For a load that has to ride through a power loss, this supercapacitor calculator finds the hold-up time between two voltages at constant power or current, including the effect of ESR, or the capacitance that hold-up time needs. It handles series and parallel packs and shows the result at end of life.
Use power for a regulator or DC-DC converter load.
Leave at 100 % if the power above is already at the capacitor.
The charged voltage, before the load connects.
Where the converter or load stops working.
Solving for capacitance holds this fixed.
Optional: flags overvoltage.
Optional: from the datasheet. The presets use the pulse or absolute maximum rating.
Hold-up time
39.45 s
Use DC ESR, the value for discharges lasting seconds. A 1 kHz figure is usually lower, and ESR also rises when the cell is cold.
Hold-up against load, this pack
| Power at the capacitor | With ESR | No ESR | Lost to ESR |
|---|---|---|---|
| 250 mW | 159 s | 160 s | 0.3 % |
| 500 mW | 79.5 s | 80 s | 0.7 % |
| 1 W | 39.5 s | 40 s | 1.4 % |
| 2 W | 19.5 s | 20 s | 2.7 % |
| 4 W | 9.46 s | 10 s | 5.4 % |
For a regulator load, t = C(V1² − V2²) ÷ (2P). A 10 F cell discharged from 3 V to 1 V into a 1 W load through a 90 % converter draws 1.11 W and lasts 36 s, or 35.5 s once its 26 mΩ ESR is included. For a constant current I, t = C(V1 − V2 − I × ESR) ÷ I. Allow for 30 % less capacitance and double the ESR at end of life.
The model behind this supercapacitor discharge calculator is an ideal capacitor in series with a fixed resistance. V1 is the charged voltage before the load connects, and V2 is the minimum voltage at the terminals.
That is Eaton’s Vdrop = I(R + t/C) rearranged for t, with the total drop set to V1 − V2.
With ESR, the load current follows from P = Vt × I and Vt = Vc − I × R, where Vc is the internal capacitor voltage. Integrating C dVc = −I dt gives a closed form with no time-stepping:
The load can only draw power P while Vc is at least 2√(R × P), which is the same limit as the data sheet figure P = V² ÷ (4 × ESR). The calculator stops there if your minimum voltage is lower. For a pack, C = C cell × strings ÷ cells in series and R = R cell × cells in series ÷ strings.
The capacitor supplies 1.11 W at 90 % efficiency. The ideal formula gives 10 × (9 − 1) ÷ (2 × 1.111) = 36 s. With 26 mΩ of ESR the terminals step to 2.99 V when the load connects, the internal voltage ends at 1.029 V, and the hold-up is 35.5 s. Current grows from 372 mA to 1.11 A at the end of the discharge.
At 100 µA the ESR drop is only 7.5 µV, so t = 3.3 × 1.2 ÷ 0.0001 = 11.0 hours (39.6 ks). Leakage now matters: adding Eaton’s nominal 15 µA shortens that to 9.6 hours, and leakage rises with temperature.
Five cells at 3.2 mΩ give 16 mΩ. At 90 % efficiency the pack supplies 33.3 W, and the formula gives 37.7 F from 12 V to 6 V. Allowing for 2 × ESR and a 30 % capacitance loss raises it to 54.7 F for the pack, or 274 F per cell. At 12 V the cells share an average of 2.4 V, but a ±20 % capacitance spread with no balancing would put 3.27 V on the smallest one, above a 2.7 V rating.
Rated values, computed energy and power limit, and a single-cell hold-up at 5 W from rated voltage to 1 V including the maximum initial ESR.
| Cell | C | Rated | Max ESR | Stored energy | V²/(4 ESR) | Hold-up at 5 W |
|---|---|---|---|---|---|---|
| Eaton TV1020-3R0605-R | 6 F | 3 V | 35 mΩ | 27 J | 64.3 W | 4.36 s |
| Eaton TV1030-3R0106-R | 10 F | 3 V | 26 mΩ | 45 J | 86.5 W | 7.46 s |
| Eaton TV1840-3R0606-R | 60 F | 3 V | 13 mΩ | 270 J | 173 W | 46.4 s |
| Eaton TV1860-3R0107-R | 100 F | 3 V | 11 mΩ | 450 J | 205 W | 77.7 s |
| Maxwell BCAP0360 | 360 F | 2.7 V | 3.2 mΩ | 1.31 kJ | 570 W | 224 s |
The fraction of stored energy between the two voltages is 1 − (V2/V1)². It does not depend on the capacitor, so it is the first check when choosing a voltage window.
| V2 / V1 | Energy used | Energy left behind |
|---|---|---|
| 0.80 | 36.0 % | 64.0 % |
| 0.75 | 43.8 % | 56.3 % |
| 0.67 | 55.6 % | 44.4 % |
| 0.50 | 75.0 % | 25.0 % |
| 0.33 | 88.9 % | 11.1 % |
| 0.25 | 93.8 % | 6.3 % |
Capacitance and ESR are treated as constants, but real supercapacitors have a distributed structure: voltage recovers a little after a pulse, and capacitance is lower for very short pulses. ESR rises at low temperature, so check the cold case. Keep the charged voltage at or below the rating: Eaton notes that elevated voltage and temperature shorten life, and that a 10 °C rise cuts lifetime by about half. Converter efficiency usually falls at low input voltage, so use the efficiency at the low end of the window. In a series string, also protect against reverse voltage on a weak cell when the pack is fully discharged. Datasheet capacitance tolerance, often −10 to +30 %, is separate from aging.
At constant power, t = C(V1² − V2²) ÷ (2P) for an ideal capacitor. A 10 F cell from 3 V to 1 V at 1.11 W gives 36 s; including its 26 mΩ ESR gives 35.5 s. At constant current, t = C(V1 − V2 − I × ESR) ÷ I.
Use constant power when the load is behind a regulator or DC-DC converter, because its input current rises as the capacitor voltage falls. Use constant current for a load that draws a fixed current whatever the voltage, such as an RTC or a circuit behind an LDO.
ESR causes an instant voltage step when the load connects, and it wastes I²R during the discharge. It matters most for high power and when the minimum voltage is close to the start voltage. At very high power the load cannot run at all: the limit is V²/(4 × ESR).
The usable fraction is 1 − (V2/V1)². Discharging to half the start voltage uses 75 % of the stored energy, and the rest stays behind because the load’s minimum voltage has been reached. The calculator above reports the energy stored, delivered, lost in ESR and left at cutoff.
The calculation is the hold-up formula solved for C, then raised for aging. A 30 W load for 60 s through a 90 % converter from 12 V to 6 V needs 37.7 F as a new pack, or 54.7 F with the end-of-life margin.
Yes. Supercap and ultracapacitor are other names for the same parts, most often electric double-layer capacitors, so the same formulas apply.
End of life is commonly defined as a 20 to 30 % capacitance loss and a doubled ESR. Eaton’s TV series allows up to 30 % and 200 % of the initial ESR, Maxwell’s BCAP0360 20 % and twice its maximum initial ESR. The calculator shows the result at C × 0.7 and ESR × 2.
Yes, unless the voltage is far below the rating. Each cell in a series string takes the same charge, so a cell with low capacitance rises fastest. Leakage differences then move the voltages further over time. Eaton suggests passive resistors passing at least 50 times the worst-case leakage, and recommends passive balancing only for packs that do not regularly charge and discharge.
For long hold-ups, yes. Eaton’s 3.3 F TV0820 has a nominal leakage of 15 µA after 72 hours of charging. That is small against most loads but it shortens a 100 µA RTC reserve from 11.0 to 9.6 hours.
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