I want to power my TI-84+SE calculator with a couple of super capacitors. How many farads would i need for 48+ hours of use?

I'd be more concerned with getting the circuitry to make sure you don't blow out the calc's circuits.

A true answer to this question will require a bit of experimentation (namely, maximum current draw, and minimum acceptable supply voltage). For the sake of argument, I'll assume the calculator draws about 100 mA when in use.

Based on 100 mA current draw, 100 mA * 48 hours gives us 17.28 kC. Substituting that charge into Q=CV for a capacitor at 6 Volts, we get C=2880 Farads. You'd actually need (significantly) more capacitance in practice due to the exponential discharge curve of the capacitor, but exactly how much is hard to say without knowing the calculator's minimum operational supply voltage.

I suspect the 100 mA figure is too high, though. Anybody want to do a bit of experimentation?

I've heard that 10mA is closer to the proper figure, with spikes during Flash writes. However, even 288 Farads at 6V is pretty substantial. Let me pull out my multimeter later and see what kind of numbers I can get.

When capacitors run out the voltage drops, could this damage the TI-84+SE?

No, it would just shut off and/or refuse to perform Flash operations. Doing Flash modifications with low battery can damage the Flash, but luckily the calculator checks the battery level before Flash writes.

Ah good.

The peak that the OS uses is 30mA when garbage collecting. You can see the measured values here.

You could throw in a regulator. That would keep the voltage locked no matter what until it died.

Kind of pointless, though, when the 84+ already has one internally IIRC.

Excellent resource, thanks for finding that. I was just about to grab my tools and re-ascertain those numbers. Let's say that on average the calculator will be using about 12mA at 6V while on. If I am using this supercap calculator correctly, it seems to be indicating that a 2 Farad capacitor would do the trick, combined with a 353Kohm resistor.

I think you're using it wrong. I get .23 hours of operation with V_bat between 3.5 and 6 Volts (I_typ=6 mA) on a 2 Farad capacitor.

I'd guess your units on current are wrong, since that utility takes current figures in nanoamps.

I put in 12000nA for I_typ and 16000nA for I_max. :/