How it works
A supercapacitor (EDLC — electric double-layer capacitor) stores energy electrostatically like a normal capacitor, but at 1000–10,000× the capacitance per unit volume because the charge separation happens across a molecular-scale double layer instead of a dielectric film. That makes it the right tool for hold-up power (bridging a brownout or clean shutdown window) and wrong for long-term energy storage (a battery still wins on energy density and self-discharge).
Two formulas cover almost every sizing question:
Constant current: t = C × (V1 − V2) / I
Constant power: t = C × (V1² − V2²) / (2 × P)V1 is the starting voltage (fully charged, or your normal operating rail). V2 is the cutoff voltage — the point where your downstream circuit stops working, not zero. I or P is the load during discharge.
Constant current vs constant power
A raw resistive or current-source load (an LED, a fixed-current sensor) is well modeled as constant current — current stays flat as voltage drops.
Anything behind a switching regulator is constant power. A buck converter holds its output voltage and output power constant, so as the supercap’s input voltage sags, input current rises to compensate (P = V × I, so I climbs as V falls). This drains the cap faster than the constant-current formula predicts near the end of discharge, but the total energy budget (E = ½C(V1² − V2²)) is the same either way — only the discharge shape differs.
Get the load model wrong and the calculator error compounds: modeling a buck-converter load as constant current overestimates hold-up time, because it assumes current stays at the initial (lower) value instead of rising as voltage drops.
Worked example
A sensor node needs 200 ms of hold-up at 50 mW (running off a buck converter) to write its last reading to flash before power drops. Available supercap: 1 F, 5.5 V rated, ESR ≈ 3 Ω. Supply rail runs at 5.0 V nominal; the buck converter’s minimum Vin is 3.0 V.
V1 = 5.0 V, V2 = 3.0 V, P = 0.05 W, C = 1 F
t = C × (V1² − V2²) / (2 × P)
t = 1 × (25 − 9) / (2 × 0.05)
t = 16 / 0.1
t = 160 s160 seconds of hold-up against a 200 ms requirement — wildly oversized. A 0.01 F (10 mF) cap would give t = 1.6 s, still 8× margin. This is typical: EDLC hold-up capacitors for a few hundred milliseconds of write-on-brownout protection are usually millifarad-range parts, not the multi-farad modules used for full-power ride-through.
ESR: the number the nameplate formula ignores
Every supercapacitor has equivalent series resistance (ESR) from the electrode material, electrolyte, and current collectors. The instant a load turns on, voltage sags by I × ESR before any capacitive discharge happens:
V_after_sag = V1 − I × ESRIf V_after_sag ≤ V2, the cap is functionally dead on arrival for that load. This is the single most common sizing mistake: a designer picks a cap using the nameplate C = It/V formula, ignores ESR, and finds the circuit browns out immediately under load.
Small coin-cell-style supercaps (0.1–1 F) commonly have ESR in the 3–30 Ω range. A 100 mA pulse through 30 Ω sags 3 V instantly — larger than the entire usable window on a 5.5 V-rated part with a 2.7 V floor. Large modules (100 F+) drop ESR to single-digit milliohms, making sag negligible even at several amps.
Common mistakes
Using nameplate capacitance without a tolerance margin. Supercapacitors typically carry −20%/+80% tolerance. For hold-up applications where failure means lost data, design against the minimum guaranteed capacitance, not the nominal value stamped on the part.
Setting V2 = 0. Nothing useful happens below your regulator’s minimum input voltage or your MCU’s brownout threshold. Energy stored below V2 is real but unrecoverable — set V2 to what your circuit actually needs, not zero.
Ignoring self-discharge on standby-heavy designs. Supercapacitors self-discharge faster than batteries or film capacitors — leakage current of a few µA to a few hundred µA depending on part and voltage, dropping several percent of charge per day. For a device that charges the cap once and expects to use it weeks later (rare, but it happens in commissioning/storage scenarios), self-discharge dominates over the discharge-time math here. Check the datasheet’s leakage current spec at your operating voltage and temperature.
Assuming ESR is constant across temperature and age. ESR roughly doubles from 25 °C to −20 °C for many EDLC chemistries, and increases 2–3× over a rated cycle life (typically 500,000–1,000,000 cycles, or 10 years shelf life) as the electrolyte degrades. A design with zero ESR margin at 25 °C fresh-off-the-reel may fail in the field at low temperature or after years in service.
Confusing series-stacked cell voltage with cell voltage. Supercapacitor modules stack cells in series to reach higher voltages (a 2.7 V cell stacked 3× gives 8.1 V nominal). Series stacks need active or passive voltage balancing — an unbalanced stack can overvoltage individual cells even though the pack voltage looks fine. This calculator assumes a single cell or an already-balanced pack; it doesn’t model balancing circuit losses.
When the rule-of-thumb breaks down
The t = C(V1−V2)/I and t = C(V1²−V2²)/(2P) formulas assume ideal capacitive behavior: linear voltage-charge relationship, constant capacitance, and no leakage during the discharge window. Real EDLCs deviate in three ways that matter at the margins:
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Capacitance is voltage-dependent. Measured capacitance can be 5–15% higher near the rated voltage than at low voltage, because the double-layer’s effective area changes slightly with charge density. The formulas here use nameplate capacitance, which is usually measured at a specific test current and voltage window — check the datasheet’s test conditions if you’re sizing at the edge of the tolerance band.
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Rate capability drops at high current. Above the datasheet’s rated continuous current, the effective usable capacitance drops because charge can’t redistribute across the porous electrode fast enough. For pulse loads well above rated current, budget extra margin beyond what the ESR-sag calculation alone predicts.
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Long discharge windows (minutes to hours) bring self-discharge into play. The formulas above model an instantaneous discharge process and don’t subtract leakage current. For discharge times under a few minutes, leakage is negligible. For hold-up times measured in tens of minutes or hours, add the datasheet’s leakage current as a small constant subtracted from your load current.
For anything safety-critical or data-integrity-critical, measure actual discharge time on the bench with the real load and real ambient temperature. These formulas get you to the right order of magnitude and the right part number to buy; they are not a substitute for validation.