Top of Descent Calculator

The 3 to 1 rule says start down about 3 nautical miles before the target for every 1000 feet you need to lose. For 30000 feet that is roughly 90 nautical miles, close to the exact 3 degree value.

Descent rate in feet per minute equals groundspeed times the tangent of the descent angle times 6076.12, divided by 60. For 3 degrees a quick estimate is groundspeed times 5.

Divide the altitude to lose by the descent gradient in feet per nautical mile. The gradient is the tangent of the angle times 6076.12, which is about 318 feet per nautical mile at 3 degrees.

The exact descent rate for 3 degrees is groundspeed times about 5.3, so groundspeed times 5 slightly underestimates it. It is close enough for a quick mental cross-check.

Use groundspeed. The descent geometry is over the ground, so a tailwind needs an earlier top of descent and a higher rate than airspeed alone would suggest.