First time poster here -- Hello all !
The radiant elements in stoves or kettles are close to 100% efficient, meaning all the energy is turned into heat. The differences, if any, during heating occur if some of the heat is lost to the surroundings rather than going into the water. Surroundings can be the container the water is in, or the environment. Microwaves come very close to converting 100% of electricity to heat that does go into the water container and water. This is as good as it gets if the heat source is electricity.
Conclusion #1: if you are using a stove-top, try to use a pot that covers the entire heating surface. If you prefer a kettle, buy an well-insulated one.
Second, any heated water not used is wasted. Even if it is used later, the amount it cooled down is wasted. This is the problem with kettles that keep the water warm -- heat is lost continuously from the less than perfectly insulated kettle.
Conclusion #2: Heat up only what you are using right now.
My choice: I heat up one cup at a time in the microwave.
Theoretical best option: if you have tap hot water from natural gas, fill up a thermos with hot water from the tap. Microwave the amount you are using right now for a few seconds to bring it to boiling. I say theoretical because one usually has to account for the wasted heat going down the drain until the water is hot. However, if you have a habit say of washing dishes in warm water, you could fill thermos at that time and avoid the warm-up penalty. Nowadays I pay 11 cents a kwh for electricity, and 2.4 cents a kwh for natural gas. My local boiler is 67% efficient, so my actual cost to add a kwh of energy to water is 2.4/0.67 = 3.6 cents a kwh. A decent thermos probably will retain 80% of heat for 6 hours (my guess,) so the cost per kwh using tap hot water is 3.6/0.8 = 4.5 cents -- less than half of electricity.
For those interested in environmental cost, natural gas tends to be a much preferred source to heat stuff up than electricity because grid electricity usually has a large component of coal, and central power plants are in general only one half as thermally efficient as a natural gas burner in our homes.
