From Latin 'gradus' (a step), from 'gradī' (to walk) — every sense preserves the step metaphor: rank, slope, or quality level.
A particular level of rank, quality, or intensity; a mark indicating the quality of a student's work; the gradient of a slope; to arrange in or allocate to grades; to evaluate and assign a mark to.
From French grade or directly from Latin gradus (a step, a pace, a degree, a rank, a stage), from gradi (to walk, to step, to advance), from PIE *ghredh- (to walk, to stride). A grade is literally a step — a single level in a hierarchy, a single increment in a slope, or a rung on a scale. The same root produced degree (de- + gradus, a step down), degrade, ingredient (stepping
American English uses 'grade' for both school years ('fifth grade') and academic marks ('she got a good grade'), while British English uses 'year' for school years and 'mark' for academic evaluations. The American usage preserves the Latin metaphor more completely: each school year is literally a 'step' that the student climbs, and each mark is a 'step' on a quality scale. A 'grade school' is a school organized in steps.