Gra"di*ent (?), a. [L. gradiens, p. pr. of gradi to step, to go. See Grade.] 1. Moving by steps; walking; as, gradient automata. Wilkins.

2. Rising or descending by regular degrees of inclination; as, the gradient line of a railroad.

3. Adapted for walking, as the feet of certain birds.

Gra"di*ent, n. 1. The rate of regular or graded ascent or descent in a road; grade.

2. A part of a road which slopes upward or downward; a portion of a way not level; a grade.

3. The rate of increase or decrease of a variable magnitude, or the curve which represents it; as, a thermometric gradient.

• A slope or incline.
  
• A rate of inclination or declination of a slope.
  
• (calculus) Of a function y = f(x) or the graph of such a function, the rate of change of y with respect to x, that is, the amount by which y changes for a certain (often unit) change in x.
  
• (physics) The rate at which a physical quantity increases or decreases relative to change in a given variable, especially distance.
  
• (vector) A vector operator that maps each value of a scalar field to a vector equal to the greatest rate of change of the scalar. Notation for a scalar field φ: \nablaφ