So then, assuming the 1/5 claim is true, gas in your location costs 1/5 of what electricity costs and the dishwasher heats cold tap water with electricity, then handwashing could be cheaper.
If the difference is that big you'll want a dishwasher that can make use of hot tap water.
@clacke Same amount, but different price. In some countries hot water is provided from local powerplants as a coproduct of electricity generation, so it's quite cheap. Also some dishwashing machines use hot water from tap, so we need introduce quite a number of variables in the discussion
@polydraft I haven't checked, but have always been assuming that dishwashers that take in hot water are still prepared to heat it further if necessary, which should make the spreadsheet interesting when the hotwater starts cold.
@clacke > can make use of hot tap water Theoretically yes, but there're nuances like "water in hot tap is not hot when the machine is starting, so it need to waste some not-hot-enough water to raise the temperature or wash poorly with warm water" or cost of machine repair and consumables, or ....