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Pilot Math Cheat Sheet

Published by PilotDeskSources, testing & corrections

This is the compact version: the formulas worth recognizing, the units that usually trip people up, and a link to the exact PilotDesk calculator when you want to check the arithmetic. It is built for study and classroom use—not as a substitute for the POH, AFM, regulations, charts, or current weather.

Read the full explanations

Time · speed · distance

Distance = Groundspeed × Time
Time = Distance ÷ Groundspeed
Groundspeed = Distance ÷ Time

Knots are nautical miles per hour. Convert minutes to hours when using knots directly.

Quick check: 120 kt = 2 NM/min.Calculator →

Nautical miles per minute

NM/min = Knots ÷ 60

Useful for quick timing, descent, and climb-gradient work.

90 kt = 1.5 NM/min · 150 kt = 2.5 NM/min.Calculator →

Fuel

Fuel used = Flow × Time
Endurance = Usable fuel ÷ Flow

Use hours with gallons per hour or pounds per hour.

Actual planning may need start, taxi, climb, reserve, alternate, holding, and contingency fuel.Fuel calculator →

Crosswind / headwind

Crosswind = Wind × sin θ
Along-runway = Wind × cos θ

θ is the smallest angle between runway direction and wind direction.

30° ≈ 50% crosswind · 45° ≈ 71% · 60° ≈ 87%.Calculator →

Pressure altitude

PA ≈ Field elevation
+ (29.92 − Altimeter) × 1,000

A quick inHg/feet estimate. Lower pressure raises pressure altitude.

For performance work, use the altitude input and method specified by the aircraft data.Calculator →

ISA temperature

ISA ≈ 15°C − 2°C
per 1,000 ft pressure altitude

Useful lower-atmosphere mental estimate.

ISA deviation = OAT − ISA temperature.Calculator →

Density altitude estimate

DA ≈ PA + 120 × (OAT − ISA)

PA and DA in feet; temperatures in °C.

The 120 ft/°C relationship is an approximation, not a precision atmosphere model.Calculator →

Climb gradient → FPM

FPM = (ft/NM) × (GS ÷ 60)

Groundspeed matters. A stronger tailwind requires more FPM to maintain the same climb gradient.

Calculator →

3° descent

Exact ≈ GS × 5.3
Mental shortcut ≈ GS × 5

Groundspeed in knots gives approximate vertical speed in FPM.

The ×5 rule is intentionally a shortcut; the exact trigonometric value is slightly higher.Calculator →

Load factor in a level turn

n = 1 ÷ cos(bank angle)

Applies to a coordinated, constant-altitude turn.

60° bank = 2 G.Calculator →

Accelerated stall

Vₛ(turn) = Vₛ(1G) × √n

Use the appropriate 1-G stall speed and load factor for the condition being studied.

At 2 G, theoretical stall speed is about 1.414× the 1-G value.Calculator →

Pivotal altitude

Pivotal altitude (ft AGL)
≈ Groundspeed² ÷ 11.3

Use groundspeed in knots, not indicated airspeed.

100 kt → about 885 ft AGL.Calculator →

Moment and CG

Moment = Weight × Arm
CG = Total moment ÷ Total weight

The math finds the loaded CG. The approved envelope decides whether it is acceptable.

Calculator →

Percent MAC

%MAC = (CG − LEMAC) ÷ MAC × 100

Use the aircraft's actual LEMAC and MAC dimensions.

Calculator →

Reciprocal heading

Add or subtract 180°

Add 180° below 180°, or subtract 180° at or above it. Write a zero result as 360°.

075° ↔ 255°.Calculator →

Dynamic hydroplaning estimate

Vₚ ≈ 8.6 × √main-tire pressure

FAA Airplane Flying Handbook estimate: pressure in PSI, result in knots. At 36 PSI, 8.6 × 6 = 51.6 kt. The rounded 9× shortcut gives 54 kt.

It is not a runway-performance guarantee or substitute for aircraft guidance.Calculator →

Do not memorize a fake universal formula

Takeoff distance, landing distance, climb performance, VMC, best glide, and aircraft limitations are aircraft-specific. A generic internet shortcut cannot replace the current POH/AFM. Maneuvering speed also deserves care: use the approved data and the aircraft's stated method rather than treating a forum mnemonic as a universal certification rule.

What to actually memorize

Memorize the relationships well enough to recognize a bad answer. If your crosswind is larger than the reported wind, 120 knots somehow becomes 10 NM per minute, or a warmer-than-standard day produces a dramatically lower density altitude with unchanged pressure, stop and check the inputs and units.

Source trail: PilotDesk's longer Pilot Math Formulas reference links each topic to its calculator and explanation. For controlling material, use current FAA handbooks and the exact aircraft POH/AFM. See Sources & Methods.

Study and planning aid only.