What take-off distance means and which number matters
Two distances describe a take-off. The ground roll is brake release to the wheels leaving the surface. The distance to 50 ft adds the air segment needed to climb to 50 ft above the surface, and it is roughly 1.5 to 1.8 times the ground roll in a typical light aeroplane. The second number is the one that decides whether a runway is usable, because a departure that leaves the ground with 200 ft remaining and a hedge at the end has not succeeded.
Take-off is far more sensitive to conditions than landing is. The reason is physical. Landing dissipates energy through brakes and drag, which work almost as well in thin air. Take-off has to produce that energy, and a normally aspirated engine loses power as density falls, a propeller loses thrust in the same thin air, and the aeroplane must reach a higher true airspeed to generate the same lift. Three penalties act at once, which is why density altitude costs about 10% per 1,000 ft for take-off against about 5% for landing.
Weight behaves the same way. It costs about 20% per 10% increase, twice the landing penalty, because the aeroplane must accelerate more mass to a higher lift-off speed with the same thrust. That means the last two passengers and full tanks routinely add a third to the runway required, which is precisely the combination that appears in accident reports from short strips on hot afternoons.
Each correction and why it takes the value it does
Density altitude is the master variable, and it is not the same as field elevation. A 1,000 ft strip at 30 °C has a density altitude around 3,000 ft. The calculator derives it from pressure altitude and temperature using DA = PA + 118.8 × (OAT − ISA temperature), where the ISA temperature falls 1.98 °C per 1,000 ft from 15 °C at sea level. The density altitude calculator covers the derivation in full, and the pressure altitude calculator converts a QNH and an elevation into the pressure altitude this page wants.
Weight is measured against the weight the flight manual chart was produced at, which is not necessarily maximum take-off weight — check the small print on the chart. The factor is 1 + 2 × (fractional weight increase), so 5% heavy is 1.10 and 10% heavy is 1.20.
Wind is scaled against lift-off speed rather than applied per knot, because a 10 kt wind is a sixth of the take-off speed for a microlight and a fifteenth for a light twin. A headwind equal to 10% of lift-off speed takes off 5%; a tailwind of the same size adds 20%. Tailwind take-offs also raise the ground speed at rotation, which increases the energy in any rejected take-off — a risk the distance figure alone does not show.
Slope costs about 10% per 2% of upslope. Where a runway has both slope and wind, the two often conflict: departing downhill with a tailwind is frequently worse than uphill into wind, and the only way to settle it is to compute both directions and compare.
Surface matters more for take-off than for landing, because rolling resistance acts against acceleration for the whole run. Short dry grass on firm ground costs about 20%; long grass or soft ground can cost half again. Wet paving barely affects the take-off run itself, which is why it does not appear as an option here — but it matters enormously to a rejected take-off, where stopping distance is the constraint.
The 1.33 safety factor is the factored take-off distance required for public transport operations, equivalent to demanding that the aeroplane get airborne and to 50 ft within 75% of the distance available. Private flights are not required to apply it. Applying it anyway is one of the cheapest safety decisions available, because the demonstrated figures assume a technique no ordinary departure quite matches.
Worked example: full aeroplane off a grass strip on a hot day
The flight manual gives 900 ft of ground roll and 1,500 ft to 50 ft, at 2,400 lb and sea level in ISA. Today you depart at 2,400 lb from a field with a pressure altitude of 2,000 ft at 30 °C, from short dry grass, with a 4 kt headwind and a level runway. Lift-off speed is 60 kt. The strip offers 2,600 ft.
- ISA temperature at 2,000 ft. 15 − 1.98 × 2 = 11.04 °C.
- Density altitude. 2,000 + 118.8 × (30 − 11.04) = 2,000 + 2,252 = 4,252 ft.
- Density altitude factor. 1 + 0.10 × 4.252 = 1.4252.
- Weight factor. At the reference weight, so 1.000.
- Wind factor. 10% of 60 kt is 6 kt, so a 4 kt headwind is 0.667 of a unit: 1 − 0.05 × 0.667 = 0.9667.
- Slope factor. Level, so 1.000.
- Surface factor. Short dry grass, 1.20.
- Combined. 1.4252 × 1.000 × 0.9667 × 1.000 × 1.20 = 1.6534.
- Corrected distances. Ground roll 900 × 1.6534 = 1,488 ft; to 50 ft, 1,500 × 1.6534 = 2,480 ft.
- Factored at 1.33. 2,479.9 × 1.33 = 3,298 ft.
- Margin. 2,600 − 3,298 = −698 ft.
The aeroplane is at its certified weight, the wind is helping, and the strip is more than two and a half times the book ground roll. It is still not enough once the corrections and the factor are applied. Note where the damage came from: the density altitude factor alone added 42.5%, and the grass another 20%, and they multiplied rather than added. Wait until the evening and a drop to 18 °C brings density altitude to 2,827 ft, the combined factor to 1.4879, and the factored distance to 2,968 ft — better, and still short.
Reading the margin, and what to do when it is thin
Judge the margin as a fraction of the distance available. Anything under about 20% deserves a decision rather than a shrug, because the factor method already assumes the book technique and a serviceable aeroplane, and it makes no allowance for a rough surface, a late rotation or an engine producing slightly less than rated power.
When the margin is thin, the levers in order of effectiveness are weight, temperature and surface. Weight is the strongest and the most controllable: taking 10% out of the aeroplane removes 20% of the distance, so leaving two hours of fuel or one passenger behind can transform a marginal departure. Temperature is free if you can wait — a 12 °C drop between mid-afternoon and evening is worth about 1,400 ft of density altitude, which is 14% of distance. Surface you usually cannot change, but you can often choose a different runway or a different part of the day when the grass is dry.
What does not help as much as pilots hope is technique. A soft-field or short-field technique flown well matches the book figure; it does not beat it. The flight manual number already assumes the short-field procedure where one is published, so planning to make up a deficit by flying better is planning to use up the margin the factor was protecting.
One more check the distance number does not make: the climb after 50 ft. A hot, high, heavy departure that just fits inside the runway may still not out-climb the terrain beyond it, and the climb gradient calculator is the tool for that question. Take-off distance and climb performance fail in the same conditions, so when one is marginal the other usually is too.
Take-off correction factors, and how they compare with landing
| Condition | Take-off factor | Landing factor |
|---|---|---|
| Density altitude, per 1,000 ft | +10% | +5% |
| Weight, per 10% increase | +20% | +10% |
| Headwind = 10% of take-off speed | −5% | −5% |
| Tailwind = 10% of take-off speed | +20% | +20% |
| Slope 2% against you | +10% (upslope) | +10% (downslope) |
| Short dry grass, firm ground | +20% | +20% |
| Long grass or soft ground | +50% | varies with braking |
| Regulatory safety factor | ×1.33 | ×1.43 |
These are the generic planning factors taught where the flight manual has no chart for the actual condition. Manufacturer data for your type always takes precedence.
What density altitude does to a 1,500 ft book distance
| Density altitude | Factor | Corrected distance | Factored at 1.33 |
|---|---|---|---|
| Sea level | 1.00 | 1,500 ft | 1,995 ft |
| 1,000 ft | 1.10 | 1,650 ft | 2,195 ft |
| 2,000 ft | 1.20 | 1,800 ft | 2,394 ft |
| 3,000 ft | 1.30 | 1,950 ft | 2,594 ft |
| 4,000 ft | 1.40 | 2,100 ft | 2,793 ft |
| 6,000 ft | 1.60 | 2,400 ft | 3,192 ft |
| 8,000 ft | 1.80 | 2,700 ft | 3,591 ft |
The linear 10% per 1,000 ft rule understates the penalty for a normally aspirated engine at high density altitude, where power falls away faster than the rule assumes. Above about 8,000 ft use the flight manual chart.
Assumptions and limits of this method
- It assumes the book technique and a serviceable aeroplane. Full power available, correct flap setting, correct rotation speed, brakes released cleanly.
- It applies one combined factor to both the roll and the distance to 50 ft. That is the conventional simplification; the air segment does not scale identically with the ground roll, and separate flight manual charts are better where you have them.
- It does not compute an accelerate-stop distance. The distance to reject a take-off and stop is a different and usually longer number, and it is where wet paving matters.
- It says nothing about the climb after 50 ft. Obstacle clearance is a gradient question, not a distance question.
- The linear density altitude rule breaks down when the engine does. Turbocharged and turbine aeroplanes hold power to altitude and are less penalised; normally aspirated engines are penalised more than the rule suggests above roughly 8,000 ft.
- Grass factors are generic. Length, firmness, moisture and even the direction of the cut change rolling resistance, and a strip that was firm in the morning can be soft after rain.
- It is a planning tool. The flight manual is the legal reference and the pilot in command owns the decision.
Compute both runway directions before you choose
On a sloping strip with a light wind, the better direction is genuinely not obvious. A 2% upslope costs 10%; a 5 kt tailwind on a 60 kt lift-off speed costs about 17%. Departing downhill with that tailwind therefore beats uphill into wind on the distance alone — but the downhill direction also produces a higher ground speed at lift-off and may point at rising terrain. Run the numbers both ways, then let the obstacles and the rejected take-off case break the tie. Use the crosswind component calculator to resolve the reported wind into the along-runway component for each direction, since a wind that is nearly across the strip can carry several knots of tailwind one way and headwind the other.
Where take-off distance sits in the wider performance picture
Take-off performance is one of three calculations that fail together on a hot, high, heavy day. The distance grows, the climb gradient shrinks, and the true airspeed at every indicated speed rises. Assess all three: this page for the runway, the climb gradient calculator for the obstacle, and the weight and balance calculator for the loading that drives both.
The mirror calculation is landing, which uses the same factor structure with roughly half the sensitivity to density altitude and weight. It is worth running the landing distance calculator for the same strip in the same conditions, because the classic trap at a short field is arriving comfortably in the cool of the morning and finding the departure impossible at four in the afternoon with full tanks.
For multi-engine and turbine operations the vocabulary expands — balanced field length, V1, accelerate-stop and accelerate-go distances, and net rather than gross flight paths. Those are genuinely different calculations rather than refinements of this one, because they turn on what happens when an engine fails at the worst moment rather than on what happens when everything works. The factor method here answers only the all-engines-operating question.
Key terms
- Take-off run available (TORA)
- The length of runway declared available and suitable for the ground run of an aeroplane taking off.
- Take-off distance available (TODA)
- TORA plus any clearway - the distance available for the ground run and the initial climb to screen height.
- Distance to 50 ft
- Brake release to 50 ft above the surface. The figure that decides whether a runway with obstacles at the end is usable.
- Density altitude
- Pressure altitude corrected for temperature: the altitude in the standard atmosphere at which the air has the density you are taking off in.
- Factored take-off distance
- The corrected distance multiplied by a regulatory margin, 1.33 for public transport operations.
- Lift-off speed
- The airspeed at which the aeroplane leaves the ground, used here to scale the wind correction as a proportion of take-off speed.