Double Layer Capacitance Calculator
Find specific and total electrochemical double-layer capacitance from the capacitive current, electrode area, and scan rate measured in a non-Faradaic cyclic voltammetry region.
🔋 What is Double Layer Capacitance?
Double-layer capacitance (Cdl) describes how much charge accumulates at an electrode-electrolyte interface for each volt of applied potential, arising purely from ions in solution lining up against the charged electrode surface, with no chemical reaction involved.
Electrochemists rely on this measurement constantly, to estimate the electrochemically active surface area of catalysts and porous electrodes, to separate capacitive background current from Faradaic reaction current in a voltammogram, to characterize supercapacitor electrode materials, and to diagnose whether an electrode surface has become rougher or more porous over repeated cycling.
A common point of confusion is treating Cdl as identical for every electrode of the same geometric area. It isn't, real electrode surfaces are rarely perfectly smooth, so their measured (total) capacitance often exceeds what a flat, ideal surface of the same footprint would show, which is exactly what surface-area-normalized specific capacitance is meant to reveal.
This calculator takes the capacitive current measured in a non-Faradaic region of a cyclic voltammogram, along with electrode area and scan rate, and computes both the specific capacitance (per unit area) and the total capacitance of the electrode.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Smooth Planar Electrode
ic=1 µA, A=1 cm², ν=50 mV/s
Example 2 — Smaller Electrode, Faster Scan
ic=2.5 µA, A=0.5 cm², ν=100 mV/s
Example 3 — Larger Electrode, Slow Scan
ic=0.8 µA, A=2 cm², ν=20 mV/s
❓ Frequently Asked Questions
🔗 Related Calculators
What is electrochemical double-layer capacitance?
The electrical double layer forms when ions in solution accumulate near a charged electrode surface, behaving like a parallel-plate capacitor. Double-layer capacitance (Cdl) quantifies how much charge this interface stores per volt of applied potential, typically expressed per unit electrode area in µF/cm².
How do you calculate double-layer capacitance from cyclic voltammetry?
In a potential window with no Faradaic reaction, the measured current is purely capacitive: ic = Cdl x A x ν, where A is electrode area and ν is scan rate. Rearranging gives Cdl = ic / (A x ν), so measuring the capacitive current at a known scan rate and area directly yields Cdl.
Why measure Cdl at multiple scan rates instead of just one?
Plotting capacitive current against scan rate for several scan rates produces a straight line through the origin with slope Cdl x A. Fitting a line through multiple points averages out measurement noise and gives a more robust Cdl estimate than relying on a single scan rate.
What is a typical value for double-layer capacitance?
Smooth, planar metal electrodes typically show 10-40 µF/cm2 of specific double-layer capacitance. Rough or porous electrodes, such as catalyst-coated carbon supports used in fuel cells and batteries, can show much higher apparent capacitance because their true surface area is larger than their geometric footprint.
How is double-layer capacitance used to estimate electrochemically active surface area (ECSA)?
ECSA is estimated by dividing the measured total double-layer capacitance of a rough electrode by a reference specific capacitance value for a smooth surface of the same material. A higher measured Cdl relative to the geometric area implies a proportionally higher electrochemically active surface area.
What potential window should be used to measure Cdl?
Choose a potential range where the cyclic voltammogram is flat and featureless, with no oxidation or reduction peaks, so that the recorded current is purely non-Faradaic (capacitive) charging current rather than a mix of capacitive and Faradaic current.
What units does this calculator use?
Capacitive current is entered in microamps (µA), electrode area in square centimeters (cm2), and scan rate in millivolts per second (mV/s). The output specific capacitance is in µF/cm2 and total capacitance is in µF.
Does double-layer capacitance depend on scan rate?
In an ideal, purely capacitive potential window, Cdl itself is a constant material property and does not depend on scan rate, only the measured current does (current scales linearly with scan rate). If calculated Cdl varies noticeably across scan rates, it often signals a non-ideal or partially Faradaic response.
How does double-layer capacitance differ from pseudocapacitance?
Double-layer capacitance stores charge purely electrostatically, through ion accumulation at the interface, with no chemical reaction. Pseudocapacitance involves fast, reversible Faradaic reactions at or near the surface, it can store much more charge per unit area but behaves electrically similar to a capacitor over a limited voltage range.
Why is Cdl important for supercapacitor and battery electrode design?
Higher double-layer capacitance per unit area generally means a material can store more charge electrostatically, which is central to supercapacitor performance. It also affects the non-Faradaic background current in battery electrodes, which must be separated from the Faradaic (charge-storage) current during analysis.