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1 BTU = 1.055 kilojoules. (1 joule per second = 1 watt, or 1 joule = 1 watt-sec)

1 kWh = 3.6 megajoules (1000 x 3600 watt-sec = 3600 kilojoules)

3600000/1055 = 3412.3

So 1 kWh is the energy equivalent of 3412.3 BTUs.
The reverse conversion is that 1 BTU = 0.000293 KWh

*However, a kWh is energy used in work over time, while BTUs are energy content.

WattHours (Wh) or BTU's are measurements of Energy: which is how much energy is used (a certain amount). Conversely, watt and hp are measurements of power, which is how fast energy is being used (a certain rate).

Over the last century Wh, KWh, and MWh has replaced BTU in all non-heating uses of energy, except in scientific use (prefers the joule, J). In describing thermal energy use however, BTU (larger amounts of energy) and calories (smaller amounts of energy) and sometimes therms (very large amounts) are still used.
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