EIS Impedance Calculator
Calculate impedance components for Randles cell and extract electrochemical parameters from EIS data.
What EIS Measures
Direct-current measurements give a single resistance and cannot distinguish which physical process caused it. Electrochemical impedance spectroscopy applies a small alternating voltage across a wide frequency range and measures the response, because different physical processes respond on different timescales and can therefore be separated by frequency.
The standard interpretation uses the Randles equivalent circuit: a solution resistance Rs in series with a parallel combination of charge transfer resistance Rct and double layer capacitance Cdl.
| Element | Physical meaning | Where it appears |
|---|---|---|
| Rs | Resistance of electrolyte and contacts | High-frequency intercept on the real axis |
| Rct | Resistance to electron transfer at the interface | Diameter of the Nyquist semicircle |
| Cdl | Charge stored in the electrical double layer | Sets the frequency of the semicircle peak |
| Warburg (W) | Diffusion of reactants to the surface | 45° tail at low frequency |
Reading a Nyquist Plot
The Nyquist plot shows imaginary impedance against real impedance, with frequency increasing right to left. Its shape is read directly:
| Feature | Interpretation |
|---|---|
| Left-hand intercept | Rs — solution and contact resistance |
| Semicircle diameter | Rct — larger means slower electron transfer |
| Peak frequency ωmax | Equals 1/(RctCdl), giving the time constant |
| 45° low-frequency tail | Diffusion-limited behaviour (Warburg impedance) |
| Two semicircles | Two distinct processes, e.g. a coating plus the interface beneath it |
At high frequency the capacitor short-circuits Rct, so only Rs is measured. At low frequency the capacitor blocks entirely and the total is Rs + Rct. The semicircle is the transition between those two limits, and its width therefore gives Rct directly.
In corrosion work Rct is inversely related to corrosion rate through the Stern–Geary relationship — a large semicircle means slow corrosion and a well-protected surface. In batteries a growing Rct over cycles is a standard signature of interfacial degradation.
Worked Examples
Common Mistakes
EIS assumes a linear response, which requires a perturbation of typically 5 to 10 mV. Larger amplitudes push the system into non-linear behaviour and the equivalent circuit analysis becomes invalid.
Almost any spectrum can be fitted by adding enough elements. Each element should correspond to a real physical process, or the extracted parameters are meaningless numbers.
A 45° low-frequency feature indicates diffusion control. Fitting only a semicircle and ignoring it gives a wrong Rct and misattributes the limiting process.
A full spectrum can take many minutes at low frequency. If the electrode changes during that time — corroding, discharging, or drifting — the data violate the stationarity assumption.
Frequently Asked Questions
Formula Explorer connections
Interpretation: This formula links electron transfer, charge, potential, current or ionic transport in an electrochemical system. Assumption: Balance electron count and half-reactions, preserve sign conventions, and use consistent concentration, temperature and electrical units. Real cells include losses and overpotential.