How do you calculate climb gradient as a percentage?
Divide the gradient in feet per nautical mile by 6,076 and multiply by 100, so 200 ft/nm is 3.29 % and 1 % is about 61 ft/nm going the other way. E6B Calc's free Climb & Descent screen shows both figures from altitude, ground speed and rate, but it has no box where you type a published ft/nm and read the percent straight off.
A nautical mile is 6,076.1 ft. A percent gradient is feet gained over feet travelled, so ft/nm divided by 6,076.1, times 100. That is the whole formula. The trouble is the charts: a departure procedure quotes ft/nm, an approach plate may quote percent or degrees, and feet per statute mile is a different number again. Those are easy to mix up on paper, and the mistake is not always obvious.
| Gradient | Percent | Angle |
|---|---|---|
| 150 ft/nm | 2.47 % | 1.41° |
| 200 ft/nm | 3.29 % | 1.89° |
| 250 ft/nm | 4.11 % | 2.36° |
| 300 ft/nm | 4.94 % | 2.83° |
| 350 ft/nm | 5.76 % | 3.30° |
| 400 ft/nm | 6.58 % | 3.77° |
A 3° path is 5.24 %, about 318 ft/nm. If you remember one pairing, make it 200 ft/nm and 3.3 %.
Where the gradient comes from in E6B Calc
The screen does not ask for a gradient. It works it out from a climb you describe, which is the more reliable way to check a real climb anyway.
- On E6B, open Climb & Descent under Performance.
- Type Altitude to change in feet, then Ground speed and Rate in fpm.
- Read Time and Distance covered, then the two Gradient rows (ft/nm first, percent second) and Angle.
For 4,500 ft at 90 kt and 500 fpm, it shows 9 min, 13.5 nm, 333 ft/nm, 5.49 % and 3.14°. Worked by hand: 4,500 / 13.5 = 333.3 ft/nm, divided by 6,076.1 gives 5.49 %. They agree, and checking a figure by hand once is a reasonable way to confirm trust in the screen.
Converting a charted ft/nm without a climb
At 60 kt you cover exactly 1 nm a minute, so the rate in fpm equals the gradient in ft/nm. Type 200 in Altitude to change, 60 in Ground speed and 200 in Rate. The screen returns 1 min, 1.0 nm, 200 ft/nm and 3.29 %. It works, but it is a trick, and it feels like one.
Will the climb clear the obstacle?
Fill Obstacle height, Distance to obstacle and leave Clearance wanted at its 200 ft default. With a 1,200 ft obstacle 4 nm out, Gradient to clear it reads 350 ft/nm, and since the climb above makes only 333, the Will not clear warning appears. The needed gradient is shown in ft/nm only; 350 is 5.76 %, so you divide it yourself.
The sum assumes the climb starts at zero, so the obstacle height has to be measured from the same level as the start of the climb, normally the departure end of the runway.
A limitation worth knowing
What a SID asks for is a rate: 300 ft/nm at 90 kt needs 450 fpm, and 350 ft/nm needs 525. The formula is ft/nm times ground speed over 60. The screen will not solve for it. You can nudge Rate until Gradient matches, or multiply it directly. A percent works too: 2.5 % is 152 ft/nm, so 228 fpm at 90 kt.
All of it is free and works offline. Descents use the same screen: 6,500 ft at 140 kt and 500 fpm gives 13 min, 30.3 nm, 214 ft/nm, 3.53 % and 2.02°.
Questions and answers
How do I convert climb gradient from ft/nm to percent?
How do I convert a climb gradient to a rate of climb in fpm?
What is 200 ft/nm as a percentage?
Does the Climb & Descent screen need internet or a purchase?
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