Modern Headlights

What kind of amps do headlights draw

Watts divided by volts equals amps. Be careful to use the right watts and volts, though. Wattages are a little more difficult to compare than it might seen, because there are nominal wattages and actual wattages.

The "12v, 60/55w" rating of a common H4 or 9003 bulb (found on the bulb package and in the owner's manual), for example, is a nominal rating at 12.0 volts. The regulation
governing car headlamp bulbs in North America lists maximum ratings at 12.8 volts, while the regulation in Europe (used throughout the rest of the world) gives nominal 12v and maximum 13.2v wattage ratings. Because wattage increases with voltage, all of these numbers are different. Here are all of the specs on that "12v, 60/55w" bulb:

International regulation says:
60/55w at 12.0v, nominal wattage
75/68w at 13.2v, maximum wattage

US regulation says:
72/65w at 12.8v, maximum wattage

This is not three different bulbs, it is the permissible specifications of ONE bulb at three different test voltages!

No need to go digging through the regulations to find the actual wattage specs for whatever type of bulb you're working with; just apply a 25% margin (multiply the nominal "on the box" wattage by 1.25) and divide by 12.8v and you'll get amp figures that are a little overstated, but that just means you'll wind up using wires and parts a little heavier-duty than they have to be; nothing wrong with that.

So, still looking at that "12v, 60/55w" H4 bulb:

60 × 1.25 = 75
55 × 12.5 = 69

75 ÷ 12.8 = 5.9 amps on high beam
69 ÷ 12.8 = 5.4 amps on low beam

Per headlamp.

I like to use relays with capacity well in excess of what's needed. Reliable-brand 20A or 30A relays are readily available in a variety of configurations.