E6B formulas, written out
A mechanical E6B is these equations rendered as a slide rule, which is why its answers carry the slide rule's resolution rather than the formula's. Each one below is the exact expression, what every variable means, and the place it stops being reliable.
By Renzo Madueño, former Airbus A320 First Officer (Avianca), FAA commercial pilot · Written September 2026
Wind correction angle (WCA)
WCA = arcsin( (WS / TAS) × sin(WD − TC) )
- WS
- — wind speed, knots
- TAS
- — true airspeed, knots
- WD
- — wind direction, degrees TRUE, the direction it blows FROM
- TC
- — true course, degrees true
True heading is TC + WCA. A positive WCA means crab right. The arcsine is undefined when wind speed exceeds true airspeed — which is the formula telling you, correctly, that the course cannot be held.
Wind correction calculator →Ground speed
GS = √( (TAS·sin TH − WS·sin WD)² + (TAS·cos TH − WS·cos WD)² )
- TH
- — true heading, degrees true (TC + WCA)
- TAS
- — true airspeed, knots
- WS, WD
- — wind speed and direction
Vector subtraction, written out. It is why a pure crosswind costs you almost no ground speed while changing your heading a great deal, and why a headwind costs you the full component.
Pressure altitude
PA = Field elevation + ( (29.92 − altimeter setting) × 1000 )
- altimeter setting
- — inches of mercury
- Field elevation
- — feet MSL
The approximation used on every written exam: roughly 1,000 ft per inch of mercury. Set 29.92 in the Kollsman window and read the altimeter and you get the same number without arithmetic.
Pressure altitude calculator →Density altitude
DA = PA + 120 × (OAT − ISA temperature at PA), ISA temp = 15 − 2 × (PA / 1000)
- PA
- — pressure altitude, feet
- OAT
- — outside air temperature, °C
120 ft per degree of ISA deviation. It is an approximation and the FAA accepts it, but it drifts at extremes — very high altitudes or very large deviations. Performance charts, not this formula, are what you plan a short-field departure with.
Density altitude calculator →True airspeed from calibrated airspeed
TAS ≈ CAS × √( ρ₀ / ρ ) · rule of thumb: TAS ≈ CAS + 2% per 1,000 ft of DA
- CAS
- — calibrated airspeed, knots
- ρ
- — air density at altitude; ρ₀ = sea-level standard density
- DA
- — density altitude, feet
The 2% rule is what an E6B effectively implements and what the exam expects. It holds well below about 10,000 ft and at ordinary light-aircraft speeds; it is not a transport-category number.
True airspeed calculator →Speed, distance and time
Speed = Distance / Time · Distance = Speed × Time · Time = Distance / Speed
- Speed
- — ground speed, knots — not true airspeed
- Time
- — hours (minutes ÷ 60)
Trivial as algebra, and the most common source of wrong answers on a written exam, because the question gives you true airspeed and a wind and expects you to solve the triangle first.
Flight time calculator →Fuel burn and endurance
Fuel used = Fuel flow × Time · Endurance = Fuel on board / Fuel flow
- Fuel flow
- — gallons or litres per hour
- Fuel on board
- — usable fuel — not tank capacity
Endurance here is to dry tanks. Reserves come off the top before this number means anything operationally, and unusable fuel comes off the bottom.
Fuel burn calculator →Descent rate and top of descent
Rate (fpm) = (Altitude to lose / Distance) × GS / 60 · 3° ≈ GS × 5
- Altitude to lose
- — feet
- Distance
- — nautical miles
- GS
- — ground speed, knots
The second form is the one used in the air: ground speed times five gives feet per minute for a three-degree path, close enough to fly.
Descent rate calculator →Crosswind and headwind components
Crosswind = WS × sin(angle) · Headwind = WS × cos(angle)
- angle
- — difference between wind direction and runway heading, degrees
At 30° off the nose the crosswind component is half the wind speed; at 60° it is about 87%. Those two numbers cover most of what you need on a runway without a calculator.
Crosswind calculator →Take this E6B to the airplane — it is now an iPhone & iPad app
Rotate E6B Flight Computer does the same math you just ran, offline, in the cockpit. You are on a computer now, so we will send the App Store link to your email — open it on your phone.
One email with the link, nothing else. Or see it on the App Store. Free download. Wind triangle, crosswind, time/speed/distance, fuel and conversions are free for good; weight & balance, density altitude, TAS and the FAA practice set are a $9.99 one-time unlock. No subscription.
Run all of these in one place
The free online E6B implements every formula on this page with exact trigonometry rather than a slide rule's resolution, so it is a fair way to check your working.
These formulas are exam questions before they are flight planning
Practise them the way the FAA asks them, with the working shown for every answer.
See the question bank