Instrument Rating Formula Collection

A comprehensive formula reference for the Instrument Rating, covering navigation calculations, radio aids, altimetry, and essential rules of thumb.

Navigation & Bearing Diagram

West (-) / East (+) / WCA rechts (+)

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Rules of Thumb

Speed

Knots to km/h: (Knots x 2) — 10% = km/h

Altitude

m -> ft	m * 3.28	(m * 3) + 10%
ft -> m	ft / 3.28	(ft / 3) — 10%

15,000 ft = 4.75 km

Distance / Speed

km -> NM	km / 1.852	(km / 2) + 10%
NM (kts) -> km (/h)	NM * 1.852	(NM x 2) — 10%

Descent Rate (ft/min) for 3-Degree Standard Approach

GS (in kts) x 5

Fuel Volume

Liters -> US-Gal	Liters / 3.78	(Liters / 4) + 5%
US-Gal -> Liters	US-Gal * 3.78	(US-Gal * 4) - 5%

• 92 gal = 348 liters (Full refueling Cirrus SR22)
• 46 gal = 174 liters (To the tabs — half refueling Cirrus SR22)

Cloud Height

Cloud Height (ft AGL) = Spread (in Kelvin) x 400

Surface and Altitude Wind

• 2000 ft AGL: + 30 degrees wind veering to the right, wind speed x 2

Stall Speed in Turns

Bank Angle	0°	30°	45°	60°	75°
Factor	1	1.1	1.2	1.4	2.0

True Airspeed (TAS)

Indicated airspeed (IAS) plus 2% of the indication per 1000 ft altitude.

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Radio Navigation Formulas

VOR/DME Range

Range (NM) = 1.25 x (√height_station + √FL(ft))
FL(ft) = (Range(ft) / 1.25 - √height)²

Wind Correction Angle (WCA)

WCA = Wind Diff Angle x Wind Speed / TAS

RMI Bearing

RB = QDM(ADF pointer) - MH

If negative: add 360°

Distance to DME

Distance = Altitude(ft) / 6000

(6000 ft = 1 NM above DME)

NDB Bearings

• Towards NDB → relative bearing = 0°
• Away from NDB → relative bearing = 180°

Slant Range

Slant range = (time(ms) - 50) / 12.36
DMEdist² = dist_hor² + height²

Wave Length

Wave length = speed of light (300,000 km/s) / frequency (Hz)

Rate of Descent

Rate of Descent = GS x 5

Every 10 kt in GS = 50 ft/min

1:60 Rule

At 60 NM → 1° = 1 NM At 100 NM → 1° = 1.5 NM; 5 NM offset at 100 NM = 3°

Max Radar Range

Range = c / (2 x PRF)
PRF = c / (2 x Range)

• c = 3 x 10⁸ m/s (for meters or km)
• c = 162,000 NM/s (for NM)

GS on ILS with Glideslope Out

GS out → LOC approach (GS out)

Headwind Component

Headwind = cos(angle°) x Wind Speed

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Altimetry & Pressure

ISA Temperature at Altitude

T(ISA) = 15° - (FL / 10) x 2

(-2°C per 1000 ft, -0.65°C per 100 m)

Pressure Altitude Corrections

At Altitude	1 hPa =
MSL	27 ft
10,000 ft	36 ft
18,000 ft / 5,500 m	50 ft / 15 m

QFE / QNH Relationship

• QFE from QNH: 27 ft = 1 hPa
• QFE < QNH above MSL
• Temp > ISA → QNH > QFF (below sea level: inverted)

Layer Thickness

Layer thickness = Δ height(ft) + (0.004 x Δ height(ft) x Δ temp(°C))

Altitude Correction Chain

PA  (Altimeter set to ISA)
 + Δ QNH
QNHA (Altimeter set to QNH)
 + Δ temp
TA   (dangerous Δ — instrument over-reads)

Memory aid: H → L → T → R → H

Standard ISA Pressure Levels

Pressure	Flight Level	Temperature
700 hPa	FL100	-5°C
500 hPa	FL180	-21°C
300 hPa	FL300	-45°C

Density, Pressure, Temperature

Temperature rises → pressure rises (density: linear, pressure: negative with temp)

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Conversions

• 1000 ft = 0.305 km (rule of thumb: /3 - 10%)
• 1000 m = 540 NM
• 1 km = 0.54 NM

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Airspeed Conversions

I AS  — Indicated Airspeed (read from airspeed indicator)
  ↓ Instrument & Position error (if absent: CAS = IAS)
C AS  — Calibrated Airspeed (Pt - Ps)
  ↓ Compression (>200 kt)
E AS  — Equivalent Airspeed
  ↓ + Density (fall in temp)
T AS  — True Airspeed (increases with height)

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Gyroscopic Precession (Apparent Drift)

Latitude	Drift Rate
0° (equator)	0°/h
30°N	7.5°/h to right (~1/4)
45°N	10.5–11°/h to right
60°N	13°/h to right
90°N (pole)	15°/h max

Southern hemisphere: drift is to the left (30°S = 7.5°/h to left).