2
\$\begingroup\$

I'm looking at an LED light and it says it takes 2.2 watts with a 3.7V / 900 mAh battery. How do I calculate how long the LED light will last if it's on continuously?

The item in question is this

\$\endgroup\$
  • 1
    \$\begingroup\$ Given that information, you can't. You also need to know the voltage. Then it's easy. \$\endgroup\$ – Brian Drummond Sep 3 '17 at 10:40
  • \$\begingroup\$ I might be wrong but considering your LED is 3.3v: 0,9Ah * 3.3V = 2,97W of power you've available, meaning your it will last 1,32h because the LED will take 2.2W every hour. \$\endgroup\$ – TCB13 Sep 3 '17 at 10:40
  • 1
    \$\begingroup\$ @TCB13 I'm being pedantic here but a watt is power and power is instantaneous so you can't "take 2.2W every hour". The battery stores energy not power so you can take 2.2W continuously for an hour \$ (2.2\text{ watt} \cdot \text{hour}) \$ or you can express this energy in Joules. \$\endgroup\$ – Warren Hill Sep 3 '17 at 10:51
  • 2
    \$\begingroup\$ @TCB13 Yes, you're wrong. You're multiplying the forward voltage of the LED by the battery capacity (in Ah. It's a charge, not a current!), this does not mean anything. You need also the battery voltage, to know how much energy the battery has (battery capacity * battery voltage). When you have that energy, you divide it by the LED's consumption. That's the best time you can hope for, assuming a 100% efficiency of the DC/DC convertery you'll probably must insert between the battery and the light. \$\endgroup\$ – next-hack Sep 3 '17 at 10:54
  • 2
    \$\begingroup\$ @TCB13 it's not "not extremely correct". It's plain wrong. \$\endgroup\$ – Marcus Müller Sep 3 '17 at 11:14
1
\$\begingroup\$

If your battery voltage is V, its capacity (in Ah) is Q, and your lamp's power is P, and if you're using a DC/DC converter with efficiency: $$\eta$$

Then, the time is simply: $$\eta\frac{QV}{P}$$

Of course, to get the numerical result in hours, Q must be in Ah and P in W, and V in Volts.

This is a simplification, as it assumes a constant battery voltage V, until the battery is fully depleted.

| improve this answer | |
\$\endgroup\$
  • \$\begingroup\$ This is the item rads.stackoverflow.com/amzn/click/B072QL568M 3.7V \$\endgroup\$ – Jack Sep 3 '17 at 11:30
  • \$\begingroup\$ then looking at the specs put $$\eta=1$$ and V = 3.7. \$\endgroup\$ – next-hack Sep 3 '17 at 11:39
  • \$\begingroup\$ I get 1.513... Is that supposed to be in hours? \$\endgroup\$ – Jack Sep 3 '17 at 12:29
  • \$\begingroup\$ @Jack Yes. Still I guess it could be an overestimation. \$\endgroup\$ – next-hack Sep 3 '17 at 13:02
1
\$\begingroup\$

Considerations: Your LED runs at 3.3v.

  • mAh how much energy you have on your battery;
  • Know how much you'll be using every hour;
  • Consider that an amperage is a coulomb per second;

The Math: Calculate how long the battery will last by dividing its total charge in mAh by your LED load in mA.

900 mAh / 666mA = 1,36h (I've considered your LED is 3.3V meaning 2,2/3,3 = 666mA).

If you're unsure about my math, you can also use this online calculator that will give your the same result: http://ncalculators.com/electrical/battery-life-calculator.htm

| improve this answer | |
\$\endgroup\$
  • 2
    \$\begingroup\$ This assumes, that there is a linear regulator and not a switching converter, otherwise the answer is unknown without the battery voltage. \$\endgroup\$ – Arsenal Sep 3 '17 at 11:08
  • \$\begingroup\$ This is the item rads.stackoverflow.com/amzn/click/B072QL568M 3.7V \$\endgroup\$ – Jack Sep 3 '17 at 11:32

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.