How to use it
- Pick Take-off or Landing.
- Type the distance from your flight manual (POH/AFM): the take-off distance to 50 ft, or the landing distance from 50 ft, for sea level, ISA, no wind and a paved dry runway.
- Fill in the aerodrome elevation, QNH and temperature, the mass, the wind component along the runway, the slope and the surface.
- Type the distance available (TODA or LDA, from the AIP or the aerodrome chart) to see the margin.
If your manual has a chart and you already read today’s altitude, temperature, mass and wind from it, tick the box under the distance. The calculator then only adds slope, surface and the safety factor, so nothing is counted twice.
What each correction means
Mass
A heavier aircraft accelerates more slowly and needs a higher speed to lift off. On take-off the distance grows roughly with the square of the mass: 10 % heavier means about 20 % more distance. On landing it is about 10 % more for 10 % more mass. Lighter than the manual figure gives no credit here.
Pressure altitude and temperature
Thin air does two things at once: the engine and propeller give less thrust, and the same indicated speed means a higher true speed over the ground. The calculator first finds the pressure altitude from elevation and QNH (about 27 ft per hPa), then the ISA temperature at that altitude. Every 1,000 ft of pressure altitude adds about 10 % on take-off and 5 % on landing, and every 10 °C above ISA adds the same again. The density altitude is shown so you can compare with your chart.
Wind
A headwind lowers your ground speed at lift-off, a tailwind raises it, and the distance changes with the square of the ground speed. Because wind is never steady, only 50 % of a headwind is counted and 150 % of a tailwind. A tailwind of just 10 % of your lift-off speed already adds about 20 % before that extra margin.
Slope
Rolling uphill, part of the aircraft’s weight pulls it backwards. Each 1 % of slope adds 5 % to the distance: uphill counts on take-off, downhill on landing. The slope that helps you is ignored.
Surface
Grass drags on the wheels during the take-off roll and the brakes grip less on landing. The factors used are: dry grass ×1.2 on take-off and ×1.15 on landing, wet grass ×1.3 and ×1.35, soft ground or snow ×1.25, and a wet paved runway ×1.15 on landing. Long grass, standing water or mud can need much more.
Safety factor
Manual figures come from a new aircraft, a test pilot and a perfect technique. For private flights the UK CAA recommends multiplying the corrected distance by 1.33 for take-off and 1.43 for landing. The landing factor is the same as stopping within 70 % of the landing distance available.
The formulas behind the numbers
Every bar in the chart is the previous distance multiplied by one factor. These are the factors, in the order the calculator applies them. PA is the pressure altitude, V the lift-off speed (or touchdown speed on landing), w the wind along the runway and T the outside air temperature at the aerodrome.
| Step | Take-off | Landing |
|---|---|---|
| Pressure altitude | PA = elevation + (1013 − QNH) × 27 ft | |
| ISA temperature | ISA = 15 − 2 × PA/1000 °C | |
| Mass (only if heavier) | (m / mref)² | m / mref |
| Altitude | 1.10PA/1000 | 1.05PA/1000 |
| Temperature above ISA | 1.10(T − ISA)/10 | 1.05(T − ISA)/10 |
| Headwind | (1 − 0.5·w / V)² | |
| Tailwind | (1 + 1.5·w / V)² | |
| Slope against you | 1 + 0.05 × slope % | |
| Surface | grass dry 1.2 wet 1.3 soft/snow 1.25 | grass dry 1.15 wet 1.35 soft/snow 1.25 wet paved 1.15 |
| Safety factor | 1.33 | 1.43 |
Why some factors have powers
Altitude and temperature. The CAA rule is “×1.1 for every 1,000 ft”. For 2,000 ft you apply it twice, 1.1 × 1.1 = 1.1². For 1,335 ft the power is simply 1.335. Temperature works the same way, in steps of 10 °C. Compared with a straight-line rule the difference is small (1.136 instead of 1.134), but it stays right at high, hot aerodromes.
Mass on take-off, squared. A heavier aircraft needs a higher lift-off speed and also accelerates more slowly, and the two effects multiply. That is why 10 % more mass gives 1.1² = 1.21, the CAA’s “+20 %”. On landing the effect is close to straight-line, so 10 % more mass means 10 % more distance.
Wind, squared. The ground roll depends on the square of the speed over the ground. A headwind lowers that speed, a tailwind raises it. As a check, a tailwind of 10 % of V gives 1.1² = 1.21, again the CAA figure, before the 150 % safety rule is applied.
d = POH_distance d = d × (m / m_ref)² # only if heavier d = d × 1.10 ^ (PA / 1000) # only above sea level d = d × 1.10 ^ ((T − ISA) / 10) # only if warmer than ISA d = d × (1 − 0.5 × headwind / V)² # or (1 + 1.5 × tailwind / V)² d = d × (1 + 0.05 × upslope_%) d = d × surface_factor required = round_up(d × 1.33) # 5 m or 10 ft
Worked example
Take-off from a dry grass strip at 1,200 ft, QNH 1008, 28 °C, with 6 kt of headwind and a 1 % upslope. The manual gives 380 m to 50 ft at sea level, ISA, mass as in the figure.
- Pressure altitude: PA = 1,200 + (1013 − 1008) × 27 = 1,335 ft
- ISA temperature: 15 − 2 × 1.335 = 12.3 °C, so the air is ISA +15.7 °C
- Altitude: 1.101.335 = 1.136 → 380 × 1.136 = 432 m
- Temperature: 1.101.57 = 1.161 → 501 m
- Wind: only half of the 6 kt headwind counts, 3 kt. (1 − 3/55)² = 0.894 → 448 m
- Slope: 1 + 0.05 × 1 = 1.05 → 470 m
- Dry grass: × 1.2 → 564 m
- Safety factor: × 1.33 = 750.6 m, rounded up to 755 m required
On an 800 m strip that leaves a margin of about 45 m. On a 700 m strip it would not be enough, even though the 564 m before the safety factor looks comfortable.
Questions pilots ask
Why only 50 % of the headwind and 150 % of the tailwind?
Wind changes from minute to minute. EU air operations rules and the UK CAA ask you to count no more than half of a reported headwind and at least one and a half times a reported tailwind, so that a gust dropping or a wind shift does not leave you short of runway. Many manual charts already include this, which is why the chart box switches the wind correction off.
Why is the take-off safety factor 1.33 here and 1.25 in the ATPL books?
1.33 and 1.43 are the CAA recommendations for private flights. Commercial operations with single-engine aircraft follow the EU air operations rules, which use different factors (for example 1.25 against the take-off run available). This tool is meant for private and training flights.
Does a downhill runway shorten my take-off in the calculator?
No. A downslope helps on take-off and an upslope helps on landing, but the guidance gives no credit for them, so the calculator does not either.
Why is my density altitude so high on a warm day?
Every degree above ISA adds about 120 ft of density altitude. At 28 °C on a 1,200 ft aerodrome you are already at about 3,200 ft for the aircraft, which is why summer take-offs feel so long.
Can I use the result instead of my flight manual?
No. The calculator is for training and for checking your own calculation. The flight manual of your aircraft always comes first, and its own corrections replace the general factors used here.
Sources
- UK Civil Aviation Authority, Safety Sense Leaflet 09, Weight, balance and performance: correction and safety factors.
- EASA Air Operations, performance class B (CAT.POL.A.305 and CAT.POL.A.330 in Regulation (EU) No 965/2012): 50 % headwind and 150 % tailwind.
For training and reference only, not for operational use. Always use the flight manual (POH/AFM) of your aircraft. General factors cannot replace the data for a specific aircraft.