Rate of climb
In aeronautics, the rate of climb (RoC) is an aircraft's vertical speed - the rate of change in altitude. In most ICAO member countries (even in otherwise metric countries), this is usually expressed in feet per minute (ft/min). Elsewhere, it is commonly expressed in metres per second (m/s). The rate of climb in an aircraft is indicated with a vertical speed indicator (VSI) or instantaneous vertical speed indicator (IVSI).
The rate of decrease in altitude is referred to as the rate of descent or sink rate. A decrease in altitude corresponds with a negative rate of climb.
Speed and rate of climb 
There are a number of designated airspeeds relating to optimum rates of ascent, the two most important of these are Vx and Vy.
Climbing at Vx allows pilots to maximize the altitude gain per unit ground distance. That is, Vx allows pilots to maximize their climb while sacrificing the least amount of ground distance. This occurs at the speed for which the difference between thrust and drag is the greatest (maximum excess thrust). In a jet airplane, this is approximately minimum drag speed, or the bottom of the drag vs. speed curve.
Climbing at Vy allows pilots to maximize the altitude gain per unit time. That is, Vy, allows pilots to maximize their climb while sacrificing the least amount of time. This occurs at the speed for which the difference between engine power and the power required to overcome the aircraft's drag is the greatest (maximum excess power). Climb rate is proportional to excess power.
Vx increases with altitude and Vy decreases with altitude. Vx = Vy at the airplane's absolute ceiling, the altitude above which it cannot climb using just its own lift.
See also 
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