Cyclic Voltammetry Peak Current Calculator (Randles-Sevcik)
Find the cyclic voltammetry peak current of a reversible, diffusion-controlled reaction using the Randles-Sevcik equation.
📈 What is Cyclic Voltammetry Peak Current?
Cyclic voltammetry peak current is the maximum current recorded at the characteristic peak potential when a potential is swept linearly and reversed. For a reversible, diffusion-controlled reaction, the Randles-Sevcik equation predicts that peak current from electrode area, diffusion coefficient, concentration, and scan rate.
Electrochemists use this constantly, to design cyclic voltammetry experiments before running them, to confirm whether a measured reaction is diffusion-controlled by checking the peak current against scan rate relationship, to extract diffusion coefficients or concentrations from measured peak currents, and to teach the fundamentals of voltammetric analysis.
A common misconception is that peak current scales linearly with scan rate. It doesn't, for a diffusion-controlled reversible reaction it scales with the square root of scan rate, which is exactly the diagnostic signature used to confirm diffusion control in the first place.
This calculator computes the peak current and current density from your inputs for electrons transferred, electrode area, diffusion coefficient, concentration, and scan rate, and plots the standard peak current versus square-root-of-scan-rate diagnostic line with your point marked.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — One-Electron Reaction at 100 mV/s
n=1, A=0.07 cm², D=7.6×10⁻⁶ cm²/s, C=5 mM, ν=100 mV/s
Example 2 — Smaller Electrode, Dilute Solution
n=1, A=0.03 cm², D=6.5×10⁻⁶ cm²/s, C=2 mM, ν=50 mV/s
Example 3 — Two-Electron Reaction at Fast Scan Rate
n=2, A=0.05 cm², D=10×10⁻⁶ cm²/s, C=1 mM, ν=200 mV/s
❓ Frequently Asked Questions
🔗 Related Calculators
What is the Randles-Sevcik equation?
The Randles-Sevcik equation gives the peak current of a reversible, diffusion-controlled redox reaction in cyclic voltammetry: ip = 2.69x10^5 * n^1.5 * A * D^0.5 * C * v^0.5 at 25 degrees Celsius, where A is electrode area, D is the diffusion coefficient, C is bulk concentration, and v is scan rate.
Why does peak current depend on the square root of scan rate?
Faster scan rates give the diffusion layer less time to grow before the peak potential is reached, so the diffusion layer is thinner and the concentration gradient (and thus current) is steeper. This tradeoff works out mathematically to a square-root, not linear, dependence on scan rate.
How can Randles-Sevcik confirm a reaction is diffusion-controlled?
If you measure peak current at several scan rates and plot ip against the square root of scan rate, a straight line through the origin confirms diffusion control. Curvature or a line that doesn't pass through the origin suggests adsorption, kinetic limitations, or another non-ideal effect.
What does each variable in the Randles-Sevcik equation mean?
n is the number of electrons transferred, A is the electrode's geometric area, D is the analyte's diffusion coefficient, C is its bulk concentration, and v is the potential scan rate. The constant 2.69x10^5 already bundles the Faraday constant, gas constant, and temperature at 25 degrees Celsius.
Does this equation work for irreversible reactions?
No, the standard Randles-Sevcik equation as used here assumes fully reversible electron transfer. Irreversible and quasi-reversible systems follow related but different equations that include an electron-transfer coefficient and rate constant, and generally give a lower peak current for the same conditions.
How is peak current used to determine an unknown concentration?
Since ip is directly proportional to concentration C (with all other variables fixed), running a calibration series of known concentrations and measuring their peak currents lets you build a linear ip versus C calibration curve, then read an unknown sample's concentration from its measured peak current.
What units does this calculator use?
Number of electrons is dimensionless, electrode area is in square centimeters (cm2), diffusion coefficient is entered as a value times 10^-6 cm2/s, concentration is in millimolar (mM), and scan rate is in millivolts per second (mV/s). Output peak current is in microamps (µA).
Why is the exponent on n equal to 1.5 and not 1?
The 1.5 power arises from the full mathematical derivation of the diffusion-limited peak current, it combines the n-dependence of the Nernst equation (which sets the peak potential and shape) with the separate n-dependence of Faraday's law relating charge to moles reacted.
How does peak current relate to the double-layer capacitance calculator?
This calculator's Faradaic peak current is the signal of interest in a voltammogram, while double-layer capacitance produces a separate, non-Faradaic background current in the same experiment. Distinguishing the two is essential when analyzing real cyclic voltammetry data, especially at high scan rates where capacitive current grows relatively larger.
What is a typical diffusion coefficient to use in this calculator?
Small molecules and ions in aqueous solution typically have diffusion coefficients around 0.5 to 2 x 10^-5 cm2/s. This calculator's default value of 7.6x10^-6 cm2/s is representative of a moderately sized redox-active molecule in solution.