One quantity, many units
Energy is the capacity to do work, and every unit here measures the same thing on a different scale. The SI unit is the joule, the work done pushing with one newton over one meter. A kilojoule is 1,000 J and a megajoule a million. The calorie was defined as the heat that raises one gram of water by one degree Celsius, fixed at 4.184 J; the Calorie printed on a US nutrition label is a kilocalorie, 4,184 J, which is why the label capitalizes it. The British thermal unit does the same job in customary units, raising one pound of water by one degree Fahrenheit, and equals 1,055.056 J.
Electric utilities bill in kilowatt-hours: a kilowatt drawn for one hour, which is 3,600,000 J or 3.6 MJ. Gas utilities bill in therms, defined as 100,000 BTU, so a therm is 105,480 kJ or 29.30 kWh. Mechanical work in the US is often quoted in foot-pounds at 1.35582 J each, and physicists shrink all the way down to the electronvolt, 1.602177 x 10 to the minus 19 joules, the energy an electron gains crossing one volt.
Worked examples
Your bills: one kWh is 3,412 BTU. If a gas furnace burns 60 therms in a cold month, that is 6,000,000 BTU or 1,758 kWh of heat. At $1.40 per therm that month costs $84; buying the same heat as electricity at 17.5 cents per kWh would cost $308, which is why gas heat still dominates in cold states. A 1,500 W space heater running eight hours uses 12 kWh, about $2.10, and delivers 40,946 BTU.
Food and exercise: a 250-Calorie granola bar holds 250 kcal = 1,046 kJ = 0.29 kWh, roughly what a laptop uses in six hours. Running a 5K burns about 300 Calories, or 1,255 kJ. Batteries: a phone battery marked 4,000 mAh at 3.85 V stores 15.4 Wh = 55,440 J, while an electric car with a 75 kWh pack stores 270 MJ, the energy in about 2.2 gallons of gasoline at 114,000 BTU per gallon.
Which calorie, which BTU
There are several slightly different definitions of the calorie and the BTU, differing by a fraction of a percent depending on the starting water temperature. This converter uses the thermochemical calorie (4.184 J) and the International Table BTU (1,055.056 J), the two most common choices in US engineering and nutrition. The therm is the US definition, 105,480 kJ. Differences at this level never matter for a utility bill or a diet, but they can matter in laboratory work, so check which convention a standard specifies.
Keep energy and power straight: joules and kWh are energy, while watts and BTU per hour are rates. Multiply a power by a time to get energy, and divide energy by time to get power. Also note that a therm of gas and a kWh of electricity are not interchangeable in practice, since furnaces are 80 to 97 percent efficient while resistance heaters are 100 percent and heat pumps can exceed 300 percent.