What top of descent is and why it is a distance
Top of descent, universally shortened to TOD, is the point on your track where you leave cruise altitude to make a crossing restriction or a destination altitude. You plan it as a distance from a fix rather than as a time, because the descent geometry depends on distance. A steeper path needs fewer track miles; a shallower one needs more; the clock does not enter into it until you bring ground speed in.
The number matters because a descent has an asymmetry built into it. Starting down early costs fuel, since you spend minutes at low level burning at a higher rate than you would in the thin air above. Starting down late costs options. Once you are above the profile you can only fix it by increasing the rate of descent, and that rate is limited by the airframe, by speedbrake availability, by the passengers' ears and, on some arrivals, by a published maximum. Being 2,000 ft high at a fix with a hard altitude is a level bust; being three miles early is a rounding error on the fuel log.
The same arithmetic runs in reverse for a climb, which is why the climb gradient calculator and the rate of climb calculator share this page's geometry. What changes is the sign of the height difference and which constraint binds.
The geometry behind the rule of three
Every descent problem reduces to one right-angled triangle. The vertical side is the altitude you have to lose. The horizontal side is the track distance available. The angle between the hypotenuse and the horizontal is the flight path angle, written γ.
The height lost per unit of track distance is therefore tan γ. Convert that into aviation units by multiplying by the 6,076.115 ft in a nautical mile and you get feet lost per nautical mile. At 3 degrees that is 6,076.115 × 0.0524078 = 318.4 ft per NM. Invert it and you need 3.14 NM to lose 1,000 ft.
The rule of three — three miles for every thousand feet — is that same number rounded to something you can do in your head. It corresponds to 333.3 ft per NM, a gradient of 5.486%, and a path angle of 3.14 degrees. It is slightly steeper than a 3.00 degree glidepath, which is why it is a serviceable rule of thumb for planning: it puts TOD a shade closer in, so you arrive a shade high rather than a shade low, and being high with idle thrust and speedbrake available is the recoverable side of the error.
The rate of descent falls out of the same triangle. If you cover GS nautical miles in an hour and lose tan γ of that in height, then in one minute you lose GS × 6,076.115 × tan γ ÷ 60 feet. The constant 6,076.115 ÷ 60 is 101.27, which is where the cockpit form ROD = GS × 101.27 × tan γ comes from. At 3 degrees, tan γ = 0.05241 and 101.27 × 0.05241 = 5.31, which pilots round to five times ground speed. That rounding is not neutral: five times ground speed corresponds to a 2.83 degree path, so it under-calls the rate needed on a true 3 degree slope by about 6%.
Worked example: FL350 to 5,000 ft at 450 knots ground speed
You are cruising at FL350 and the arrival requires you to cross a fix at 5,000 ft. Your ground speed through the descent averages 450 kt. You plan on the rule of three and allow 5 NM to level off and slow down.
- Altitude to lose. 35,000 − 5,000 = 30,000 ft.
- Convert to thousands. 30,000 ÷ 1,000 = 30.
- Apply the rule. 30 × 3 NM = 90 NM of geometric descent distance.
- Add the allowance. 90 + 5 = 95 NM. That is where you ask for descent.
- Required rate. The rule of three is 333.3 ft per NM. At 450 kt you cover 7.5 NM per minute, so you lose 7.5 × 333.3 = 2,500 ft/min.
- Check it the other way. ROD = GS × 101.27 × tan γ, with tan γ = 1,000 ÷ (3 × 6,076.115) = 0.0548596. So 450 × 101.27 × 0.0548596 = 2,500 ft/min. The two routes agree.
- Time in the descent. 90 NM ÷ 450 kt = 0.2 hours = 12 minutes. Equivalently 30,000 ft ÷ 2,500 ft/min = 12 minutes.
Now do it on a 3.00 degree path instead. Feet per NM becomes 318.4, so the distance grows to 30,000 ÷ 318.4 = 94.2 NM and the rate falls to 450 × 101.27 × 0.052408 = 2,388 ft/min. Four extra track miles and 112 fewer feet per minute — the entire difference between the rule of thumb and the geometry it approximates.
How to read the answer in flight
Treat the TOD distance as the moment to ask, not the moment you will get it. Air traffic control owns the descent clearance, and on a busy arrival you will often be kept high. The number you use in the cockpit after that is the check-point table below the result: at every distance to go it gives the altitude that keeps you on the planned slope. Comparing your actual altitude with that row is the fastest way to know where you stand.
If you are above the profile you have three levers and they are not equal. Increasing the rate of descent at constant speed is the cheapest and is bounded by comfort and by the airframe. Extending speedbrake trades a lot of drag for noise and, in some types, buffet. Slowing down raises the path angle you can hold at idle but also reduces ground speed, which stretches the time available — it helps less than pilots expect.
A required rate above 3,000 ft/min is a signal rather than a limit. In a pressurised jet it is achievable but uncomfortable, and it usually means the plan needed to start earlier. In an unpressurised piston aeroplane the cabin descends with the aircraft, and 500 to 700 ft/min is the range most passengers tolerate without ear pain — which is why light-aircraft descents are planned around a chosen rate first and the distance taken as whatever falls out. That inversion is worth understanding: jets pick the path and accept the rate, light aircraft pick the rate and accept the path.
Ground speed is the input pilots get wrong most often. Ground speed, not indicated or true airspeed, sets both the time to fly the distance and the rate required, so a 60 kt tailwind at altitude that fades away lower down makes the early part of the descent demand a higher rate than the late part. Work your average from the wind forecast, or get it from the ground speed calculator and the wind correction angle calculator.
Rate of descent by ground speed and path angle
| Ground speed | 2.5° | 3.0° | Rule of three (3.14°) | 4.0° |
|---|---|---|---|---|
| 90 kt | 398 | 478 | 500 | 637 |
| 120 kt | 531 | 637 | 667 | 850 |
| 150 kt | 663 | 796 | 833 | 1,062 |
| 210 kt | 929 | 1,115 | 1,167 | 1,487 |
| 250 kt | 1,105 | 1,327 | 1,389 | 1,770 |
| 300 kt | 1,326 | 1,592 | 1,667 | 2,124 |
| 400 kt | 1,769 | 2,123 | 2,222 | 2,833 |
| 450 kt | 1,990 | 2,388 | 2,500 | 3,187 |
| 480 kt | 2,122 | 2,547 | 2,667 | 3,399 |
Values are the formula evaluated at each pair and rounded to the nearest ft/min. The rule-of-three column is exactly GS × 5.5556, which is why it is the easiest one to do mentally.
Track miles needed for a given altitude loss
| Altitude to lose | 2.5° (265 ft/NM) | 3.0° (318 ft/NM) | Rule of three (333 ft/NM) | 4.0° (425 ft/NM) |
|---|---|---|---|---|
| 5,000 ft | 18.8 | 15.7 | 15.0 | 11.8 |
| 10,000 ft | 37.7 | 31.4 | 30.0 | 23.5 |
| 15,000 ft | 56.5 | 47.1 | 45.0 | 35.3 |
| 20,000 ft | 75.4 | 62.8 | 60.0 | 47.1 |
| 25,000 ft | 94.2 | 78.5 | 75.0 | 58.8 |
| 30,000 ft | 113.1 | 94.2 | 90.0 | 70.6 |
| 35,000 ft | 131.9 | 109.9 | 105.0 | 82.4 |
Distance does not depend on speed at all, only on the angle. Speed decides how quickly you fly that distance, which is what sets the rate of descent.
Mistakes that put you above the profile
- Planning on true airspeed instead of ground speed. A 70 kt tailwind at FL350 does not change the track miles you need, but it raises the rate of descent required to stay on them in direct proportion to ground speed.
- Forgetting the deceleration miles. The geometric answer gets you to the altitude, not to the altitude at the right speed. Slowing from 300 kt to 210 kt in level flight consumes several track miles; slowing while descending flattens the path instead. Build the allowance in rather than discovering it.
- Ignoring track miles that are not on the direct line. A downwind leg, a procedure turn or radar vectoring adds distance you will actually fly. Descent planning uses track miles to the fix, not the direct distance you would get from the great circle distance calculator.
- Treating a crossing restriction as the destination. If a STAR says cross at or above 11,000 ft and then at or below 6,000 ft twelve miles later, the binding constraint is the tighter of the two. Compute the segment that demands the steepest path and plan to that.
- Assuming idle thrust will hold the angle. A clean jet at idle descends at roughly 3 degrees at normal descent speeds. Anything appreciably steeper needs drag, and drag at high speed is loud, uncomfortable and in some types restricted by altitude or airspeed.
- Rounding twice. Using ground speed × 5 for the rate and 3 NM per 1,000 ft for the distance combines a 2.83 degree rate with a 3.14 degree distance. Those are not the same path. Over the worked example's 90 NM at 450 kt, 12 minutes at 2,250 ft/min loses only 27,000 ft of the 30,000 ft required, leaving you 3,000 ft high at the fix.
This is planning geometry, not a performance calculation
The triangle here knows nothing about your aeroplane. It does not check whether idle thrust actually produces the angle you asked for at your weight and speed, whether the descent stays inside placarded limits, or whether anti-ice bleed is holding the engines above idle and flattening your path. Use it to decide where to start down and what rate to expect, then fly the aeroplane's own indications — the vertical deviation from the flight management system, or altitude against distance to go — as the authority once you are on the way down.
Where this fits among the other descent tools
Three related calculations get confused with one another. This one answers where do I start down. The descent rate and glidepath calculator answers what rate holds a published glidepath at my speed, which is the same equation applied at a different moment — on final approach the distance is fixed by the procedure and only the rate is yours to choose. The glide distance calculator answers a different question entirely: with the engine gone, the glide ratio is a property of the airframe rather than a choice, and the unknown becomes how far you can reach.
Published procedures express the same geometry in a third form. SIDs and STARs quote gradients in percent or in feet per nautical mile, and instrument approach charts publish a descent angle to two decimal places alongside a rate-of-descent table by ground speed — the same table this page generates. When a chart gives a gradient in percent, that number is 100 × tan γ, so 5.2% is 2.98 degrees and 6.5% is 3.72 degrees.
For the flight-planning stage rather than the arrival, pair this with the flight time and ETA calculator to turn descent distance into an arrival time, and with the aviation fuel burn calculator to see what an early descent costs. Twenty track miles of early descent is a few minutes at low-level fuel flow, which is small — but it is not zero, and repeated daily it is the sort of thing that separates a tidy operation from a sloppy one.
Key terms
- Top of descent (TOD)
- The point at which the aircraft leaves cruise altitude for the descent, expressed as a distance before the fix or destination it is planned against.
- Flight path angle (γ)
- The angle of the flight path below the horizontal, measured against the ground track. A 3 degree path is the standard for an ILS glidepath and the usual target for a jet arrival.
- Gradient
- The same quantity as the flight path angle expressed as a percentage: 100 × tan γ. Charts use it because it multiplies straight into distance without a trigonometric step.
- Rate of descent (ROD)
- Vertical speed downwards in feet per minute. Unlike the angle it depends on ground speed, so the same path demands very different rates in a training aeroplane and an airliner.
- Track miles
- The distance you will actually fly over the ground including turns and vectors, as opposed to the direct distance to the fix. Descent planning always uses track miles.