 60 Hz | Leading | 120 | 2.094395 | 0.333333 |
Formula Used
φ = 2πfΔt = 360°fΔt
φ = 2π(Δx / λ) = 360°(Δx / λ)
φ = ωΔt
Δt = φ / (2πf)
Here, φ is phase angle, f is frequency, Δt is time delay, ω is angular frequency, Δx is path difference, and λ is wavelength.
This calculator treats a leading wave as positive and a lagging wave as negative. It also reports the principal phase within one cycle.
How to Use This Calculator
- Select the calculation mode that matches your known quantities.
- Choose whether the shifted wave is leading or lagging.
- Enter values using the correct units for frequency, delay, length, wavelength, or angle.
- Press Calculate Phase Shift to display the result above the form.
- Review degrees, radians, cycle fraction, classification, and any equivalent delay information.
- Use the graph and export buttons to inspect or save your work.
FAQs
1. What does phase shift mean in physics?
Phase shift shows how far one periodic signal is displaced from another. The displacement can be described in degrees, radians, cycles, time delay, or path difference.
2. What is the difference between leading and lagging?
A leading wave reaches the same point earlier than the reference wave. A lagging wave reaches it later. This calculator uses positive values for leading and negative values for lagging.
3. When should I use the time delay formula?
Use it when you know the signal frequency and the measured delay between two matching waveform points, such as peaks, zero crossings, or rising edges.
4. When is path difference more useful?
Path difference is useful for waves traveling through space, especially sound, light, and interference problems, where one wave travels farther than another before arriving.
5. Why does the calculator show a principal angle?
A phase angle can exceed one full cycle. The principal angle reduces the result to an equivalent angle between 0° and 360°, which is easier to interpret.
6. What does quadrature mean?
Quadrature means the two waves differ by 90° or 270°. One wave is a quarter cycle ahead of or behind the other.
7. Can this calculator handle unit conversions?
Yes. It converts common frequency, time, length, and angle units automatically before calculating the phase result.
8. Why might equivalent time delay show N/A?
Equivalent time delay needs frequency information. If your chosen mode does not include frequency or angular frequency, the calculator cannot convert phase shift into time delay.