ClimbCheck
Interactive pilot tool

Interactive Koch Chart Calculator

Learn how the original Koch chart connects airport temperature and pressure altitude to generalized takeoff-distance and climb-performance effects, then use ClimbCheck’s Precise model or compare it with Legacy Koch.

Open ClimbCheck with Precise See how the original chart works

Every weather, elevation, runway, and aircraft-baseline value remains editable. A METAR fetch is optional.

What a Koch chart estimates

A Koch chart is a pilot-training nomogram that relates pressure altitude and temperature to approximate changes in takeoff distance and rate of climb. ClimbCheck’s Legacy Koch option turns that historical line-drawing method into a digital comparison while keeping the inputs visible and editable.

Important: Koch-style percentages are generalized awareness estimates. They do not replace the aircraft-specific AFM/POH, which accounts for the actual airplane, engine, propeller, weight, configuration, runway, and test conditions.

How the original Koch chart works

The traditional chart uses three groups of scales. Airport temperature appears on the left, pressure altitude appears on the right, and the two center scales show the approximate increase in takeoff distance and decrease in rate of climb.

Recreation of the original FAA Koch chart layout A temperature scale on the left and a pressure-altitude scale on the right are connected with a straight example line. The line crosses center scales for takeoff-distance increase and rate-of-climb decrease. Traditional Koch chart layout Connect airport temperature to pressure altitude, then read both center scales −40 −30 −20 −10 0 10 20 30 40 50 60 70 80 90 100 110 120 AIRPORT TEMPERATURE (°F) −2 0 2 4 6 8 10 12 14 16 PRESSURE ALTITUDE (THOUSANDS OF FEET) 0 20 40 60 100 140 200 ≈230 260 ADD THIS PERCENTAGE TO NORMAL TAKEOFF DISTANCE 0 20 40 60 70 ≈76 80 90 PERCENT DECREASE IN RATE OF CLIMB Example line: 100 °F ↔ 6,000 ft pressure altitude 1Find airport temperature on the left. 2Find pressure altitude on the right. 3Read both center scales.
ClimbCheck vector recreation of the traditional chart layout for readability. The scanned original appears in FAA Safety Team — Density Altitude, FAA-P-8740-2, page 3.
  1. Find the airport temperature. Use the left scale in degrees Fahrenheit.
  2. Find pressure altitude. Use the right scale in thousands of feet. Pressure altitude is the altitude indicated when the altimeter is set to 29.92 inHg.
  3. Connect the two values. Draw a straight line from the temperature point to the pressure-altitude point.
  4. Read the center scales. Where the line crosses the center, read the approximate percentage increase in takeoff distance and percentage decrease in rate of climb.
Reading the FAA illustration: the example line connects approximately 100 °F with 6,000 ft pressure altitude. It crosses near a 230% takeoff-distance increase and roughly a 76% decrease in rate of climb. These are broad training estimates from standard sea-level reference values, not aircraft-specific predictions.

How ClimbCheck digitizes the Koch concept

The Legacy Koch model first uses a temperature-based density-altitude estimate, then applies two generalized relationships:

Estimated takeoff-distance increase = 12.5% × density altitude in thousands of feet
Estimated climb / power loss = 9.6% × density altitude in thousands of feet
Line graph of Legacy Koch-style takeoff distance increase and climb or power loss versus density altitude, including a worked example at 5,520 feet.
Original ClimbCheck visualization of the Legacy Koch relationships. The graph shows generalized factors, not aircraft-specific performance.

Concise worked example

Consider a training scenario with a pressure altitude of 3,000 ft, an outside-air temperature of 30 °C, a 1,200 ft baseline takeoff distance, and a 4,000 ft runway.

Rule-of-thumb DA≈ 5,520 ft
Legacy TO increase≈ 69%
Adjusted baseline≈ 2,028 ft
  1. Estimate ISA temperature. At 3,000 ft, ISA temperature is approximately 9 °C.
  2. Estimate density altitude. 3,000 + 120 × (30 − 9) gives approximately 5,520 ft.
  3. Apply the Legacy Koch takeoff factor. 5.52 × 12.5% gives approximately a 69% increase.
  4. Adjust the baseline. A 1,200 ft baseline becomes approximately 2,028 ft.
  5. Compare with runway length. The arithmetic remainder is approximately 1,972 ft, but that number is not an operational safety margin by itself.

The corresponding Legacy Koch climb/power indication is approximately −53%. That result is deliberately attention-getting: it is a prompt to consult the aircraft AFM/POH and use conservative operational judgment.

Use the interactive version

The calculator opens with Precise selected because that model uses pressure altitude, temperature, and dew point to estimate air density. It can fetch a current METAR, accept pasted METAR text, or work entirely from manually entered values. Legacy Koch remains available in the model selector for a direct comparison with the historical chart.

Direct route: Open ClimbCheck with Precise preselected. Legacy Koch remains available for side-by-side comparison.

How Legacy Koch differs from the other ClimbCheck models

ModelAtmospheric approachBest use
Legacy KochTemperature-based density-altitude approximation with classic Koch-style percentage factorsHistorical comparison, training, and quick awareness
PreciseUses pressure altitude, temperature, and dew point to estimate air densityMore complete atmospheric comparison inside ClimbCheck
Rule of thumbUses pressure altitude and temperature difference from ISAFast mental-model and scenario check