Choose a model and enter your parameters. Get radians, degrees, delay time, and cycles together. Download clean tables, then verify phase relationships easily today.
| Scenario | Inputs | Key output |
|---|---|---|
| Time shift | f = 1 kHz, Δt = 0.1 ms, delayed | φ ≈ −36° |
| Path difference | λ = 50 cm, Δx = 12.5 cm, extra path | φ ≈ −90° |
| RC low‑pass | R = 1 kΩ, C = 0.1 µF, f = 500 Hz | φ ≈ −17.4° |
| Series RLC | R = 10 Ω, L = 10 mH, C = 100 µF, f = 100 Hz | φZ ≈ −43.7° |
sin(ω(t−Δt)) has phase shift φ = −ωΔt.
If the signal is advanced, use φ = +ωΔt.
φ = −2π(Δx/λ).
With wave speed v, the equivalent time shift is Δt = Δx/v.
x = ωRC. Across capacitor: H = 1/(1 + jx), so φ = −atan(x).
Across resistor: H = jx/(1 + jx), so φ = atan(1/x).
x = ωL/R. Across resistor: φ = −atan(x).
Across inductor: φ = atan(1/x).
Z = R + j(ωL − 1/(ωC)).
Phase of impedance is φZ = atan2(ωL − 1/(ωC), R).
Resonance: ω0 = 1/√(LC).
Phase shift quantifies timing differences between periodic signals. It supports vibration testing, communications, control loops, and interferometry. Small phase errors can distort demodulation, reduce lock‑in sensitivity, or destabilize feedback. This calculator unifies common models so you compare mechanisms with one sign convention.
Angles are reported in radians and degrees, plus cycles (φ/2π). Wrapped values map phase into one cycle, using (−π, π] and (−180°, 180°]. Wrapped phase helps when comparing measurements across frequencies, where raw phase can span many rotations.
For a sinusoid delayed by Δt, the phase shift is φ = −ωΔt. At 1 kHz, a 0.1 ms delay produces φ ≈ −0.628 rad (−36°). The tool also reports Δt/T, the fraction of a period, for timing budgets and scope interpretation.
In propagation, extra path length causes extra delay. With wavelength λ, φ = −2π(Δx/λ). For Δx = λ/4, the shift is −90°. If λ is unknown, the calculator derives it from speed v and frequency f using λ = v/f.
First‑order RC filters introduce frequency‑dependent phase. For a low‑pass output across the capacitor, φ = −atan(ωRC). At ωRC = 1, the phase is −45° and the magnitude is 0.707. For the high‑pass output across the resistor, phase approaches +90° at low ω and 0° at high ω.
RL networks use x = ωL/R. Across the resistor (low‑pass), φ = −atan(x). Across the inductor (high‑pass), φ = atan(1/x). The corner frequency is fc = R/(2πL). These relations appear in current sensing, coil drivers, and actuator models.
For a series RLC, Z = R + j(ωL − 1/(ωC)). The impedance phase is φZ = atan2(ωL − 1/(ωC), R). At resonance ω0 = 1/√(LC), reactances cancel and φZ ≈ 0°. The calculator reports Q = ω0L/R and BW ≈ f0/Q.
When reporting phase, state the reference direction (lead/lag), frequency, and whether angles are wrapped. For measured data, compute at multiple frequencies and check trends expected from the chosen model. Exporting CSV supports quick plotting, while PDF tables attach traceable numbers to lab notes. Include component tolerances, because RC and RLC values shift phase. Use consistent units and document measurement bandwidth.
A positive phase means the output leads the reference. A delay or extra path is treated as lag, producing a negative phase. You can flip the interpretation using the “delayed/advanced” or “extra/shorter path” options.
Degrees are convenient for quick intuition and oscilloscope work. Radians are standard in formulas and simulation code. This tool reports both, plus cycles, so you can move between engineering and analytical conventions without manual conversions.
Raw phase can accumulate beyond one rotation when ωΔt or Δx/λ is large. Wrapped phase maps the result into a single cycle range, making comparisons easier. Use raw phase when counting full rotations is physically meaningful.
It depends on where the output is taken. Across the capacitor (low‑pass), the output lags and phase is negative. Across the resistor (high‑pass), the output can lead at low frequencies and approaches 0° at high frequencies.
For low‑pass outputs, the phase approaches −90° as the reactive element dominates. For high‑pass outputs, the phase approaches 0° at high ω because the transfer becomes nearly real. Magnitude trends are also shown through |H|.
Near resonance, net reactance is close to zero, so the impedance phase approaches 0° and the circuit looks mostly resistive. A higher Q indicates a sharper resonance and smaller bandwidth. Compare φZ above and below f0 to see capacitive or inductive behavior.
These formulas assume steady‑state sinusoidal components. For non‑sinusoidal waveforms, decompose the signal into harmonics and compute phase at each frequency. The CSV export is helpful for building frequency‑by‑frequency tables.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.