Two stresses, one budget
Almost nothing in a plant is loaded once. A stress that cycles between a maximum and a minimum is described by two numbers, and both matter. The alternating amplitude is the size of the swing; the mean stress is where the swing is centred. Both are stresses, both in MPa.
Each is charged against its own limit. The swing is charged against , the corrected endurance limit — the fully reversed amplitude the part would survive forever. The mean is charged against , the ultimate tensile strength. Goodman's line adds the two accounts: — read aloud, sigma-a over S-e plus sigma-m over S-u equals one over n, where is the factor of safety against fatigue, a bare number with no units.
Read the sum as a budget. If the two fractions add to 1, the part sits exactly on the line and : no margin. If they add to 0.5, half the budget is unspent and . That reciprocal catches people out, so make it a habit — compute the sum, THEN flip it. And the reason the mean stress belongs in the account at all is the reason this line was drawn: a tensile mean holds a microcrack open, so the same swing does more damage riding high than it does about zero. A part can sit far under on amplitude alone and still fail.