Cyclic Voltammetry Peak Current Calculator
Calculate the peak current of a reversible redox reaction from cyclic voltammetry using the Randles-Ševčík equation, or solve backwards for the diffusion coefficient, concentration, scan rate, or number of electrons transferred. Includes a reversibility checker for peak separation and the ipa/ipc ratio.
Choose what to solve for, then fill in the rest of the cyclic voltammetry parameters.
Advanced: reversibility checker
Optional — enter your anodic/cathodic peak potentials and currents to check whether the couple behaves reversibly.
Peak current (ip)
Equation used: ip = (2.69×10⁵) n^1.5 A √D C √v
1
Electrons (n)
0.071 cm²
Electrode area
7.800e-6
Diffusion coeff.
0.1 V/s
Scan rate
Reversibility diagnostics
Peak separation (ΔEp)
60 mV
ipa / ipc ratio
1.023
Implied n from ΔEp (59/n mV rule)
0.99
Verdict
Behaves reversibly
A textbook reversible one-electron couple has ΔEp near 59 mV and ipa/ipc near 1 at 25 °C. Larger separation or a ratio far from 1 points to slow electron transfer or a coupled chemical step.
Randles-Ševčík Plot: ip vs √(scan rate)
For a diffusion-controlled, reversible reaction, peak current rises in a straight line through the origin when plotted against the square root of the scan rate.
Curvature away from a straight line, or a line that misses the origin, usually signals adsorption, a slow chemical step, or a non-ideal diffusion regime rather than simple linear diffusion.
Step-by-Step Randles-Ševčík Calculation
Here's exactly how this answer was calculated, one step at a time.
Given: n = 1, A = 0.071 cm², D = 7.800e-6 cm²/s, C = 0.001 M, v = 0.1 V/s
Step 1: Convert every input into base CGS-electrochemistry units
The Randles-Ševčík constant 2.69×10⁵ only works when area is in cm², diffusion coefficient in cm²/s, concentration in mol/cm³, and scan rate in V/s.
A = 7.100e-2 cm², D = 7.800e-6 cm²/s, C = 1.000e-6 mol/cm³, v = 0.1 V/sStep 2: Write the Randles-Ševčík equation
ip = (2.69×10⁵) n¹.5 A √D C √vStep 3: Substitute the values
ip = 2.69×10⁵ × 1¹.5 × 7.100e-2 × √(7.800e-6) × 1.000e-6 × √(0.1)Step 4: Result
ip = 1.687e-5 A = 16.86778 uA
Result:
16.86778 uA
Cyclic Voltammetry Peak Current Calculator: The Randles-Ševčík Equation Online
This cyclic voltammetry peak current calculator uses the Randles-Ševčík equation to predict how large a peak current a reversible, diffusion-controlled redox reaction should produce on a cyclic voltammogram. Enter the number of electrons transferred, the electrode area, the diffusion coefficient of the electroactive species, its bulk concentration, and the scan rate, and it works out the expected peak current instantly, with the full calculation shown step by step.
It also runs in reverse. If you already have a measured peak current from a real experiment, this tool can solve backwards for the diffusion coefficient, the bulk concentration, the scan rate, or even the number of electrons transferred, which is exactly the kind of calculation used every day in electroanalytical chemistry labs to characterize a new redox-active compound or validate an electrode surface.
The Randles-Ševčík Equation
The Randles-Ševčík equation describes the peak current for a reversible electrochemical reaction that is limited purely by diffusion of the electroactive species to the electrode surface. At 25 °C, the practical form of the equation is ip = (2.69 × 10⁵) × n^(3/2) × A × √D × C × √v, where ip is the peak current in amps, n is the number of electrons transferred per molecule, A is the electrode area in cm², D is the diffusion coefficient in cm²/s, C is the bulk concentration in mol/cm³, and v is the scan rate in V/s.
The constant 2.69 × 10⁵ bundles together Faraday's constant, the gas constant, and temperature at exactly 25 °C, so this simplified form is only strictly valid near room temperature. This calculator handles all the unit juggling for you — you can type your concentration in mM or µM, your scan rate in mV/s, and your diffusion coefficient in cm²/s or m²/s, and it converts everything into the base units the equation needs before running the math.
How to Use This Cyclic Voltammetry Calculator
Start by choosing what you want to solve for at the top of the form. The default mode calculates peak current from the other four parameters, which is the most common use case: predicting what peak height you'd expect to see before you even run the experiment, or checking whether an unusually tall or short peak in a real voltammogram makes physical sense.
If you already have an experimental peak current and you're trying to find an unknown property of the system instead, switch the mode to diffusion coefficient, concentration, scan rate, or number of electrons. The form adjusts automatically, hiding the field you're solving for and asking for your measured peak current instead, then rearranges the Randles-Ševčík equation to isolate that unknown.
Why Peak Current Matters in Cyclic Voltammetry
Cyclic voltammetry works by sweeping the potential applied to an electrode back and forth while measuring the resulting current, and the shape of that current-versus-potential curve reveals an enormous amount about the chemistry happening at the electrode surface. The height of the peak current — how much current flows at the point where the reaction rate is fastest — is one of the most information-rich features of that curve.
Because peak current depends on concentration, diffusion coefficient, electrode area, scan rate, and the number of electrons transferred, measuring it under controlled conditions lets electrochemists back-calculate any one of those quantities if the others are known. That's exactly why this calculator supports solving in every direction rather than only the forward calculation.
Diffusion-Controlled vs. Adsorption-Controlled Peaks
The Randles-Ševčík equation assumes the electroactive species reaches the electrode purely by diffusion through solution, which is the normal situation for a dissolved redox-active molecule. Under these conditions, peak current scales with the square root of scan rate, so plotting ip against √v gives a straight line that passes through the origin — a pattern this calculator visualizes directly on the Randles-Ševčík plot.
If a species is instead adsorbed onto the electrode surface rather than diffusing freely, the relationship changes: peak current becomes directly proportional to scan rate itself, not its square root. Checking whether your ip vs √v plot is genuinely linear through the origin, using several scan rates on the same sample, is one of the standard diagnostic tests electrochemists use to confirm they're dealing with a diffusion-controlled process before trusting a Randles-Ševčík calculation.
Checking Reversibility: Peak Separation and the ipa/ipc Ratio
The Randles-Ševčík equation strictly applies to electrochemically reversible reactions, so it's worth checking reversibility before relying on it. Two of the standard diagnostic criteria are built into this calculator's advanced panel: the separation between the anodic and cathodic peak potentials, ΔEp = Epa − Epc, and the ratio of the anodic to cathodic peak currents, ipa/ipc.
For a textbook one-electron reversible couple at 25 °C, theory predicts a peak separation of about 59 millivolts and a peak current ratio close to 1. Peak separations noticeably larger than 59/n millivolts, or a ratio that drifts far from 1, usually point to slower electron-transfer kinetics, uncompensated solution resistance, or a chemical reaction coupled to the electron transfer — any of which means the simple Randles-Ševčík equation may not describe the system perfectly.
Worked Example: Ferrocene on a Glassy Carbon Electrode
Ferrocene is a classic reversible one-electron redox couple used to calibrate electrochemical cells. Suppose a 1 mM ferrocene solution is scanned at 100 mV/s on a glassy carbon disk electrode with an area of 0.071 cm², and ferrocene's diffusion coefficient in this solvent is about 7.8 × 10⁻⁶ cm²/s.
Converting units first: n = 1, A = 0.071 cm², D = 7.8 × 10⁻⁶ cm²/s, C = 1 × 10⁻⁶ mol/cm³ (from 1 mM), and v = 0.1 V/s. Plugging into ip = 2.69 × 10⁵ × 1^1.5 × 0.071 × √(7.8 × 10⁻⁶) × (1 × 10⁻⁶) × √(0.1) gives a peak current of roughly 5.3 microamps — a number this calculator reproduces instantly, along with every intermediate step.
Solving Backwards: Finding an Unknown Diffusion Coefficient
One of the most common real-world uses of the Randles-Ševčík equation is running it backwards to measure a diffusion coefficient that isn't in the literature yet. If a lab records a peak current of, say, 4.5 µA for a 1 mM, one-electron species on a 0.071 cm² electrode at 100 mV/s, rearranging the equation to D = [ip / (2.69×10⁵ n^1.5 A C √v)]² gives the diffusion coefficient directly from that single measurement.
This calculator's diffusion coefficient mode does exactly that rearrangement automatically. It's a common technique in electroanalytical method development, since a newly synthesized redox-active molecule rarely has a published diffusion coefficient, but a single, well-controlled cyclic voltammetry run is enough to estimate one.
Solving for Concentration: Cyclic Voltammetry as a Quantitative Tool
Because peak current is directly proportional to concentration in the Randles-Ševčík equation, cyclic voltammetry can also be used as a quantitative analytical technique, not just a mechanistic one. If the diffusion coefficient, electrode area, and scan rate are already known from a calibration run, measuring the peak current of an unknown sample and solving for concentration gives a fast, sensitive way to determine how much of a redox-active species is present.
This calculator's concentration mode handles that calculation directly, converting the result into millimolar for convenience, since most real-world redox-active analytes are studied in the micromolar-to-millimolar range in aqueous or organic electrolyte solutions.
Effect of Scan Rate on Cyclic Voltammetry Results
Scan rate is one of the easiest experimental variables to control in cyclic voltammetry, and it has a predictable square-root effect on peak current for a diffusion-controlled process — doubling the scan rate multiplies peak current by roughly 1.41, not by 2. Faster scan rates also push the peaks further apart and shorten the time available for any coupled chemical reaction to occur, which is why running a range of scan rates is a standard way to probe reaction mechanisms.
This calculator's scan rate mode lets you flip that relationship around: if you know what peak current you're aiming for — perhaps to stay within an instrument's dynamic range — it tells you what scan rate would be needed to hit that target, given the rest of the system's parameters.
Number of Electrons Transferred (n) From Peak Current
Because peak current scales with n raised to the 1.5 power in the Randles-Ševčík equation, a measured peak current that's unexpectedly large or small compared to a one-electron prediction can hint at how many electrons a redox event actually involves. Solving n = [ip / (2.69×10⁵ A √D C √v)]^(2/3) from a single measurement gives an estimate, though in practice n should always come out close to a whole number — 1, 2, or occasionally 3 — since electrons transfer in discrete units.
This calculator's electrons-transferred mode performs that calculation and reminds you to round to the nearest whole number, since a value like 1.85 or 2.1 almost always means measurement uncertainty or a slightly non-ideal system rather than a genuinely fractional number of electrons.
Typical Values for Cyclic Voltammetry Parameters
A handful of typical ranges help sanity-check any Randles-Ševčík calculation. Electrode areas for common disk electrodes run from about 0.02 cm² for a small ultramicroelectrode up to around 0.2–0.3 cm² for a standard glassy carbon disk. Diffusion coefficients for small organic and organometallic molecules in typical solvents usually fall between 1 × 10⁻⁵ and 1 × 10⁻⁶ cm²/s, while larger biomolecules like proteins can be one or two orders of magnitude slower.
Concentrations in a typical benchtop cyclic voltammetry experiment range from roughly 0.1 mM up to 10 mM, and scan rates commonly span from about 10 mV/s for slow, careful mechanistic studies up to several V/s for fast kinetic measurements. If your calculated peak current comes out many orders of magnitude away from a microamp-to-milliamp range, it's worth double-checking that your inputs — especially concentration and diffusion coefficient units — are entered the way you intended.
Common Mistakes When Using the Randles-Ševčík Equation
The single most common error is a unit mismatch on concentration: the Randles-Ševčík constant 2.69 × 10⁵ requires concentration in mol/cm³, not mol/L, and mixing this up produces a peak current that's off by a factor of exactly 1000. This calculator's concentration unit selector, which converts mM, µM, and M into mol/cm³ internally, exists specifically to prevent that mistake from creeping into a real calculation.
A second frequent slip is forgetting that this simplified constant is only valid at 25 °C — running an experiment at a noticeably different temperature, such as a cold room or a heated cell, technically requires the fuller form of the equation with explicit Faraday and gas constants and the actual absolute temperature, since the diffusion-limited current does depend on temperature beyond just its effect on the diffusion coefficient itself.
Cyclic Voltammetry Peak Current FAQ and Quick Reference
The Randles-Ševčík equation at 25 °C is ip = (2.69 × 10⁵) n^(3/2) A √D C √v, with ip in amps, A in cm², D in cm²/s, C in mol/cm³, and v in V/s. It applies to a reversible, diffusion-controlled redox couple; for a quasi-reversible or totally irreversible system, the peak current depends on the electron-transfer rate constant as well, and this simplified equation only gives an approximate answer.
This free online cyclic voltammetry peak current calculator is meant to support coursework, exam preparation, and everyday electroanalytical calculations. For instrument calibration, publication-quality results, or safety-critical electrochemical work, always cross-check against your own raw voltammogram data and, where possible, a literature diffusion coefficient measured under matching solvent and electrolyte conditions.
Frequently Asked Questions
What is the Randles-Ševčík equation used for?
It predicts the peak current of a reversible, diffusion-controlled redox reaction in cyclic voltammetry, or lets you solve backwards for the diffusion coefficient, concentration, scan rate, or number of electrons transferred from a measured peak current.
What units does the Randles-Ševčík equation need?
At 25 °C, area in cm², diffusion coefficient in cm²/s, concentration in mol/cm³, and scan rate in V/s give peak current in amps. This calculator converts common lab units (mM, mV/s, µA) into these base units automatically.
Why does peak current depend on the square root of scan rate?
For a diffusion-controlled process, the thickness of the depleted diffusion layer at the moment of the peak scales with the square root of time, and time is inversely tied to scan rate, which produces the √v dependence seen in the equation.
How do I know if my cyclic voltammetry reaction is reversible?
Check the peak separation (ΔEp, ideally near 59/n mV at 25 °C) and the ratio of anodic to cathodic peak currents (ideally close to 1). This calculator's reversibility checker computes both from your peak potentials and currents.
Can this calculator find an unknown diffusion coefficient?
Yes. Switch the mode to diffusion coefficient, enter your measured peak current along with the number of electrons, electrode area, concentration, and scan rate, and it rearranges the Randles-Ševčík equation to solve for D.