Rate of climb is measured in feet per minute and it is the number on the instrument panel. Climb gradient is measured in feet per nautical mile and it is the number a departure procedure asks for. They are not the same thing, and the bridge between them is groundspeed.
gradient (ft/nm) = rate of climb × 60 ÷ groundspeed
At 700 feet a minute and 90 knots over the ground, that is 467 feet per nautical mile. Against a requirement of 200 ft/nm there is a margin of 267, which is comfortable. The climb gradient calculator does the conversion and checks it against whatever the procedure specifies.
The wind changes the requirement, not the aeroplane
Put a 20 knot tailwind behind the same aircraft. Groundspeed becomes 110 knots, and the gradient falls to 382 ft/nm. Nothing has changed about the engine, the weight or the air the wings are flying through. The aircraft is climbing at 700 feet a minute exactly as before, and it is covering more ground while it does it, so it gains less height per mile.
Read the other way round, the rate of climb needed to meet a 200 ft/nm requirement rises from 300 feet a minute at 90 knots to 367 at 110. Into a 20 knot headwind, at 70 knots over the ground, the same requirement needs only 233 feet a minute and the actual gradient becomes 600 ft/nm.
The height to gain takes the same time in all three cases, 4 minutes 17 seconds for 3,000 feet, because time depends on the rate of climb alone. What changes is the distance it takes: 5.00 nautical miles into the headwind, 6.43 in still air, 7.86 with the tailwind. If there is an obstacle out there, the tailwind is the case that matters.
Why this catches people out
A tailwind feels like help. It shortens the trip, it raises the groundspeed on every other leg, and it is usually welcome. On a climb gradient requirement it is the opposite, and it arrives on exactly the day the wind is strong, which is the day the departure matters most.
The same geometry runs in reverse on the way down. A descent angle becomes a gradient through the same conversion, and the top of descent calculator turns it into a distance to start down. A tailwind there pushes the top of descent further out rather than closer in, for the same reason.
Groundspeed is not given to you
Groundspeed has to be worked out from the wind triangle, and the wind correction angle calculator produces it alongside the heading that holds a track. It is worth noting that the crosswind component costs groundspeed too, through the cosine, even when it is not a headwind at all: a 25 knot wind 50 degrees off the nose takes 17.6 knots off a 120 knot true airspeed while asking for only 9.2 degrees of crab.
All of these pages are planning geometry rather than performance data. The aircraft flight manual and the published procedure are what govern, and a required gradient assumes all engines operating unless the procedure says otherwise. For the case where the engine is not operating, glide distance is the relevant arithmetic, and wind moves that figure in the same direction for the same reason.