Randles-Sevcik Equation Calculator

The Randles-Ševčík equation describes the relationship between the peak current observed in a cyclic voltammetry (CV) experiment and key electrochemical parameters — specifically the scan rate, diffusion coefficient, concentration, electrode area, and number of electrons transferred. It is widely used to determine diffusion coefficients, verify diffusion-controlled processes, and characterize electroactive species in solution.

Yes, but with a modification. For a fully irreversible electrochemical process, the equation becomes ip = 0.4958 · n · F · A · C⁰ · √(α · na · F · v · D / (R · T)), where α is the transfer coefficient and na is the number of electrons in the rate-determining step. The pre-factor changes from 0.4463 to 0.4958, and α replaces n in certain terms. This calculator accounts for that distinction via the Process Type selector.

The peak current ip is proportional to the square root of the scan rate (√v). This means that if you plot ip versus √v and obtain a straight line passing through the origin, it confirms that the electrochemical process is diffusion-controlled. Any deviation from linearity suggests adsorption effects, coupled chemical reactions, or other complications.

In the SI/CGS mixed convention commonly used in electrochemistry: electrode area in cm², concentration in mol/cm³, diffusion coefficient in cm²/s, scan rate in V/s, temperature in Kelvin, and the result is peak current in Amperes. Be careful with concentration units — if your concentration is in mM (millimolar), convert it to mol/cm³ by multiplying by 1×10⁻⁶ before applying the formula.

At 25 °C (298.15 K), substituting in the constants F, R, and T simplifies the equation to ip = 2.69 × 10⁵ · n^(3/2) · A · C⁰ · √(D · v). This form is convenient for quick calculations and is widely cited in electrochemistry textbooks and papers, though the full thermodynamic form is more general.

Record peak currents at multiple scan rates, then plot ip versus √v. The slope of this line equals 0.4463 · n · F · A · C⁰ · √(n · F · D / (R · T)). Rearranging for D allows you to calculate the diffusion coefficient directly from the slope. This is one of the most common experimental applications of the Randles-Ševčík equation.

The equation assumes: (1) the process is diffusion-controlled with semi-infinite linear diffusion, (2) the electrode reaction is electrochemically reversible (for the standard form), (3) there are no coupled chemical reactions or adsorption effects, and (4) the solution is unstirred. Violations of these assumptions — such as thin-layer diffusion, adsorbed species, or quasi-reversible kinetics — will cause deviations from the predicted peak current.

The n^(3/2) dependence arises because peak current has two separate n dependencies: one from the overall Faradaic charge passed (proportional to n) and one embedded inside the square-root term from the thermodynamic driving force of the reaction (proportional to √n, since the equilibrium potential shifts with n). Combining these gives the n · n^(1/2) = n^(3/2) dependence seen in the equation.