◇ Beginner to Intermediate◷ 7 min readMental Mathematics
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Introduction
Speed, distance and time calculations connect how fast you are travelling, how far you need to go and how long the journey will take.
The arithmetic is straightforward. The useful skill is choosing the right formula, keeping units consistent and working accurately under time pressure.
Start with the relationships below, then practise breaking calculations into smaller, familiar steps.
1. The three essential formulas
Identify the quantity you need to calculate before putting numbers into a formula.
Speed (S)S = D ÷ T
Distance (D)D = S × T
Time (T)T = D ÷ S
Speed: use groundspeed in knots (kt) for progress over the ground.
Distance: use nautical miles (NM) with knots.
Time: use hours with an hourly speed, or convert both to minutes.
One knot means one nautical mile per hour. Keep the same units throughout the calculation.
2. The SDT triangle
The triangle is a visual reminder of the three relationships.
Side by side means multiply. One above the other means divide.
How to use it
Cover the variable you want to find.
Cover D: multiply S × T.
Cover S: divide D ÷ T.
Cover T: divide D ÷ S.
The triangle helps you recall the formula. You still need to match the units.
3. Calculating distance
Distance = speed × time
A journey in hours
At 180 kt for 2 hours:
Distance = 180 × 2
Answer: 360 NM
A journey in minutes
At 240 kt for 15 minutes, first convert 15 minutes to ¼ hour.
Distance = 240 × ¼
Answer: 60 NM
Mental maths shortcut
Use familiar fractions of an hour instead of awkward decimals.
Dividing by half doubles the number. Dividing by a quarter multiplies it by four.
5. Calculating time
Time = distance ÷ speed
Finding time in minutes
A 45 NM leg at 120 kt takes 45 ÷ 120 = 0.375 hours.
Convert to minutes: 0.375 × 60 = 22.5.
Answer: 22 minutes 30 seconds
You can also work in nautical miles per minute: 120 ÷ 60 = 2 NM/min. Then 45 ÷ 2 = 22.5 minutes.
6. The 60 rule
Convert knots to nautical miles per minute by dividing by 60.
60 kt1 NM/min
120 kt2 NM/min
180 kt3 NM/min
When time is in minutes: time = distance × 60 ÷ speed. For 80 NM at 160 kt, cancel 80 ÷ 160 to ½, then multiply by 60: 30 minutes.
7. Breaking down difficult calculations
Split the distance into parts that are easy to handle.
72 NM at 180 kt
180 kt = 3 NM/min. Split 72 into 60 + 12.
60 ÷ 3 = 20 minutes; 12 ÷ 3 = 4 minutes.
Answer: 24 minutes
Estimate first. At about 3 NM/min, a journey of a little over 60 NM should take a little over 20 minutes.
8. Airspeed and groundspeed
Airspeed describes movement through the air. Groundspeed describes progress over the ground. Use groundspeed for the distance and time examples in this lesson.
A headwind reduces progress over the ground; a tailwind increases it. Wind at an angle needs a wind-triangle calculation rather than simply adding or subtracting the full wind speed.
9. Working under time pressure
Read the question and identify the unknown.
Check the units before calculating.
Use minutes-per-hour fractions or NM/min when convenient.
Estimate the size of the answer.
Write the unit with your answer.
Build accuracy first. Once the method feels familiar, practise with a timer.
10. Test your knowledge
Key takeaways
Choose the formula from the unknown quantity.
Keep knots, nautical miles and hours together.
Convert knots to NM/min by dividing by 60.
Use groundspeed when calculating progress over the ground.
Numbers & Arithmetic
◇ Beginner◷ 4 min readMental Mathematics
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1. Start with number sense
Break a number into hundreds, tens and ones. For 367 + 248, add 300 + 200, 60 + 40, then 7 + 8. Combine 500 + 100 + 15 = 615.
2. Follow the operation order
Work inside brackets first. Then do multiplication and division from left to right, followed by addition and subtraction from left to right.
Same numbers, different result
6 + 4 × 3 = 6 + 12 = 18.
(6 + 4) × 3 = 10 × 3 = 30.
3. Check division with multiplication
If 84 ÷ 7 = 12, multiplying 12 × 7 should give 84. An inverse operation is a quick way to check a result.
Mental maths shortcut
Learn the times tables in both directions. Knowing 8 × 7 = 56 also gives 56 ÷ 8 = 7 and 56 ÷ 7 = 8.
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Fractions, Decimals & Percentages
◇ Beginner to Intermediate◷ 5 min readMental Mathematics
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1. Recognise common equivalents
One half½ = 0.5 = 50%
One quarter¼ = 0.25 = 25%
One eighth⅛ = 0.125 = 12.5%
A decimal becomes a percentage when you multiply it by 100. A percentage becomes a decimal when you divide it by 100.
2. Find a fraction of a number
Three eighths of 240
Divide by the denominator: 240 ÷ 8 = 30.
Multiply by the numerator: 30 × 3 = 90.
Answer: 90
3. Break percentages into parts
Mental maths shortcut
Find 10% by dividing by 10. Halve it for 5%, or double it for 20%. For 15% of 240, add 24 and 12 to get 36.
To increase 80 by 25%, add 20: the new value is 100. To decrease 80 by 25%, subtract 20: the new value is 60.
4. Compare fractions
Use a common denominator: ⅔ = 8/12 and ¾ = 9/12, so ¾ is larger. Converting both to decimals is another useful approach.
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Ratios & Proportions
◇ Beginner to Intermediate◷ 4 min readMental Mathematics
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1. Understand the parts
A ratio of 2:3 means two parts of one quantity for every three parts of another. There are five parts altogether.
Sharing 150 in the ratio 2:3
Each part = 150 ÷ 5 = 30.
The shares are 2 × 30 = 60 and 3 × 30 = 90.
Check: 60 + 90 = 150
2. Scale both quantities together
If three identical items cost 24, one costs 8 and five cost 40. Find a unit rate, then scale to the quantity you need.
3. Recognise a constant rate
At a constant 120 kt groundspeed, doubling the travel time doubles the distance. For a fixed distance, doubling the speed halves the travel time. State what remains fixed before deciding how quantities change.
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Units & Conversions
◇ Beginner◷ 4 min readMental Mathematics
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1. Hours, minutes and seconds
One hour contains 60 minutes; one minute contains 60 seconds. Divide minutes by 60 to get hours. Multiply decimal hours by 60 to get minutes.
1 hour 45 minutes
45 ÷ 60 = 0.75 hours.
Total: 1.75 hours, not 1.45 hours.
2. Nautical miles and knots
One nautical mile is exactly 1,852 metres (1.852 km). One knot is one nautical mile per hour. Do not mix nautical miles with statute miles or kilometres in a single calculation without converting.
3. Volume and mass
Litres measure volume; kilograms measure mass. Converting between them needs the fuel density. A burn rate in litres per hour must be paired with fuel in litres.
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Estimation & Rounding
◇ Beginner to Intermediate◷ 4 min readMental Mathematics
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1. Round to friendly numbers
For 198 × 21, use 200 × 20 = 4,000 as a rough estimate. The exact answer, 4,158, should be close. An answer of 415.8 or 41,580 should prompt another check.
2. Know which way you rounded
398 + 47
Round 398 up to 400. Then 400 + 47 = 447.
You added two too many, so subtract two.
Answer: 445
3. Use simple bounds
For 95 ÷ 4, compare it with 80 ÷ 4 = 20 and 100 ÷ 4 = 25. Your answer must lie between 20 and 25.
An estimate checks plausibility. It does not replace an exact answer when the question asks for one.
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Mental Maths Shortcuts
◇ Beginner to Intermediate◷ 5 min readMental Mathematics
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1. Split difficult products
17 × 6
Split 17 into 10 + 7.
(10 × 6) + (7 × 6) = 60 + 42.
Answer: 102
2. Use friendly multipliers
Multiply by 5×10, then halve
Multiply by 9×10, subtract once
Multiply by 25×100, then ÷4
48 × 25
48 × 100 = 4,800. Divide by four.
Answer: 1,200
3. Cancel common factors
Before multiplying 80 × 60 ÷ 160, simplify 80 ÷ 160 to ½. The calculation becomes ½ × 60 = 30.
Mental maths shortcut
For division by 5, double the number then divide by 10. For 85 ÷ 5: double 85 to get 170, then divide by 10 to get 17.
4. Choose a method you can check
A shortcut is useful only if it is reliable. Estimate the answer first and use a second method to check unfamiliar shortcuts while practising.
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Fuel Calculations
◇ Beginner to Intermediate◷ 5 min readNavigation Skills
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1. Connect fuel, rate and time
Fuel usedRate × time
EnduranceFuel ÷ rate
Burn rateFuel ÷ time
Use hours with an hourly rate. Pair litres with litres per hour, or kilograms with kilograms per hour.
2. Calculate fuel used
36 litres per hour for 40 minutes
40 minutes = ⅔ hour.
Fuel used = 36 × ⅔.
Answer: 24 litres
Mental maths shortcut
At 36 L/h, each ten minutes uses six litres. Four ten-minute blocks use 24 litres.
3. Calculate endurance
90 usable litres at 30 litres per hour
Endurance = 90 ÷ 30.
Answer: 3 hours at that constant rate.
This is an arithmetic estimate. Real flight planning uses aircraft performance data and accounts for flight phases, conditions and applicable reserve requirements.
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Bearings & Direction
◇ Beginner to Intermediate◷ 5 min readSpatial Reasoning
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1. Read the compass
North000° / 360°
East / South090° / 180°
West270°
Bearings increase clockwise from a reference north. Keep the same reference throughout a question.
2. Follow left and right turns
350°, then right 30°
Add 30: 350 + 30 = 380.
Subtract 360 to wrap around the compass.
Answer: 020°
Add a right turn; subtract a left turn. If a result is negative, add 360. If it is 360 or more, subtract 360 until it is in the range 000–359°.
3. Find the reciprocal
The reciprocal points in the opposite direction. Add 180° to bearings below 180°; subtract 180° from bearings of 180° or more. The reciprocal of 070° is 250°.
4. Heading, track and bearing
A heading is where the aircraft points. A track is its path over the ground. A bearing is a direction to or from a point. Wind can make heading and track differ.
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Original aptitude practice lessons. Navigation reference: FAA Pilot’s Handbook of Aeronautical Knowledge. For flight planning, use approved aircraft information and applicable operating requirements.
Speed, Distance & Time (SDT) | PilotForge - Pilot Aptitude Training