© John Hewes 2010, The Electronics Club
An LED must have a resistor connected in series to limit the current through the LED, otherwise it will burn out almost instantly. 
The resistor value, R is given by:
| R = (VS – VL) / I |
VS = supply voltage
VL = LED voltage (usually 2V, but 4V for blue and white LEDs)
I = LED current (e.g. 10mA = 0.01A, or 20mA = 0.02A)
Make sure the LED current you choose is less than the maximum permitted and convert the current to amps (A) so the calculation will give the resistor value in ohms ().
To convert mA to A divide the current in mA by 1000 because 1mA = 0.001A.
If the calculated value is not available choose the nearest standard resistor value which is greater, so that the current will be a little less than you chose. In fact you may wish to choose a greater resistor value to reduce the current (to increase battery life for example) but this will make the LED less bright.
For example
If the supply voltage VS = 9V, and you have a red LED (VL = 2V), requiring a current I = 20mA = 0.020A,
R = (9V – 2V) / 0.02A = 350, so choose 390 (the nearest standard value which is greater).
Working out the LED resistor formula using Ohm’s law
Ohm’s law says that the resistance of the resistor, R = V/I, where:
V = voltage across the resistor (= VS – VL in this case)
I = the current through the resistor
So R = (VS – VL) / I
For more information on the calculations please see the Ohm’s Law page.
