How can i find how much it cost to run a air heat pump in central Illinois compared to a gas furnace?

Find out what you pay per kWh, then determine the wattage used per hour of run time of the heat pump. Then multiply the two for cost of runtime per hour. Do the same with your cost per therm (100 cubic feet of natural gas). Determine the input rate of the furnace in btu per hour (100,000 btu input would equal 1 therm used per hour of runtime). Multiply the two and you have your cost per hour of runtime.

For example: at $ 1.00 per therm cost and an input rate of 80,000 btu or .8 therms, you would have a cost of $.80 per hour of runtime with natural gas. With a cost of 11 cents per kWh and a system that uses 15 amps, 15 amps x 230 volts = 3450 watts or 3.45kW, multiply that times .11 cents and your cost per hour of runtime is .38 cents. Lastly dont forget to add in the wattage per hour of the electric strip heater you will need to go with the heat pump. Dont worry about the power consumption of the indoor fan because you will need that to operate either one. Regardless of how the cost works out for you, I personally would not entertain using a heat pump in your climate.