How to use the supercapacitor runtime calculator
- Enter the capacitance in farads, the starting voltage and the lowest voltage the load will accept.
- Enter the series resistance (ESR) from the data sheet, or 0 to ignore it.
- Choose the type of load: constant current, constant power or constant resistance, and enter its value.
- Read the run time, the energy stored and the energy between the two voltages.
Formula
Constant current I: t = C (V0 - Vmin - I x ESR) / I
Constant power P, no ESR: t = C (V0^2 - Vmin^2) / (2 P)
Constant resistance R: t = (R + ESR) C ln(V0 / Vend), with Vend = Vmin (R + ESR) / R
Energy between two voltages = C (V0^2 - Vmin^2) / 2
With ESR and constant power the page integrates C dV / I in closed form, using I = (Vc - sqrt(Vc^2 - 4 P ESR)) / (2 ESR) for the current at capacitor voltage Vc.
Three backup scenarios
A 10 F capacitor charged to 5 V, feeding a 100 mA load that stops working below 2.5 V, with 0.05 ohm of ESR, runs for 10 x (5 - 2.5 - 0.005) / 0.1 = 249.5 s, or 4.158 minutes. The energy stored is 125 J, and 93.75 J of it lies between 5 V and 2.5 V.
A 100 F capacitor at 16 V feeding a 2 W load down to 8 V, with 0.02 ohm of ESR, runs for 4,796.61 s, about 1.332 hours. A 1 F capacitor at 5 V holding up a 10 kilohm load that needs at least 2 V, with 0.2 ohm of ESR, lasts 9,162.89 s, about 2.545 hours.
Choosing a load model
The shape of the load decides how the voltage falls. A constant current load, such as an LED driver or a simple circuit, takes the same current at every voltage, so the voltage falls in a straight line. A constant power load, such as a regulator or converter, draws more current as the voltage drops, which uses the last part of the charge faster. A resistor draws less as the voltage falls, so the voltage decays smoothly toward zero.
The run time is for a single discharge from the starting voltage. For batteries, compare with the battery life calculator, and for the time constant of a resistor and capacitor, use the RC filter time constant calculator.
Limits of the estimate
Real supercapacitors lose capacitance with age and heat, leak a little all the time, and show a voltage that rebounds after a heavy load is removed. Their ESR rises as they age and when they are cold. The page treats the capacitance and ESR as constant, so treat the answer as an upper limit and keep a safety margin. For a constant power load, a converter adds its own losses, which the page does not model.
If the load is more than a capacitor can deliver through its ESR, the page tells you the largest power it can supply, which is V0 squared divided by 4 times the ESR. For voltage and current relations, see the Ohm's law calculator.
Assumptions and limits
- Capacitance and ESR stay constant during the discharge.
- Leakage current and self-discharge are not included.
- The load stops at the lowest voltage you enter, measured at the load.
- A power converter's efficiency is not included; add it to the load power yourself.
Frequently asked questions
How do I find how long a supercapacitor will last?
Divide the usable charge, C x (V0 - Vmin), by the load current for a constant current load. The page handles constant power and resistance too.
What is ESR?
The equivalent series resistance of the capacitor. It makes the voltage at the terminals drop when current flows.
Why does the answer depend on the load type?
Because the current changes differently as the voltage falls, so the charge is used at a different rate.
How much energy can I use?
The energy between the starting voltage and the lowest accepted voltage, C (V0 squared - Vmin squared) / 2, less what ESR and converters lose.