Formula to calculate energy required to power an Arduino board
In the datasheet you can read how much every mode uses (normal mode, sleep mode etc). However, it also depends on which peripherals inside the CPU are active and all electronics around it. So make sure you read the datasheet of the entire development board, and not from the CPU itself.

The mathematical formula is reasonably simple: the total power is the sum of each component's Amperage * component's Voltage. But practicially this is hard to calculate.

The easiest way (but not mathematically) is probably just to measure the amperage in the development board, and the voltage and multipley them together.