I was going to be silly and say "physics". These heating elements are just a big resistor that is fixed. The currently flow is proportional to the voltage applied. If you halve the voltage, you halve the current. Since power is voltage x current, you've halved the voltage, halved the current and therefore have to divide power by 4.
In numbers it goes like this:
4500w / 240 (rated voltage) = 18.75 Amps (current at rated voltage)
240v / 18.75a = 12.8 ohms (this means the element is 12.8 ohms fixed so all other voltages applied can be figured out around this.
120v / 12.8 = 9.375 a given the new voltage.
120v x 9.375a = 1125 watts.
Let's say your grid is actually running 111v:
111v / 12.8 ohms = 8.67a
111v x 8.67a = 962 watts actual
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