Top of descent calculator
The three-times rule — three miles per thousand feet — is a three-degree glide path expressed in units a pilot can do in their head.
ft
kt
degrees
nm
Start descent this far out
78.51nm
- Rate of descent
- 1486 ft/min
- By the three-times rule
- 75.0 nm
- Rate to lose it in your distance
- 1556 ft/min
- Angle that implies
- 3.140 degrees
- Descent time
- 16.82 minutes
- Ground speed x 5, the three-degree shortcut
- 1400 ft/min
Show the working
- Altitude to lose = 25 000
- Ground speed = 280
- Descent angle = 3
- Or a distance to lose it in = 75
- gradient = tan(rad(3)) = 0.052 407 8
- Start descent this far out = 0.052 407 8 > 0 ? 25 000 / (0.052 407 8 * 6076.115485564304) : 0 = 78.5088
- Rate of descent = 280 * 0.052 407 8 * 6076.115485564304 / 60 = 1486.03
- By the three-times rule = 25 000 / 1000 * 3 = 75
- Rate to lose it in your distance = 75 > 0 ? 25 000 * 280 / (75 * 60) : 0 = 1555.56
- Angle that implies = 75 > 0 ? deg(atan(25 000 / (75 * 6076.115485564304))) : 0 = 3.140 08
- Descent time = 1486.03 > 0 ? 25 000 / 1486.03 : 0 = 16.8233
- Ground speed x 5, the three-degree shortcut = 280 * 5 = 1400
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- descent distance = altitude / (tan(angle) x 6076 ft per nm)
- rate of descent = ground speed x gradient, or ground speed x 5 for three degrees
Multiplying ground speed in knots by five gives the feet per minute for a three-degree path to within a percent. It is the most useful mental shortcut in aviation.
This is a planning and study tool. Use certified charts, an approved flight manual and official publications for anything operational.