Definition
The total obtained by adding the absolute values (magnitudes) of two or more quantities together, ignoring their signs or directions. The arithmetic sum of +5 and -3 is 8, not 2.
Plain English
The total you get when you add numbers together while ignoring whether they are positive or negative. You just add the sizes.
Context Anchor
Seen in aviation math when a text needs to distinguish simple adding from combining values that may have opposite directions or signs.
Derivation
From Greek 'arithmos' meaning 'number,' and Latin 'summa' meaning 'total' or 'highest.' Together it means simply 'the total of the numbers' — without the complication of direction or sign.
Why Pilots Care
In some calculations (like total electrical load or combined forces), what matters is the total magnitude, not the net result. Confusing arithmetic sum with algebraic sum can lead to sizing components or loads incorrectly.
Analogy
If one person walks 3 miles north and 2 miles south, the arithmetic sum of the walking distances is 5 miles. That is different from the final position, which is only 1 mile north of the start.
Intuition Check
Do not assume arithmetic sum always means the final net result after positives and negatives cancel. Here it means the straight total of the amounts being added.
Example Sentence 1
The arithmetic sum of the two opposing forces, 40 pounds forward and 25 pounds aft, is 65 pounds.
Example Sentence 2
Add the fuel quantities from each tank to find the arithmetic sum for total fuel on board.