Mental arithmetic appears in some form at nearly every airline assessment — whether in a written technical paper, a DLR-style aptitude test, or a verbal question from a fleet captain asking you to estimate a descent rate. The good news: airlines test the same 10 formulas every time. Master these, practise under timed conditions, and mental math goes from anxiety source to easy marks.
The key principle: round aggressively, estimate confidently. You're not expected to be a calculator. An answer of "roughly 1,500 feet per minute" delivered in 10 seconds beats an exact answer of "1,485 fpm" that took 90 seconds. Interviewers test process and speed, not decimal precision.
Interview Prep Summary
- Mental Math for Pilot Interviews: 10 Formulas You Must Know - comprehensive guide with current 2026 information.
- The 10 mental math formulas tested in airline pilot interviews.
- Descent planning, fuel conversions, crosswind components, 1-in-60 rule — with worked examples and practice problems.
- The good news: airlines test the same 10 formulas every time.
- Read the full guide below for detailed analysis and actionable advice.
1. Descent Planning (3° Rule)
Distance to descend = altitude to lose ÷ 1,000 × 3
At a standard 3° descent angle, you need 3 nm for every 1,000 ft of altitude to lose. Drop the last three zeros from your altitude, multiply by 3.
Example: FL370 to FL100, need to be level by 30 nm from the field. Altitude to lose: 27,000 ft.
Distance: 27 × 3 = 81 nm for the descent, plus 30 nm = start descent at 111 nm. Add 1 nm per 10 kt of tailwind, subtract 1 nm per 10 kt of headwind. Add 1 nm per 10 kt of speed to lose.
2. Descent Rate for 3° Path
Required descent rate = groundspeed × 5
Example: Groundspeed 280 kt → 280 × 5 = 1,400 fpm. At 160 kt → 800 fpm. Some pilots prefer: groundspeed × 10 ÷ 2 (same result, sometimes easier mentally).
For ATC-assigned restrictions: altitude to lose ÷ minutes available = required fpm. Descend FL360 to FL320 in 4 minutes: 4,000 ÷ 4 = 1,000 fpm.
3. The 1-in-60 Rule
At 60 nm, 1° = 1 nm off track. Scales linearly: at 30 nm, 1° = 0.5 nm. At 120 nm, 1° = 2 nm.
Track error: offset (nm) = distance (nm) × degrees off ÷ 60. DME arc length: arc segment = DME distance × degrees of arc ÷ 60. A 90° arc at 15 DME: 15 × 90 ÷ 60 = 22.5 nm.
Glideslope check: on a 3° glideslope, altitude above threshold = DME × 300. At 5 DME you should be at 1,500 ft. At 10 DME: 3,000 ft.
4. Time-Speed-Distance
Miles per minute = groundspeed ÷ 60. Think in multiples of 60: 120 kt = 2 nm/min, 180 kt = 3 nm/min, 240 kt = 4 nm/min, 300 kt = 5 nm/min.
Time = distance ÷ miles per minute. 45 nm at 180 kt: 45 ÷ 3 = 15 minutes. 120 nm at 240 kt: 120 ÷ 4 = 30 minutes.
5. Fuel Conversions
US gallons → litres: multiply by 3.78 (use 4, then subtract ~5%). 85 USG: 85 × 4 = 340, minus 5% (~17) = 323 litres. Exact: 321.3 litres.
Litres → kg (Jet A-1): multiply by 0.8 (specific gravity varies 0.775-0.840, 0.8 is the standard planning figure). 323 litres × 0.8 = 258 kg. Kg → lbs: multiply by 2.2. 258 × 2.2 ≈ 568 lbs.
Learn the PPRuNe shortcut chain: USG × 4 (rough litres) → minus 5% (accurate litres) → × 0.8 (kg). Three steps, all doable in your head. This sequence appears in multiple PPRuNe mental math threads as the standard pilot method.
6. Crosswind Component
Use the "clock" method: at 30° off runway heading, crosswind = ½ wind speed. At 45°: ¾ wind speed. At 60° or more: full wind speed. At 15°: ¼ wind speed.
Example: Runway 27, wind 310/20. Angle off = 40°. Close to 45° → crosswind ≈ ¾ × 20 = 15 kt. Headwind ≈ ½ × 20 = 10 kt (since 40° is between 30° and 45°, headwind is between ¾ and ½).
7. Common Unit Conversions
Keep these ratios memorised — they appear in both aptitude tests and technical papers:
1 nm = 1.852 km (use 1.85 or "almost double"). 1 ft = 0.3048 m (divide feet by 3 for rough metres).
1 kg = 2.205 lbs (use 2.2). 1 inch Hg = 33.86 hPa (use 34). °C to °F: ×9÷5+32 (or double, subtract 10%, add 32).
8. Percentage Changes (ETA & Fuel)
If your groundspeed is 10% slower than planned, your leg time increases by ~10% and fuel burn for that leg increases by ~10%. This shortcut avoids recalculating from scratch.
Example: Planned GS 130 kt, actual 115 kt. Difference: 15 kt ≈ 12% slower. Planned leg time 33 min → add ~12% (4 min) = 37 min. Revise ETA and fuel accordingly.
9. Climb Gradient Conversion
ft/nm → ft/min: gradient (ft/nm) × groundspeed (nm/min). If SID requires 300 ft/nm and your GS is 150 kt (2.5 nm/min): 300 × 2.5 = 750 fpm minimum.
Percent gradient: 3.3% ≈ 200 ft/nm (≈ 3° flight path). This relationship helps cross-check obstacle clearance requirements against your aircraft's climb capability.
Practice Problems
Try these without a calculator. Aim for answers within 10% of exact, in under 30 seconds each.
| # | Problem | Answer |
|---|---|---|
| 1 | FL350 to FL80, when do you start descending? (still air) | 27,000 ft ÷ 1000 × 3 = 81 nm out |
| 2 | Groundspeed 260 kt — what descent rate for 3°? | 260 × 5 = 1,300 fpm |
| 3 | Convert 120 US gallons of Jet A-1 to kg | 120 × 4 = 480, − 5% (24) = 456 L, × 0.8 = 365 kg |
| 4 | Runway 09, wind 150/25 — crosswind component? | 60° off → full wind as xwind ≈ 25 kt (sin 60° = 0.87, so ~22 kt exact) |
| 5 | 90° DME arc at 12 nm — how long is the arc? | 12 × 90 ÷ 60 = 18 nm |
| 6 | SID requires 250 ft/nm, your GS is 180 kt — minimum fpm? | 180 kt = 3 nm/min. 250 × 3 = 750 fpm |
| 7 | How far off track are you at 45 nm with 3° heading error? | 45 × 3 ÷ 60 = 2.25 nm |
| 8 | Descend FL300 to FL250 in 3 minutes — what fpm? | 5,000 ÷ 3 ≈ 1,667 fpm |
Practise a set of 10 problems daily for two weeks before your assessment. Speed improves with repetition. Use these formulas during your actual flying to build fluency — the best preparation is using them operationally, not just in a study session.
PPRuNe pilots recommend: convert minutes to decimal hours as a first step in any time calculation. 6 min = 0.1 hr, 12 min = 0.2 hr, 15 min = 0.25 hr, 30 min = 0.5 hr. This eliminates the most common source of arithmetic errors in flight planning calculations.