heating water with a water heater vs. a microwave - time and cost

Let’s say I’m making some tea, so I need hot (boiling, or at least near-boiling) water. I can use hot or cold tap water, but the heater takes a little while to really start up. In other words, when you turn on the hot water, it comes out cold for a minute or so, then gradually becomes hot.

So, I can turn on the water, hold my hand under it until it gets fairly hot, then fill up a cup, and put that in the microwave. Or I can fill the cup immediately and put it in the microwave. It’s going to end up at the same temperature either way, it’s just that the water heater can do some of the work, or the microwave can do it all.

Which way costs less money in the long run, and which way takes less time? I know this probably depends on a zillion different factors, including the type of heater I have, the temperature of the cold tap water, the cost of electricity, etc. I don’t have that information, and honestly, I don’t really care what the answer is for practical purposes, I’m just curious. I guess I want a formula, rather than a number, if that makes sense. Any ideas?

There are too many undefined/undefinable variable to create a simple formula.
Where is your hot water heater in relation to the faucet?
Is it a conventional or “an instant on point of use” device?
What is the output temperature?
What size is the pipe?
How much water do you want/need to make a cup tea?
Four oz? Six oz?
Probably drawing a cup of cold water and using the mircowave is cheapest method!

Hot water heater is vastly less efficient. You have to clear the water in the pipes first, so cold and moderately heated water goes down the drain. (Waste of water and energy). New water gets heated by the water heater and, if you don’t use it, eventually cools. (More wasted energy.) If you’ve just done the dishes and the hot water heater and pipes are full of 120 degree water, than you’re not actually wasting energy, but you’re not saving much either. You still have to heat the water another 100 degrees or so.

An electric immersion heater or one of those hot water heaters built directly into the sink would be slightly more efficient than a microwave. However, we are talking a matter of a couple dollars over the course of a year, so it’s barely worth the effort of thinking about it.

Finagle has it exactly right. Another point is that water from the water heater (assuming you have a central water heater and not a point of use variety) is not the best water to use for cooking. It will have heavy concentrations of minerals and won’t be as tasty as water from the cold faucet.