Most of the data used by calories burned calculators has been collected by measuring the amount of oxygen consumed performing each activity. A number, called a MET (Metabolic Equivalent), is assigned to each activity to indicate its level of intensity.
An activity with a MET of one corresponds to a person's RMR (Resting Metabolic Rate), the rate at which they would burn calories resting. Other activities are assigned MET values to indicate their intensity level relative to RMR.
For example, driving a car has a MET of two and playing water polo has a MET of ten. This indicates that you would burn twice as many calories driving a car as you would sitting still, and ten times as many playing water polo.
Based on the above, it would appear that the most accurate way to calculate calories burned would be to use the number of METs assigned to the activity you select, your RMR, and the length of time you performed the activity. However, in most cases the MET data was collected using a constant based on weight alone rather than RMR. Therefore for consistency we also use a constant based on your weight rather than RMR.
Calories burned calculations reflect the total number of calories burned during the period of time calculated. Therefore when calculating how many calories you need or burn in a day, do not add your RMR or BMR.