MENTAL MATHS
Pilot mental maths: the techniques that save time
Mental maths is part of almost every pilot selection. It's not about being a genius: with a few rules of thumb and some practice, you get much faster. Here are the techniques used in flight and in the tests.
Good habits
- Read the whole question: the unit asked changes everything (minutes, NM, kg).
- Round first to get the order of magnitude, then refine: an answer 10 times too big jumps out.
- Stuck for more than 10 seconds? Skip: a skipped question costs nothing, a stuck one wastes time.
- Learn the speeds in NM/min by heart (120 kt = 2, 180 = 3, 240 = 4…) and the times tables up to 15: that's half the job.
The techniques, one by one
BASIC MATHS
Addition and subtraction
Work left to right: hundreds, then tens, then units.
- For an addition, add the hundreds first, then the rest: 347 + 286 = 347 + 200 + 80 + 6.
- For a subtraction, round then correct: 812 − 397 = 812 − 400 + 3.
- Say the running total under your breath: "547… 627… 633".
Example · 634 − 278 → 634 − 300 = 334, + 22 = 356.
BASIC MATHS
Multiplication
Split the bigger number into tens and units.
- 47 × 6 = 40 × 6 + 7 × 6 = 240 + 42 = 282.
- × 11: add the number shifted one place (34 × 11 = 340 + 34 = 374).
- × 25 = × 100 then ÷ 4. × 15 = × 10 plus half. × 12 = × 10 + × 2.
- Two numbers near 20: 18 × 23 = 18 × 20 + 18 × 3 = 360 + 54.
Example · 36 × 25 → 3,600 ÷ 4 = 900.
BASIC MATHS
Division
Think in times tables: how often the divisor fits into each chunk.
- Cut the number into easy chunks: 744 ÷ 6 = 600 ÷ 6 + 144 ÷ 6 = 100 + 24.
- ÷ 5 = × 2 then ÷ 10. ÷ 4 = half of half. ÷ 8 = halve three times.
- Check by multiplying: 6 × 124 = 744.
Example · 552 ÷ 8 → 276, 138, 69.
BASIC MATHS
Percentages
Always go through 10% (drop a zero) and 5% (half of 10%).
- 10% of 480 = 48; 5% = 24; 1% = 4.8.
- 15% = 10% + 5%. 25% = a quarter. 75% = three quarters.
- 40% = 4 × 10%. 60% = 6 × 10%, or the whole minus 40%.
- x% of y = y% of x: 16% of 25 = 25% of 16 = 4.
Example · 15% of 840 → 84 + 42 = 126.
FLIGHT MATHS
Flight time
Turn the speed into NM per minute: speed ÷ 60.
- 120 kt = 2 NM/min; 180 kt = 3; 240 kt = 4; 300 kt = 5; 360 kt = 6; 420 kt = 7; 480 kt = 8.
- Time (min) = distance ÷ NM per minute.
- If the speed is awkward, use a fraction of an hour: 150 kt and 50 NM → 50/150 = 1/3 h = 20 min.
Example · 300 kt, 75 NM → 5 NM/min → 15 min.
FLIGHT MATHS
Distance flown
Distance = NM per minute × minutes.
- First work out NM per minute (speed ÷ 60).
- Multiply by the time: 240 kt for 12 min = 4 × 12 = 48 NM.
- Other way: fractions of an hour. 15 min = 1/4 h, so 360 kt × 1/4 = 90 NM.
Example · 450 kt, 8 min → 7.5 NM/min × 8 = 60 NM.
FLIGHT MATHS
Fuel
Same logic as distance: fuel flow ÷ 60 = kg per minute.
- 1,800 kg/h = 30 kg/min; 2,400 kg/h = 40 kg/min; 3,600 kg/h = 60 kg/min.
- Multiply by the time in minutes.
- With hours and minutes, split it: 1 h 30 at 2,400 kg/h = 2,400 + 1,200 = 3,600 kg.
Example · 2,700 kg/h for 40 min → 45 kg/min × 40 = 1,800 kg.
FLIGHT MATHS
Rate of descent
3° path: rate of descent ≈ groundspeed × 5.
- Why: 3° ≈ 300 ft per NM, and groundspeed ÷ 60 gives NM per minute.
- 300 × (speed ÷ 60) = speed × 5.
- The exact factor is closer to 5.3, hence a small accepted margin.
- Headwind = lower groundspeed = lower rate.
Example · 140 kt → 700 ft/min.
FLIGHT MATHS
Top of descent
3-to-1 rule: 3 NM for every thousand feet to lose.
- Work out the height to lose: FL350 to 5,000 ft = 30,000 ft.
- Divide by 1,000: 30.
- Multiply by 3: 90 NM.
- In real life, add a few NM to slow down or with a tailwind.
Example · FL370 → 3,000 ft: 34 × 3 = 102 NM.
FLIGHT MATHS
Crosswind
Crosswind = wind × sine of the angle. Learn the clock rule.
- 10° → 1/6 of the wind; 20° → 1/3; 30° → 1/2; 40° → 2/3; 50° → 3/4; 60° and more → nearly all of it.
- Clock trick: 15° = a quarter hour = 1/4, 30° = half, 45° = 3/4, 60° = the whole wind.
- The headwind part follows the cosine: at 60°, half the wind is on the nose.
Example · 20 kt at 30° → 10 kt crosswind.
FLIGHT MATHS
Unit conversions
Learn a few factors and round: an approximate answer is accepted.
- kt → km/h: × 2 then − 7.5% (≈ × 1.85).
- NM → km: × 1.852, same trick as knots (× 2 then − 7.5%).
- ft → m: × 0.3 (divide by 10 then × 3). m → ft: × 3.3.
- kg → lb: × 2.2 (double then + 10%).
Example · 5,000 ft → 1,500 m (exact 1,524 m).
FLIGHT MATHS
Reciprocal heading
Reciprocal: + 200 then − 20, or − 200 then + 20.
- Heading under 180: add 200, subtract 20. 070 → 270 → 250.
- Heading over 180: subtract 200, add 20. 310 → 110 → 130.
- Check: the two headings always differ by 180.
Example · 047 → 247 → 227.
FLIGHT MATHS
1-in-60 rule
1-in-60 rule: 1 NM off at 60 NM = 1° error.
- Error (°) = offset (NM) × 60 ÷ distance flown (NM).
- At 30 NM each NM off is 2°; at 20 NM, 3°; at 120 NM, 0.5°.
- To reach the destination, correct by the track error plus the closing angle.
Example · 4 NM off after 40 NM → 4 × 60 ÷ 40 = 6°.
FLIGHT MATHS
Arrival time
Add the hours, then the minutes, carrying over 60.
- 14:45 + 2 h 35 → 16:45, then + 35 min = 17:20.
- Trick: first fill up to the round hour (14:45 → 15:00 = 15 min, 20 min left).
- Past 24:00, take away 24 h.
Example · 21:50 + 3 h 25 → 00:50 + 25 min = 01:15.
Frequently asked questions
What level of maths do pilot selections require?
Fast basic arithmetic (operations, percentages) and simple aviation calculations: time, distance, fuel, rate of descent, crosswind. An approximate answer is often enough for rules of thumb.
How can I improve quickly?
Learn speeds in NM per minute and your times tables up to 15, then practise a few minutes against the clock every day.