Thanks for asking a technical question, because I was biting my lip trying not to respond to a particular narrow-minded poster who has her opinion plastered onto every thread on this board. Maybe we can be free of her here, since this actually involves aviating.
The simple answer: Percent gradient is "rise" divided by "run." This is easy when determining a runway gradient: just divide the difference in runway elevations by the length of the runway.
Climb gradients are rise/run also. A 4% gradient means that your climb rate is 4% of your groundspeed, but the numbers aren't the same. The problem is that you have climb measured in ft/min, and GS measured in nm/hr.
First, you need your "Sixty Number," "Magic Number," whatever. 60 kts = 1; 120 kts = 2; 150 kts = 2.5, etc. For a given airplane, you should only need one Magic Number. 120 kts is not an unreasonable GS for V2 @ SL, upwind. So for your airplane, just know the number "2." For Colorado with a little downwind, maybe "2 1/2" (representing a 150 kt groundspeed). For a two-engine calculation, or a turn to a strong downwind, maybe "3" (representing 180 kts GS).
Owing to the fact that God made the Earth the size that he did, man was able to define a nm as approx 6000 feet. Through the miracle of mathematics,we have an easy solution to this.
Climb required for a certain percent gradient:
FPM = % x 60 x Magic Number. (This is your answer).
If a DP requires a 4% gradient, then (at 120kt), you will require a 480 fpm climb rate. (4 X 60 X 2).
If a performance chart promises you a 6 1/2% climb gradient at a certain weight/temp/press alt, then it's saying your climb rate (if the chart assumes, say, 150 kts) will be 975 fpm (6 1/2 X 60 X 2.5).
Feet per NM:
DP charts usually specify a climb gradient in ft/nm, for example: "This departure requires a climb gradient of 520 ft/nm to 7000 ft." This is easier than % gradients. In this case, simply:
FPM = Grad X Magic Number.
So that DP would require 1040 fpm to comply with, at 120 kts GS. (520 X 2).
Notice that the only difference between the two is that number "60."
Gradients can also be expressed in degrees, such as ILS glideslopes. For that I suggest the following formula:
FPM = Appr mode armed + A/P On
By using this formula, your airplane will achieve the perfect descent rate at whatever GS you care to fly.
Hope this helps.