*100W element? Sure. Just have to use up the battery in 3 calculators to figure out which one you need.*

I'll send you my solar powered calculator. I don't know how to use it..

Who needs a calculator? P = E^2 / R. Assuming you're using a water heating element (or a good fan on a space heater) so R doesn't vary too much with temperature:

(70^2) / R = 100; (120^2)/R = rating. (E^2)/R = P

(70^2)/100 = R = (120^2)/rating multiply both sides by R, divide both

by W. Brings out R, so equate.

rating*(70^2) = 100*(120^2) Drop extra "R". Multiply both sides

by rating and desired power to bring

them above the division bar.

rating = 100 * (120^2) / (70^2) Divide both sides by (70^2) to get

"rating" to stand alone.

rating = 100 * (120 * 120) / (70 * 70) Expand squares.

rating = 100 * (12*12) / (7*7) Divide top and bottom of ratios

by 10 to get rid of extra zeros.

rating = 100 * 144/49 Do the multiplies for the squares.

rating = 100 * 288/98 Double top and bottom of ratio to

get the denominator close to a

round number.

rating ~ 100 * 294/100 Adjust top and bottom up by

about 2% to get to a round

number. (A calculator would have

gotten 293.8775510. To three

significant figures (i.e. more than

we really have) that's dead on.)

Cancel the 100s and you get 294, which is within 2% of 300.

300W isn't a typical value for heating stuff (though you could parallel three 100W devices). But 250 is, and it's only low by about 16%. If you're using something that heats up a lot (like a lamp or a hot-wire space heater element) it will be running cool and have a substantially lowered resistance, so a 250W nominal device might actually pull closer to your desired 100 watts than the 83 you'd expect from assuming the resistance is the same under a factor-of-three power drop.