Takeoff Distance & Climb Penalty Calculator (Koch Chart)
Estimate how much longer the takeoff roll and how much weaker the climb rate become at high, hot airports: density altitude from pressure altitude and temperature, Koch-chart style percentage increase in takeoff distance and decrease in rate of climb, and adjusted figures from your sea-level book values.
How it works
DA ≈ PA + 118.8 × (OAT − ISA temp); σ = (1 − 6.8756×10⁻⁶ × DA)^4.2559; takeoff distance factor ≈ σ⁻⁴ (normally aspirated, Koch chart fit); climb ≈ 1 − 7.65% per 1,000 ft DA
Thin air hurts a piston aeroplane three times over: the wing needs a higher true airspeed for the same lift, the propeller produces less thrust, and a normally aspirated engine makes less power — so the takeoff roll stretches and the climb rate collapses. The Koch chart, printed in the FAA's handbooks for decades, summarises the combined effect for a typical light aircraft: at 6,000 ft and 100 °F the takeoff distance more than triples and the climb rate falls by three quarters. This calculator reproduces that chart with a density-ratio fit and applies it to your book numbers; the real POH charts for your aircraft and weight remain the authority, and turbocharged or turbine aircraft suffer far less because they hold power.
Worked example
At a 6,000 ft pressure-altitude airport on a 35 °C day (ISA +32) the density altitude is 9,800 ft and σ = 0.743. A trainer needing 1,600 ft at sea level needs about 5,250 ft (+228%) and its 700 fpm climb falls to about 175 fpm (−75%) — so a 4,500 ft runway is more than 700 ft too short.
Frequently asked questions
What is the "10% per 1,000 ft" rule?
A rough rule that takeoff distance grows 10–15% per 1,000 ft of density altitude for normally aspirated aircraft — reasonable to about 4,000 ft, but the effect compounds and the Koch chart is more realistic higher up.
How much does weight matter compared with density altitude?
Enormously — takeoff distance rises roughly with weight squared (10% more weight ≈ 21% more distance) and every pound removed helps the climb. Departing lighter or in the cool of the morning are the two practical levers.
Related calculators
Planning aid using standard flight-training rules of thumb and ISA atmosphere approximations — not a substitute for the aircraft flight manual (AFM/POH) performance charts, ATC instructions or an approved flight computer. Always apply the manufacturer's data and required safety margins.