Is My Water Heater Dying?

There's more to it than that! Electric is nearly 100% efficient. A gas WH can have a large range from 50-90% efficient. Standby losses are a little higher on gas. The gov labels should give you a good idea of the relative costs between same sized WH. Then, refactor for your local energy costs. The labels will say what numbers they used to come up with the cost.

I know of no place that heating water with electricity is cheaper than heating with gas. Not only cheaper, but way, way faster recovery so you don't need as large a heater with gas.

Gary Swart said:

I know of no place that heating water with electricity is cheaper than heating with gas. Not only cheaper, but way, way faster recovery so you don't need as large a heater with gas.

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Efficiency and cost are 2 different things.

Jadnashua is correct that electric water heaters are 100% efficient.
The element is immersed in water and there is no other place the heat can go from the element.

With a fuel fired water heater there is heat from the burner that leaves the unit without heating the water. This is the heat that goes out the vent. hence the less than 100% efficiency.

Now the cost is a whole different factor...
The electric company knows that...
Don't they use gas to boil water to make electricity?