Calculate the stored energy, power density and RC time constant of an electric double-layer capacitor (EDLC) and place the cell on a Ragone chart next to Li-ion batteries and fuel cells. Vary capacitance, rated voltage, ESR and cell mass to evaluate the fit for grid buffering, regenerative braking, UAV power and engine start.
Parameters
Capacitor type
Sets the electrode chemistry and cycle-life baseline
Capacitance C
F
Rated voltage V
V
ESR (series resistance)
Ω
DC resistance of the cell — sets the power density ceiling
Cell mass m
g
Application
Verdict is judged against the typical discharge-time band
Results
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Stored energy (Wh)
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Energy density (Wh/kg)
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Peak power (kW)
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Power density (kW/kg)
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RC time constant (s)
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Cycle life (cycle)
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EDLC cross-section — ion adsorption animation
Anions and cations adsorb on the activated-carbon pore surfaces to form the electric double layer. Colour tracks the state of charge (green → orange → red).
Ragone plot — power density vs energy density (log-log)
Storage device comparison — energy density (Wh/kg)
Stored energy E (J) and matched-load peak power P_max (W). C is capacitance, V the rated voltage, ESR the equivalent series resistance. Both energy and peak power scale with V².
Energy density E_d (Wh/kg) and power density P_d (W/kg) per unit cell mass. The Ragone plot uses these two axes to compare storage technologies.
$$\tau_{RC} = C\cdot\mathrm{ESR}$$
RC time constant. 1τ corresponds to about 63 % discharge, 5τ to essentially full discharge. A large τ rules a device out of high-speed applications.
What is the Supercapacitor EDLC Ragone Plot Simulator?
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A supercapacitor — is that a capacitor or a battery? People keep calling it the best of both worlds, but what is it really?
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Think of it as "a capacitor whose electrode is made of activated carbon riddled with pores to push the surface area through the roof." A normal ceramic cap is in the microfarads, but an EDLC can reach 100 F or even 3,000 F in the same volume. Stored energy is ½CV², so when C is orders of magnitude larger, energy grows too. Crucially, charge is not produced by a chemical reaction the way a battery does it — the ions just stick to the electrode surface. So a Li-ion at 200 Wh/kg ends up at 5–10 Wh/kg for an EDLC, while the EDLC delivers 10–30× the Li-ion power density.
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OK. So what is the "Ragone plot" showing? When I move the sliders on the left, the dot on the upper-right chart moves around.
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The Ragone plot is the "map" of energy storage with energy density (Wh/kg) on the horizontal axis and power density (W/kg) on the vertical, both log scales. Up-and-right means "stores a lot and delivers it fast" — the ideal storage — but in reality nobody gets there. Each device lies along a downward band of "P × E ≈ constant". EDLCs sit upper-left (high P, low E), Li-ion lower-right (low P, high E), fuel cells further right still (very high E, low P). For C=100 F, V=2.7 V, mass=80 g you land at E_d ≈ 1.3 Wh/kg and P_d ≈ 4.6 kW/kg, right inside the EDLC zone.
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For the application setting you list "regen braking" and "engine start". Why pick an EDLC over a regular battery there?
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Because pumping a large current in and out within seconds destroys a Li-ion. In a battery, Li⁺ ions have to diffuse through the electrode lattice while reacting; rapid cycling cracks the active material as it swells and shrinks. An EDLC just lets ions adsorb and desorb, so it can run a million cycles with little degradation. A hybrid car regen brake, for example, has to swallow ~50 kW for a few seconds — do that with a Li-ion and you lose half the capacity in five years. With an EDLC the same job lasts fifteen years. Engine start is similar: in the cold you push 1,000 A for an instant, the voltage drop is set by ESR, and a milliohm EDLC wins.
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What is the "4" in P_max = V²/(4·ESR)? The text says "matched load".
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Nice catch. Hook a source (voltage V, internal resistance ESR) to an external load R_L. The power dissipated in the load is P = V²·R_L/(ESR+R_L)². Differentiating with respect to R_L and setting it to zero gives R_L = ESR, and the maximum value works out to V²/(4·ESR). That is the "matched-load peak power". In real operation half of the energy goes to the load and half to ESR heating, so the efficiency is only 50 %. Field practice is therefore to treat 30–50 % of P_max as the usable continuous limit.
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One more — RC came out as 0.5 s. Does that mean the cell discharges in 0.5 seconds?
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No. 1τ is the time for about 63 % of the charge to leave; 5τ gives essentially full discharge (99 %). For τ = 0.5 s the cell is 63 % drained in 0.5 s and 99 % drained in 2.5 s. When τ is large (high ESR or large C) the voltage sag in fast-response use becomes too big. A UAV motor that needs 10 ms response demands τ ≤ 10 ms; a grid buffer that discharges over minutes can live with τ of several seconds. Combining the "vertical position" of the dot below with τ tells you the application fit.
Frequently Asked Questions
The electrostatic energy stored in a capacitor is the integral of the source work as it is charged from 0 to V: U = ∫₀ᵛ C·v·dv = ½CV². Charging a 100F cell to 2.7V gives U = 0.5×100×7.29 = 364.5 J ≈ 0.10 Wh. In a battery the voltage stays nearly flat (plateau) as charge moves, so U ≈ V·Q, but in an EDLC the voltage falls linearly with charge, so only half the energy of an equivalent battery charge can be drawn out.
Charge in an EDLC is stored purely by ion adsorption at the electrode surface (electric double layer) with no chemical reaction or Li⁺ lattice diffusion. The equivalent series resistance (ESR) is therefore in the milliohm range and the matched-load peak power P_max = V²/(4·ESR) is on the order of kW/kg. A Li-ion battery is limited by electrode kinetics, with a typical value around 300 W/kg. That is why EDLCs are chosen for regenerative braking, engine start and other applications that need a large current burst.
A Ragone plot has energy density (Wh/kg) on the horizontal axis and power density (W/kg) on the vertical axis, both logarithmic. Moving up and to the right means a "larger and faster" device, but no real device reaches the upper-right corner; instead each technology lies along a constant P×E band. EDLCs sit in the upper left (high P, low E), Li-ion in the lower right (high E, low P), and modern designs often combine the two as a hybrid energy storage.
A symmetric EDLC (activated-carbon electrodes) has almost no electrochemical reaction, so a million cycles at 25 °C and below rated voltage typically degrades the capacitance by only about 20 %. Raise the temperature to 65 °C, or exceed the rated voltage by 5 %, and the life can drop by a factor of ten or more. LIC (lithium-ion capacitor) has a lithium intercalation reaction on one side, giving 10,000–100,000 cycles in practice; pseudocapacitors are around 100,000. Always read cycle-life numbers together with the temperature and voltage conditions.
Real-World Applications
Grid buffering (frequency regulation): Frequency-regulation (FR) duty smooths the second-to-minute fluctuations of solar and wind output with hundreds of deep cycles per day — work that destroys a Li-ion battery's life. MW-class EDLC banks (thousands of cells in series-parallel) attach to the grid through a PCS to flatten the instantaneous power waveform. Power density and cycle life dominate the decision over energy, so the choice falls in the upper-left of the Ragone plot.
Regenerative braking on hybrid cars and electric buses: The kinetic energy recovered during deceleration (tens of kW for a few seconds) sends a charging current too large for a Li-ion, shortening its life. The standard architecture parallels an EDLC module with the Li-ion so the EDLC absorbs the sharp current peaks while only the average current flows into the Li-ion. Mazda's i-ELOOP and certain PSA / Toyota systems have shipped this approach in volume.
UAV take-off and thrust peaks: Multirotors draw 2–3× steady-flight power at the moment of take-off; sizing the battery for that peak makes the airframe too heavy. Putting a small EDLC (a few hundred farads) in parallel with the main battery and letting it deliver the climb and acceleration peaks is a growing trend. With 80 g cells and 100 F as in this tool, you can budget about 4 kW/kg of peak power density.
Large diesel and marine engine start: Cold-weather diesel cranking can require over 1,000 A — well beyond the capacity of a lead-acid battery at low temperature. EDLC start modules in 12 V / 24 V systems supply the cranking peak. ESR below a milliohm keeps the voltage drop small and ensures reliable start even at −30 °C.
Common Misconceptions and Pitfalls
The biggest pitfall is thinking that an EDLC can replace a Li-ion battery. The Ragone plot makes it obvious: at 1–10 Wh/kg the energy density is only 1–5 % of Li-ion (200 Wh/kg). Run a smartphone from EDLCs and you would need 50× the mass for the same runtime. Treat an EDLC as a device that delivers power, not one that stores energy. Plan from the start on a hybrid architecture with a battery.
Next, mistaking P_max for a usable rating. At the matched load P_max = V²/(4·ESR), half the power is dissipated in the load and half in the ESR, so efficiency is 50 % at the peak. To keep the ESR heating inside the allowable temperature, the design limit is normally 30–50 % of P_max. If this tool reports P_max = 364 W, a continuous rating of 100–150 W is the safe guideline. ESR also varies 2–5× with temperature, frequency and SoC — always re-check with the worst-case datasheet number.
Third, voltage balancing in series strings. A single EDLC is rated at only 2.5–3.0 V, so a 48 V bus needs 18–20 cells in series. Cell-to-cell spread in capacitance and leakage (±20 %) drifts the voltages apart over time; the cell that runs above rated voltage degrades fast. Always include active balancing (per-cell bleed resistors or DC-DC), keeping the deviation within ±50 mV. Skip this and the life can fall by an order of magnitude.
How to Use
Enter capacitance (F) – typical EDLC values range 1–5000 F; select cell chemistry (aqueous or organic electrolyte).
Set rated voltage (V) – aqueous cells: 0.8–1.2 V; organic: 2.5–2.7 V per cell or stack voltage for modules.
Input equivalent series resistance (ESR, mΩ) – lower ESR improves power density; typical EDLC range 0.5–50 mΩ depending on cell format.
Specify cell mass (g) – use datasheet weight or measure assembled supercapacitor; mass determines energy and power density calculations.
Click Calculate to generate Ragone plot coordinates, peak power (kW), energy density (Wh/kg), and RC time constant (τ = ESR × C).
Worked Example
A 3000 F EDLC cell rated 2.7 V with ESR 2 mΩ and mass 350 g: Stored energy = 0.5 × 3000 × (2.7)² = 10.935 Wh; Energy density = 10.935 / 0.35 = 31.2 Wh/kg. Peak power at low impedance = (2.7)² / (2 × 10⁻³) = 3645 W = 3.645 kW; Power density = 3.645 / 0.35 = 10.4 kW/kg. RC time constant = 2 × 10⁻³ × 3000 = 6 seconds. Expected cycle life ≥ 1 million cycles at 50% voltage retention.
Practical Notes
Stack multiple cells in series to reach required voltage (2–48 V systems); each cell contributes its capacitance in series formula, reducing total C but raising voltage rating.
ESR increases with temperature and cycle aging; use derating factors (typically 1.5–2.0×) for worst-case power estimates in automotive or grid storage applications.
Hybrid supercapacitor (HSC) with pseudocapacitive oxide or polymer coating increases energy density to 50–100 Wh/kg but reduces cycle life to 100 k–500 k cycles.
For load-leveling in renewable energy systems, verify power density exceeds peak load transients; for energy storage, prioritize energy density (Wh/kg) and cycle count.