How big a resistor does an LED need

Suppose that we use an LED with Maximum of 3 volts, and a safe current of 20mA.

 I’m going to limit it to 2.5 volts, to be on the safe side. We have 6 volts of battery power. Subtract 2.5 from 6 and we get 3.5. So we need a resistor that will take 3.5 volts from the circuit, leaving 2.5 for the LED.

The current flow is the same at all places in a simple circuit. If we want a maximum of 20mA to flow through the LED, the same amount of current will be flowing through the resistor.

 Now we can write down what we know about the resistor in the circuit. Note that we have to convert all units to volts, amps, and ohms, so that 20mA should be written as 0.02 amps:

 V = 3.5 (the potential drop across the resistor)
 I = 0.02 (the current flowing through the resistor)

We want to know R, the resistance. So, we use the version of Ohm’s Law that puts R on the left side: R= V/I

Now plug in the values:
R = 3.5/0.02

Run this through your pocket calculator if you find decimals confusing. The answer is:
R = 175Ω

It so happens that 175Ω isn’t a standard value. You may have to settle for 180 or 220Ω, but that’s close enough.