How a circular E6B is laid out
The front of a mechanical E6B is a circular slide rule. The outer scale is fixed and is used for miles, gallons, true airspeed, and any other quantity in the same family. The inner disk rotates and is graduated in minutes, with an hours ring just inside it. Both scales are one logarithmic decade — the ticks from 10 to 100 go once around the face, and 10, 100, and 1,000 sit on the same mark.
The angle of a value x, measured clockwise from the 10-index at the top, is:
angle(x) = 360° × log₁₀(x / 10)
with x first wrapped into the decade [10, 100). So 8.5, 85, and 850 share a tick.
The black triangle at 60 on the inner scale is the rate index. To fly 120 knots for 45 minutes, you set that triangle under 12 (the 120 tick). Forty-five on the minutes scale then sits under 90 on the miles scale, because 120 × 45/60 = 90. Fuel burn is the same identity: 8.5 gph for 2 hours 30 minutes is 21.25 gallons.
The red NAUT, STAT, and KM arrows are a fixed angle apart equal to the exact SI ratios (1 NM = 1 852 m, 1 SM = 1 609.344 m). Align the known distance under its unit mark and read the other two under their marks. Off-course problems use the same 60-index as the 1-in-60 rule: 1° off for 60 NM flown is 1 NM off course.
The TAS and density-altitude windows
In the airspeed-correction window you line up outside air temperature with pressure altitude. That rotation is chosen so the inner and outer scales differ by the incompressible E6B relation
TAS ≈ CAS / √σ
where σ = ρ / ρ₀ = (p / p₀) × (T₀ / T) is the density ratio from the ICAO Standard Atmosphere (Doc 7488 / ISO 2533) at the entered pressure altitude and OAT. The window rotation is 360° × log₁₀(1/√σ) = −180° × log₁₀(σ).
A mechanical computer stops there. This page reports the subsonic compressible true airspeed as the numeric answer — the same pitot-static formulas as the true airspeed calculator — and shows the dial at the E6B alignment so you can see the difference. At light-airplane speeds the two are close; they diverge as Mach increases. IAS equals CAS only after instrument and position error are applied from the POH.
The density-altitude window is geared to the same setting. Density altitude is the ICAO geopotential height that has the same density, inverted in the troposphere as
DA = (T₀ / L) × (1 − σ1 / (g/(R L) − 1))
or about 145 442 × (1 − σ0.234969) feet. A rule of thumb, DA ≈ PA + 120 × (OAT − ISA), is shown for comparison. Humidity is omitted here; use the density altitude calculator when dewpoint is available.
Worked TAS check: 100 KCAS at 8,000 ft in ISA conditions is 112.7 kt by the compressible formula; the dial (CAS / √σ) reads 112.8 kt. At 6,000 ft and 0 °C, 120 KCAS is 130.4 kt exact and 130.5 kt on the dial. For density altitude, 5,000 ft pressure altitude at 30 °C is 7,801 ft by the ICAO inversion; the 120 ft/°C rule gives 7,989 ft.
The wind side
The back of an E6B is a plotter: a rotating azimuth (compass rose) with a true-index marker, a large frosted circular plotting disc with a grommet at the center, and a sliding card of concentric speed arcs and radiating drift lines that rides in a slot in the instrument body, shows through the disc, and extends from the top and bottom openings of the slot. The standard method, taught in the FAA Pilot’s Handbook and in E6B computer manuals, is:
- Rotate the azimuth until the wind direction is under the true index.
- From the grommet, plot a pencil mark toward the true index a distance equal to the wind speed.
- Slide the card so the grommet sits on the true-airspeed arc (any convenient speed works for plotting the mark; this page uses TAS).
- Rotate the azimuth until the true course is under the true index. The mark stays on the frosted disc and swings with it.
- Slide the card until the wind mark lies on the true-airspeed arc. Read the wind correction angle at the mark (left or right of the centerline) and the groundspeed under the grommet. True heading is true course plus WCA, with a right correction positive (crab right when the wind is from the right).
The illustration animates those steps. The printed answers use the exact wind-triangle solution, the same closed form as the E6B wind triangle calculator:
crosswind = WS × sin(wind − course) (positive from the right)
headwind = WS × cos(wind − course)
WCA = arcsin(crosswind / TAS)
GS = √(TAS² − crosswind²) − headwind
The sliding card is a section of a large polar plot: speed lines are concentric arcs about a zero-speed origin far above the window, and drift lines radiate from that same point, so a distance along the centerline is a uniform speed scale. Because the geometry is the same as the wind triangle, a reading at the pencil mark matches the exact solution to drawing precision. Classic check case: true course 090, TAS 120 kt, wind 360 at 20 kt → the mark sits about 9.6° left of the centerline on the 120-kt arc, and the grommet sits on 118.3 kt. The result panel prints those same trig values.
Related calculators
Sources
- FAA-H-8083-25C, Pilot’s Handbook of Aeronautical Knowledge, Chapter 11 (Aircraft Performance — density altitude, true airspeed) and Chapter 16 (Navigation — dead reckoning, the wind triangle, and the mechanical flight computer).
- FAA-H-8083-3, Airplane Flying Handbook, wind-correction and ground-reference procedures consistent with the wind-side method.
- ICAO Document 7488 / ISO 2533, Standard Atmosphere:
T₀ = 288.15 K,L = 0.0065 K/m,p₀ = 1013.25 hPa,g = 9.80665 m/s²,R = 287.05287 J/(kg·K). - Standard E6B computer-manual conventions: rate index at 60, TAS window by pressure altitude and OAT, statute/nautical/kilometre conversion indexes, and the wind-up / grommet-on-TAS plotting method.
- Subsonic pitot-static relations as used in flight-test work and on the true airspeed page:
qc/p₀ = (1 + 0.2 (CAS/a₀)²)7/2 − 1,M = √{5[(qc/p + 1)2/7 − 1]},TAS = M · a(T).
The face drawn here follows those conventions. It is an original illustration, not a copy of any manufacturer’s product.
Frequently asked questions
How do you use an E6B to solve time, speed, and distance?
Place the rate index (the black triangle at 60 on the inner, minutes scale) under the groundspeed on the outer scale. Then read distance on the outer scale opposite time on the inner scale, or time opposite distance. The same setting works for fuel flow, time, and fuel quantity. This page rotates the inner disk to that alignment and highlights the answer tick.
Does the TAS window on an E6B give an exact true airspeed?
No. A mechanical E6B lines up outside air temperature with pressure altitude so the inner and outer scales are shifted by 1 over the square root of the density ratio. That is the incompressible approximation TAS ≈ CAS / √σ. The number reported here is the subsonic compressible pitot-static solution; the dial is shown with the mechanical alignment and the two values are compared.
How do you use the wind side of an E6B?
Rotate the azimuth until the wind direction is under the true index. Plot a pencil mark from the grommet toward the true index at the wind speed. Slide the card so the grommet sits on the true-airspeed arc, then rotate until the true course is under the true index. Slide again until the wind mark lies on the true-airspeed arc. Read the wind correction angle at the mark and the groundspeed under the grommet. Heading is course plus WCA (a right correction is a crab to the right). The polar grid matches the exact wind-triangle solution to drawing precision.
Is a positive wind correction angle to the right or the left?
A positive WCA is a correction to the right: true heading = true course + WCA. Wind from the right produces a right crab. This page labels a left correction as L and a right correction as R, and it uses the same sign convention as the E6B wind triangle calculator.
Can I use this E6B instead of the POH or a certified flight computer?
No. This is a training and illustration aid. It is not a substitute for the Pilot’s Operating Handbook or Aircraft Flight Manual, a certified flight computer, official weather, or a navigation log used for flight. Always defer to those sources.