Stick with E12 series resistance values if possible. 10,12,15,18,22,24,27,33,39,56,68,82 repeated, multiplied or divided by a factor of 10.
- 1.0, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2,
- 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82,
- 100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820,
- 1 k, 1.2 k, 1.5 k, 1.8 k, 2.2 k, 2.7 k, 3.3 k, 3.9 k, 4.7 k, 5.6 k, 6.8 k, 8.2 k,
- 10 k, 12 k, 15 k, 18 k, 22 k, 27 k, 33 k, 39 k, 47 k, 56 k, 68 k, 82 k,
- 100 k, 120 k, 150 k, 180 k, 220 k, 270 k, 330 k, 390 k, 470 k, 560 k, 680 k, 820 k,
- 1 M, 1.2 M, 1.5 M, 1.8 M, 2.2 M, 2.7 M, 3.3 M, 3.9 M, 4.7 M, 5.6 M, 6.8 M, 8.2 M,
- 10 M
https://en.wikipedia.org/wiki/E_series_of_preferred_numbers
For your circuit assuming red led with Vf of 1.2v and max current of 20mA
V=IR (14.2-1.2)/0.02=R
R=650
nearest preferred value=680 Ohm
Wattage rating for resistor W=VI or substituting I=V/R W=V^2/R 13^2/680
=0.248W. So at least a 1/4W resistor rating 0.25W
A 12V battery is never 12V. It varies between fully charged 14.2, to 11 flat, for a lead acid battery. Use the worst possible voltage for your safety calculations.
This is true for ANY battery.
If you are using a fully regulated power supply that fixed voltage is what you'd use. However, fully regulated supplies can fail. How critical is your circuit? What happens when the power supply fails?
There was a power supply I used to use that would chuck out 32V when it failed. And it did fail. We had to get a special circuit to protect the rest of the equipment as it was over $1000 downstream of the power supply. Plus the chaos it caused. So these things can, and do happen. We eventually used another brand.
