The cost of running the dishwasher or washing machine doesn’t change very much however full or empty it is. Neither does its energy use.

Someone regularly washing with a 50% load who switches to running full loads might halve their machine use, running costs including water and energy usage by waiting a little longer and washing only when full. It may same them time loading and unloading the machine too. In addition, the amount of detergents used is much reduced over the year and this has benefits beyond the home since it reduces the quantity of detergent being released into the waste water.