For any angle up to about 20°, if the adjacent side of a right-angled triangle is
60 units long, then the length of the opposite side (in the same units) is numerically equal to the angle in degrees.
In flight: if you have travelled 60 NM along-track and you are N NM off-track, your track error angle is approximately N degrees.
Figure 1 — The 1 in 60 Rule — a right-angled triangle with an adjacent side of 60 units: the angle z° equals the opposite side in the same units
This is an enormously useful tool for in-flight calculations, removing the need for a protractor. The rule works because:
When the adjacent = 60, tan(z°) ≈ z/60 for small angles (up to ~20°)
Equivalently: one radian = 57.3° ≈ 60° for this approximation
2. Measuring Angles in Flight
Suppose you are flying on a planned track of 100°(T). After 60 NM from your last on-track fix, you identify a ground feature that is 4 NM right of track.
✎ Applying the rule directly:
Adjacent = 60 NM, Opposite = 4 NM → Track Error Angle = 4° right
Your Track Made Good (TMG) = 100° + 4° = 104°(T)
No protractor needed — simply read off the angle from the numbers. The next chapter covers what to do once you have the error angle.
3. Geometry of the 1 in 60 Rule — The Radian Derivation
Why does this rule work? The key lies in the definition of a radian.
Figure 2 — A circle of 1 metre radius — travelling 1 metre along the circumference subtends angle θ at the centreFigure 3 — The arc of 1 metre on a unit circle subtends θ = 57.3° at the centre (1 radian)
The Radian Calculation
Step-by-step derivation
Circle circumference: 2πr = 2 × 3.142 × 1 = 6.284 m
Full circle = 360° corresponds to 6.284 m of arc
1 metre of arc corresponds to θ, where: θ/1 = 360°/6.284 → θ = 57.3°
Scaling: This ratio holds for any circle radius — 57.3° always corresponds to an arc = radius
Strictly, this should be the "1 in 57.3 rule". But 57.3 is awkward for mental arithmetic at high workload in the cockpit. Rounding to 60 introduces only ~5% error, which is perfectly acceptable for navigation.
4. The Tangent Explanation
An alternative derivation shows why the rule works for a flat right-angled triangle (rather than an arc).
Figure 4 — Right-angled triangle with angle z — adjacent, opposite, and hypotenuseFigure 5 — Tangent table: values of tan z for angles 1° to 20°Figure 6 — Expanded table: 60 × tan z compared with z — showing the close numerical correlation
The Tangent Table
Angle z
1°
2°
5°
10°
15°
20°
tan z
0.017
0.035
0.087
0.176
0.268
0.364
60 × tan z
1.02
2.10
5.22
10.56
16.08
21.84
Up to about 10°, the correlation between angle z and 60 × tan z is excellent (within 1%). Above 15°–20° the error grows, but in practice you should rarely need the rule for angles that large.
⚠ Validity Limit
The 1 in 60 rule is acceptably accurate for angles up to ~20°. Above this, the tangent relationship becomes significantly non-linear. For track errors larger than 20°, use the nav computer or trigonometry.
5. Expanding or Contracting the Triangle
Fixes don't always occur at exactly 60 NM intervals. The 1 in 60 rule can be adapted for any along-track distance using the principle of similar triangles.
Figure 7 — 8 NM off track in 60 NM — track error = 8°Figure 8 — Same 8° track error at 30 NM along-track gives only 4 NM off track — similar triangles
✎ Scale the Cross-Track Distance
For a given track error angle, the cross-track error scales proportionally with along-track distance:
4 NM off in 30 NM = 8 NM off in 60 NM → track error = 8°
10 NM off in 120 NM = 5 NM off in 60 NM → track error = 5°
6. The Formula & Worked Applications
Track Error Angle
z = (Distance Off / Distance Gone) × 60
Or rearranged: Distance Off = (z × Distance Gone) / 60
Applications
Use case
Known
Find
Formula
Track error angle
Distance off, distance gone
Angle z
z = (off/gone) × 60
Cross-track distance
Angle z, distance gone
Distance off
off = (z × gone) / 60
Along-track distance
Angle z, distance off
Distance gone
gone = (off × 60) / z
Glide slope height
GS angle, range
Height
H = (angle × range_ft) / 60
Glide slope range
GS angle, height
Range
range_ft = (H × 60) / angle
✈ TMG vs Track Error
Track Made Good (TMG) = planned track ± track error angle
If aircraft is left of track: TMG = planned track − error (track is less than planned)
If aircraft is right of track: TMG = planned track + error (track is more than planned)
✎ Glide Slope Worked Example
GS angle 3°, range 2 NM (1 NM = 6 000 ft):
Range = 2 × 6 000 = 12 000 ft
Height = (3 × 12 000) / 60 = 600 ft
GS angle 2.5°, height 1 000 ft QFE (1 NM = 6 000 ft):
Range (ft) = (1 000 × 60) / 2.5 = 24 000 ft
Range (NM) = 24 000 / 6 000 = 4 NM
Closing angle: z = (2 / 40) × 60 = 3° Direction: Aircraft is left of track. To close onto R, turn right (increase track). Track to R = 125° + 3° = 128°(T)
Note: When flying toward the destination with a closing angle, the correction adds to or subtracts from the planned track to point at R — not at a parallel offset.
Instructor's Note: Source key: 128°(T). Verified.
Q12. Flying S to T, planned track 272°(T). Position: 50 NM from T, 5 NM right of track. What track must you fly to arrive overhead T?
Closing angle: z = (5 / 50) × 60 = 6° Direction: Aircraft is right of track. To close onto T, turn left (decrease track). Track to T = 272° − 6° = 266°(T)
Instructor's Note: Source key: 266°(T). Verified.
Master Reference Tables — Chapter 10
The 1 in 60 Formulae
Find
Formula
Notes
Track error angle
z = (off / gone) × 60
z in degrees
Cross-track distance
off = (z × gone) / 60
Units consistent
Along-track distance
gone = (off × 60) / z
—
Glide slope height (ft)
H = (angle × range_ft) / 60
1 NM = 6 000 ft for calcs
Glide slope range (ft)
range_ft = (H × 60) / angle
Then ÷ 6 000 for NM
Key Facts
Parameter
Value
Exact value (radians)
57.3°
Practical approximation
60° (~5% error)
Valid angle range
up to ~20°
Left of track → TMG
planned − error (TMG less than planned)
Right of track → TMG
planned + error (TMG more than planned)
Closing angle (left)
planned + closing angle
Closing angle (right)
planned − closing angle
Answer Key — No ⚑ Flags
Q
1
2
3
4
5
6
7
8
9
10
11
12
Ans
7°L
4°R
4°R
8°L
042°T
224°T
306°T
44 m
600 ft
4 NM
128°T
266°T
DGCA CPL/ATPL General Navigation Study Notes
Chapter 10 — The 1 in 60 Rule Capt. Pankaj Pahil | www.ghostaviator.com For personal study use only. Ghost Aviator Interactive Colour Edition.
