A BTU is the amount of energy needed to raise 1 lb of water 1 deg. Time is of no relevance in this formula up to this point. So, lets look at a real life example. My pool holds 45,000 lbs of water. My heater is rated at 100,000 BTU input and 80,000 of output. This puts my heater at 80% efficiency. This is about where most pool heaters come in at and is also something most forget. This is also the hourly burn rating of the heater. It does not burn 100,000 BTU's of gas instantly or constantly but, rather over an hours time it consumes 100,000 BTU worth of fuel (nat gas)
So, at 80,000 output (the other 20,000 goes up the chimney) and 45,000 lbs of water, I can raise my pool temp 1.77 deg (calculated). Real world will be a bit different as ambient air temp, wind and sun exposure will all contribute to an increase or decrease in actual temp change. This summer, my effective gas cost per therm varied by month from $.18 - $.25/therm. With that, when I went out on a Sat morning and turned the pool heater on for 5 hours, I consumed about 5 therms of fuel for a cost of $1.25 (.25/therm) and was able to bring the pool temp up with the help of the sun, about 2 Deg/hr. Now, my schedule and time commitments during the week do not allow me to use the pool much during the week, so I don't bother heating it then. My wife and I do use it on occasion on the weekends, so that is when I heat it. I may also do the same on Sunday mornings if I feel the water is a bit too cool for us so figure anywhere from 5-15 hours of run time on the weekends. I also use a solar cover on the pool at night as the night time temps around here can sometimes drop into the upper 50's but, mostly are in the mid 60's. This is important as Greater differences in temp will contribute to greater evaporation/heat loss. All that considered, my weekly heating costs for my pool are ~$5.00
Next, my friends pool...He keeps his 100,000 lbs of water at 85-90 deg all the time. He also refuses to use a solar cover at night as his wife hates not only the look of it but, also having to take it off and put it on. Since he keeps his pool heater "on" all the time it cycles off and on all day/night long. This contributes to a higher energy bill in both electric cost to run the pump full time as well as an increase in gas costs. We figured his heater runs about a total of 10 hours/day for a cost, roughly, of $5.00/day (250,000 BTU heater ~ $.50/hr of fuel)So a monthly cost of $150 is not unrealistic in his case.
Bigger pools = bigger heaters = bigger bills