Free tool
Polarization curve analyzer
Paste one or more fuel cell or electrolyzer polarization curves. Get HFR-corrected curves, Tafel slope and exchange current density, power density, and voltage efficiency at the current density you care about, side by side.
Runs entirely in your browser. Nothing is uploaded. Sample curves are synthetic.
Reading a polarization curve
A polarization curve splits cell losses into three regions. At low current density the steep drop (or rise, for an electrolyzer) is activation loss, governed by electrode kinetics and described by the Tafel slope. The straight middle section is dominated by ohmic loss, the membrane and contact resistance measured as HFR. At high current density the curve bends again as reactant or product transport limits the cell.
Correcting for HFR first is what makes the Tafel analysis meaningful: without it, ohmic loss leaks into the kinetic region and the slope comes out too large. The Tafel slope guide and the HFR guide walk through both steps, and the EIS Nyquist plotter reads HFR from impedance data.
Beginning of life versus end of test
Comparing curves is where the analysis pays off: a higher HFR points to membrane or contact changes, a larger Tafel slope or lower j₀ to catalyst degradation, and an earlier bend at high current to transport problems. Load the two sample curves to see the pattern, then try your own data.
FAQ
What columns does the analyzer need?
Current density (A/cm² or mA/cm²) or current (A) plus the active area, and cell voltage (V). An optional HFR column (Ω·cm², or Ω which is multiplied by the area) is used point by point for iR correction. Without it you can enter one HFR value for the whole curve.
How is the iR correction done?
The ohmic loss j × HFR is added back to the measured voltage for a fuel cell and subtracted for an electrolyzer. The dashed curves show the iR-free result.
How is the Tafel slope calculated?
Overpotential is the reversible potential minus the iR-free voltage for a fuel cell, or the iR-free voltage minus the reversible potential for an electrolyzer. A straight line is fitted to overpotential against log10(current density) over the range you choose; the slope in mV per decade is the Tafel slope, and the current density where the line reaches zero overpotential is the exchange current density j₀.
Which current range should I use for the Tafel fit?
The kinetic region: low current densities where activation losses dominate, typically below about 0.1 A/cm² for PEM fuel cells. Check that R² is close to 1 and that the fitted line follows the points on the log plot; move the range if it does not.
How is efficiency defined here?
Fuel cell voltage efficiency uses the lower heating value of hydrogen (V / 1.253 V). Electrolyzer efficiency uses the higher heating value, or thermoneutral voltage (1.481 V / V). Both are voltage efficiencies and ignore Faradaic and system losses.
Is my data uploaded?
No. Everything runs in your browser and nothing leaves your computer.