power - How to calculate battery life

How do I calculate how long a battery operated product will run?

Here's what I've got:

1. 2 AA, 1.5V, 2700mAH batteries


2. Voltage Regulator with a Iq of 25 uA


3. Voltage Regulator Eff = 80%


4. Active Current = 50mA


5. Sleep Current = 1uA


6. Duty Cycle = 99.9% (only active 0.1% of the time)


7. Active Voltage is 3.3V

I've gone the current route and got an answer. I went the power route and got a TOTALLY different answer (days vs years different).

How do you do this?

Answer

My calculation, probably missing something, but here's what I did:

$$1 \mathrm{\ \mu A} + (50 \mathrm{\ mA} \times 0.1\%) + 25 \mathrm{\ \mu A} = 76 \mathrm{\ \mu A}$$

$$\frac{76 \mathrm{\ \mu A}}{ 80 \, \% \mbox{ efficiency}} = 88 \mathrm{\ \mu A}$$

Round up to $100 \mathrm{\ \mu A} = 0.1 \mathrm{\ mA}$

$$\frac{2700 \mathrm{\ mAh}}{ 0.1 \mathrm{\ mA}} \approx 3 \mbox{ years}$$

If you're using rechargeable batteries, they'll discharge on their own long before that. Or if any of your other calculations are off (like maybe it's a 98% instead of 99.9% sleep), that will affect it a lot too.