Does hand washing or machine washing dishes costs less? A lot depends on how much water you use when washing by hand. If you leave the water running through the whole wash and rinse process that will use a lot of water. If you run a couple inches of water in each sink or in dishpans and wash and rinse using just that, well, that’s a whole lot less.
You can compare for yourself and know for sure. First find out how much water your machine uses. It will say in the manual or on the manufacturer’s website.
Then wash a comparable amount of dishes by hand and track how much water you use. You can use dishpans or whatever large containers you have and measure how much water they contain. Or, you can use the sink directly and measure the water as you put it in, perhaps by filling a quart pitcher repeatedly and pouring it into the sink.
Luckily you only have to do this tedious stuff once, just to find out the comparison quantity of water. When figuring comparative costs you also have to factor in the cost of buying, maintaining and repairing the dishwasher itself, where hand washing has none of those costs. Hand washing still uses electricity to heat the water, but doesn’t use any to power the washing, nor for drying.