Navigation Planning
All six E6B functions in one digital flight computer — wind triangle, time·speed·distance, fuel planning, true airspeed, winds aloft, and off-course correction. Live visual diagrams. Results on every keystroke.
Select a function below — all calculations update instantly
Usage Guide
The E6B has two sides — this digital version covers all six primary calculations with live results.
Enter True Course, True Airspeed, and the wind direction (FROM) and speed. The calculator returns True Heading, Groundspeed, and Wind Correction Angle instantly. Optionally add magnetic variation to get Magnetic Heading, and compass deviation for Compass Heading. The vector diagram updates in real time.
Enter any two of the three values and leave one blank — the third is calculated. Time can be entered as HH:MM (e.g. 1:30) or decimal hours (1.5). Speed and distance unit dropdowns let you work in knots/nm, mph/sm, or kph/km without manual conversion.
Enter fuel available and burn rate to get endurance and total endurance after deducting regulatory reserves. Switch reserve mode between VFR day (30 min), VFR night (45 min), IFR (45 min + alternate time), or custom. Fuel units match your fuel quantity gauge units.
Enter CAS, pressure altitude, and OAT for precise TAS using the temperature ratio formula. Mach number, speed of sound at altitude, ISA deviation, and density altitude are all computed simultaneously. Use the Density Altitude Calculator to get PA from QNH and field elevation first.
Navigation Fundamentals
Every cross-country flight converts from the chart to the cockpit through a chain of four corrections. Understanding each step eliminates navigation errors.
Wind Triangle Theory
The wind triangle is the fundamental vector relationship in aviation navigation. Every cross-country flight is a wind triangle problem.
The direction the aircraft points (TH) and its speed through the air mass (TAS). This is what the engine and wings produce — movement through the air, independent of where that air mass is moving.
The direction the wind is blowing (TO) and its speed. Note that wind direction is always given as the direction FROM which the wind blows — a wind of 270° blows FROM the west TO the east.
The result of the air vector plus the wind vector. This is what actually happens — the track over the ground (TC) and the speed over the ground (GS). This is what GPS measures. The pilot cannot control this directly, only through adjusting the air vector.
For crosswinds, WCA ≈ (WS × sin(angle between wind and track)) ÷ TAS × 60. For quick mental calculation: divide wind speed by TAS and multiply by the crosswind component factor. A 30-knot crosswind at 90° to a 120-knot aircraft gives WCA ≈ arcsin(30/120) ≈ 14.5°.
Student Pilot Workflow
This is the sequence every student pilot must master before their first solo cross-country. Each step feeds the next. Skip one and the error compounds.
Worked Example
One complete cross-country scenario using all six E6B functions in sequence. Follow along using the calculator above.
Magnetic Variation
Every E6B wind triangle ends with a variation correction. Understanding why variation exists — and where to find it — prevents systematic heading errors.
The geographic North Pole (True North) and the Magnetic North Pole are different locations. The magnetic pole is currently in the Canadian Arctic, approximately 500 km from the geographic pole, and moves slowly year by year. Magnetic compasses point toward the magnetic pole. The angle between True North and Magnetic North at any location is magnetic variation, also called magnetic declination.
When the magnetic pole is to the EAST of True North from your position, variation is East. When it is to the WEST, variation is West. In the United Kingdom, variation is approximately 2–4°W. In the eastern USA, variation is approximately 8–14°W. In the Pacific, some areas have East variation. The agonic line (zero variation) runs through parts of the USA and South America.
Variation is shown on aeronautical charts (VFR sectionals, topographic charts, En-Route charts) as dashed magenta lines called isogonic lines, labelled with the variation value and year. Always use the chart for your area. Do not rely on memorised values — variation changes slightly year by year and varies significantly across different parts of the world.
Mnemonic: "East is Least, West is Best." To convert from True Heading to Magnetic Heading: East variation — subtract (East is Least). West variation — add (West is Best). Example: TH = 270°, variation 5°W → MH = 270 + 5 = 275°. Example: TH = 270°, variation 5°E → MH = 270 − 5 = 265°. Get this backwards and every heading in the navlog is systematically wrong.
Variation is a geographic property — it applies to all aircraft flying in the same area. Deviation is an aircraft-specific error — the individual magnetic compass is affected by the aircraft's own metal structure and electrical systems. Deviation is small (typically ±1–5°) and is measured during compass swings. The deviation card inside the aircraft records the correction for each heading. Apply variation first (True → Magnetic), then deviation (Magnetic → Compass).
The magnetic pole moves. Variation values printed on charts include a year and an annual change figure (e.g. "4°W (2020) decreasing 0.1° annually"). For practical navigation, the annual change is small enough to ignore unless using a very old chart. However, always use current charts — an old chart with outdated variation values could introduce a systematic error of several degrees over a long route.
Instrument & Commercial
A diversion to an alternate is a time-critical situation. The E6B gives you bearing, distance, ETE, and fuel required to the alternate in under two minutes.
Tell ATC immediately. Squawk 7700 if unable to communicate. Note the time — your ETE calculation starts from now.
From your current position on the chart, draw a line to the alternate. Measure the True Course with a plotter. Apply variation to get Magnetic Course.
Use the plotter or 1:500,000 scale. For a quick mental estimate, use a visual reference: 1° of latitude = 60 nm, 1 minute of latitude = 1 nm.
Enter the diversion TC, your TAS, and the current wind (from last ATIS/METAR or winds aloft). Get TH and GS. Total elapsed time since last accurate position fix determines how far you have drifted from your DR position.
Time = Distance ÷ GS. Fuel = Time × burn rate. Check fuel remaining against fuel required. If insufficient, declare fuel emergency and divert to closest suitable aerodrome, not the planned alternate.
Before entering a wind into the E6B, you need wind direction and speed. The sources in order of preference:
Current surface wind from the destination or departure airport. Broadcast as "Wind 270 degrees 15 knots." Enter 270 and 15 directly. Remember: ATIS wind is MAGNETIC at most airports. Convert to True before entering the wind triangle by subtracting East variation or adding West variation.
Wind group format: 27015KT (270° magnetic, 15 kt). 27015G22KT = gusting 22. VRB03KT = variable 3 kt. Use the steady-state wind, not gusts, for E6B. For planning, use forecast wind (winds aloft forecast) at your planned altitude, not surface METAR.
Published as True direction and knots at specific flight levels. 2715 = 270°T, 15 kt. 9900 = calm or light and variable. 731960 = 73° True, 119 kt at FL390 (hundreds subtracted from first two digits when >100 kt). These go directly into the E6B without variation correction.
Compare actual TH and GS (from GPS or DME) against planned TC and TAS. Use the Winds Aloft tab to calculate what the actual wind must be. This real-time correction can significantly improve subsequent leg accuracy.
ATIS surface winds are given in Magnetic degrees. Winds aloft forecasts are in True degrees. The E6B wind triangle uses True throughout. Always convert ATIS/METAR wind from Magnetic to True before entering it. Apply the same variation correction as for headings: East variation subtract, West variation add.
ATPL & Commercial Knowledge
PNR and PSR are the critical fuel-planning concepts tested in every ATPL examination and applied on every long-range commercial flight. Both are solved with E6B logic.
The PNR is the furthest point along the route from which the aircraft can return to the departure aerodrome with minimum fuel reserve. Beyond the PNR, the flight must continue to the destination — return is not possible with the fuel remaining.
Example: Safe endurance E = 5 hr, GS outbound = 420 kt (with tailwind), GS homebound = 360 kt (headwind on return).
The PSR (also called the Critical Point or CP) is the point at which continued flight to the destination and return to departure require equal time. It determines whether it is faster to continue or return — critical for emergency decision making. At the PSR, both options take the same time.
Example: D = 2,000 nm, GS outbound = 420 kt, GS homebound = 360 kt.
Beyond 923 nm, it is faster to continue to destination than to return. The CP divides the route into the "continue" zone and the "return" zone for emergency planning.
Modern RNAV, FMS, and GPS systems do not eliminate the need for E6B skills — they change where those skills are applied. The FMS computes wind triangles, time-speed-distance, and fuel planning automatically, but it requires the pilot to input the correct data and to sanity-check the outputs. A pilot who cannot mentally verify an FMS fuel calculation has no defence against a data entry error.
Type rating and line check examiners regularly present scenarios where the FMS is unreliable or unavailable, requiring manual calculation. ATPL examination syllabi explicitly include E6B-level calculations in the Navigation and Mass & Balance subjects. The correct mental model — position from heading, speed, and time — is the same mental model that makes an instrument pilot confident, not anxious, when automation degrades.
Common Questions
The E6B flight computer is a circular slide rule specifically designed for aviation calculations. It was originally a mechanical device — a circular disc with rotating inner and outer scales — developed in the 1930s and used by pilots worldwide through to the present day. The E6B has two sides: the calculator side performs arithmetic calculations including time-speed-distance, fuel planning, and true airspeed; the wind side performs vector calculations for the wind triangle, including wind correction angle, groundspeed, and true heading. Every private pilot is required to understand and be able to use the E6B as part of their ground school training, and many commercial and instrument examinations still include E6B problems. Digital E6B calculators perform the same functions but solve them trigonometrically rather than through slide rule interpolation.
Wind correction angle (WCA) is the angle between the true course (the direction you want to travel over the ground) and the true heading (the direction the nose of the aircraft must point to compensate for wind drift). When flying into a crosswind, the nose must be pointed into the wind to prevent the aircraft from drifting off course. The WCA is calculated using the formula: WCA = arcsin((WS / TAS) × sin(WD − TC)), where WS is wind speed, TAS is true airspeed, WD is wind direction (the direction FROM which the wind blows), and TC is true course. The true heading is then TH = TC + WCA. Groundspeed is calculated as: GS = TAS × cos(WCA) − WS × cos(WD − TH). A headwind reduces groundspeed below TAS; a tailwind increases it above TAS.
True course (TC) is the intended track over the ground, measured from true north. Magnetic course (MC) is the track measured from magnetic north — apply magnetic variation (easterly variation is subtracted, westerly is added) to convert. True heading (TH) is the direction the nose of the aircraft must point to compensate for wind drift and fly the true course — it equals TC plus the wind correction angle. Magnetic heading (MH) is the heading corrected for magnetic variation. Compass heading (CH) is the heading corrected for both magnetic variation and compass deviation (errors in the magnetic compass itself). The sequence from chart to cockpit is: TC → add variation → MC → add WCA → MH → add deviation → CH. Remembering "East is least, West is best" helps with variation: east variation is subtracted, west variation is added.
Winds aloft can be determined from a flight if you know your true course, true heading, true airspeed, and groundspeed. The calculation uses reverse wind triangle geometry. The aircraft's velocity vector (true heading at TAS) plus the wind vector must equal the ground track vector (true course at groundspeed). By subtracting the aircraft's velocity vector from the ground track vector, the wind vector is revealed. Mathematically: wind components are computed as Wx = GS×sin(TC) − TAS×sin(TH) and Wy = GS×cos(TC) − TAS×cos(TH), then wind speed = √(Wx² + Wy²) and wind direction (FROM) = atan2(Wx, Wy) + 180°. This is the reverse function of the standard wind triangle and is used for airborne winds aloft verification.
True airspeed is calculated from calibrated airspeed (CAS) using the temperature ratio at the actual pressure altitude: TAS = CAS × √(T_actual / T_ISA), where temperatures are in Kelvin. T_ISA is the ISA standard temperature at the current pressure altitude (T_ISA = 288.15 − 0.0019812 × PA_feet, in Kelvin). T_actual is the outside air temperature in Kelvin (OAT°C + 273.15). In practice, a useful rule of thumb is that TAS is approximately 2% higher than IAS for each 1,000 ft of altitude in standard conditions. At 10,000 ft ISA, TAS is approximately 20% higher than IAS. This is why fuel burn per nautical mile (fuel ÷ TAS) is a better efficiency measure than fuel ÷ IAS.
The 60:1 rule is a mental arithmetic shortcut based on the fact that 1 nautical mile subtends approximately 1 degree at a distance of 60 nautical miles (since 60 × tan(1°) ≈ 1 nm). It is used for off-course correction and track error angle calculations. If you are 6 nm off course after flying 60 nm, your track error angle (TEA) is approximately 6°. To return to course at the destination, double the TEA for the closing angle: fly an additional 6° correction to converge with the intended track. For a direct return to destination, the correction angle equals TEA × (distance remaining / distance flown) added to the TEA. The 60:1 rule gives exact results for small angles and is useful for quick mental calculations during cross-country flight when GPS is not available or as a sanity check.
Fuel calculations on the E6B use the time-speed-distance framework, treating fuel burn rate as the "speed" and fuel quantity as the "distance." Fuel required = burn rate × time. Endurance = fuel quantity ÷ burn rate. Burn rate = fuel quantity ÷ time. The E6B calculator side handles all three with the same scales. For example, if an aircraft burns 10 US gal/hr and the flight is 2.5 hours, fuel required = 25 US gal. Add reserve fuel per regulations (VFR: 30 min day, 45 min night; IFR: alternate plus 45 min) and convert to weight for weight and balance using fuel density. Always plan fuel for the total block time (taxi, climb, cruise, descent, approach, alternate, reserve) not just cruise time.
Mach number is the ratio of the aircraft's true airspeed to the speed of sound at the ambient temperature: M = TAS ÷ a, where a = 661.47 × √(T/288.15) knots and T is the ambient temperature in Kelvin. Mach number becomes operationally relevant above approximately 25,000 ft and in high-performance aircraft. At Mach 0.82, shock waves begin to form on some wing sections (the critical Mach number, Mcrit). At Mach 1.0, the aircraft equals the speed of sound. Mach number is used instead of airspeed for high-altitude aircraft because aerodynamic effects depend on the ratio of airspeed to sound speed, not on absolute airspeed. Commercial aircraft fly at approximately Mach 0.78–0.85. Mach limit (MMO) is a structural certification limit that must not be exceeded.
Indicated airspeed (IAS) is the raw reading from the airspeed indicator, uncorrected for instrument error. Calibrated airspeed (CAS) is IAS corrected for position error — the error caused by the location of the pitot-static ports in non-ideal airflow. CAS is published in the POH as a correction table. Equivalent airspeed (EAS) is CAS corrected for compressibility effects at high speeds — at low speeds EAS ≈ CAS. True airspeed (TAS) is EAS corrected for air density — the actual speed of the aircraft through the air mass. TAS is what determines fuel burn per nm, wind triangle calculations, and aerodynamic effects. Groundspeed (GS) is TAS corrected for wind — it is the speed over the ground. V-speeds in the POH are given in IAS or CAS because these are what the pilot reads in the cockpit.
E6B proficiency is typically developed during cross-country training in the private pilot syllabus, before the first solo cross-country flight. The FAA Private Pilot Airman Certification Standards (ACS) requires applicants to demonstrate the ability to plan a cross-country flight using E6B or equivalent, including calculation of fuel requirements, estimated times en route, true heading, magnetic heading, and wind correction angle. Most flight schools introduce the E6B concurrently with cross-country planning lessons, typically around the 20–30 hour mark. ATPL candidates also need comprehensive E6B knowledge for examinations. Modern GPS and EFBs have reduced the day-to-day use of mechanical E6Bs, but they cannot eliminate the need to understand the underlying calculations — which the E6B forces students to learn.