2 LED Series driven by 12 volts - resistor recommendation

I am using a uln2803a transistor array to drive a LED series ( 2 ) . The LEDs are 5 mm LED. blue and white. This is using 6 pins total of 12 LEDs of the uln2803a . The. What is recommended for the current limiting resistor for the LEDs ( 12 volt is the source ), ? I was using 200 ohm resistors ( 1/4 watt ). There is some heat i am noticing. Do i need to use 1/2 watt resistor instead? This will be in a closed box with little air flow.

The uln2803a is driven by a Arduino Nano using PWM /digitical pins ( 6 of them ) to the uln2803a–not sure if that is relevant or not.

Thanks for any guidance here. If i need to explain more I will. Will throw together a diagram if needed. Hopefully it is just some math i need to work through.

thanks!

Leds have typical forward voltages , depending on the colour, and you can look those up ( Vf) Or assume around 2volts
Say for example it’s Two leds in series off 12v . Each drops 2v so you have 8v across the resistor .
If you want to drive then at 10mA ( typical value) , then you need 8/10 1000 ohms , 800ohms . Pick an 820
Resistor . Power dissipated is V^2/R . In this case 8
8/800= 0.08 watts

Ok. thanks hammy

. I am using blue LED ( from the datasheet ) it is 3.2 volt 20mA.

so..
Total drop will be 6.4 ( series of two LED )
volts remaining across the resistor will be 5.6.
I would like to drive this at 20ma.
5.6/20 * 1000 = 280ohm
Power is
5.6* 5.6/280 = .112 watts
1/4 watt resistor should be good for handling the heat?
did i do this correctly?

Your calculations look good to me!

...If the LEDs are bright-enough you may not need to run them at 20mA and a higher-value resistor might be OK.

Add about 1V voltage drop on the Darlington driver.