Navigation arithmetic makes up a large part of the numerical side of aircrew testing. The maths itself is trivial. Almost nobody gets these wrong because they cannot divide. They get them wrong because they are working in the wrong units, or because they spent forty seconds on a question worth the same as one they never reached.
The only three formulas you need
Everything in this family comes from one relationship, rearranged three ways.
- Distance = speed × time
- Time = distance ÷ speed
- Speed = distance ÷ time
Learn to write it as a triangle if that helps, with distance on top and speed beside time underneath. Cover the one you want and the layout tells you whether to multiply or divide.
Trap one: minutes are not hours
This is where most marks are lost. A speed in knots is nautical miles per hour, so any time you use with it has to be in hours. Sixty minutes is one hour, thirty minutes is 0.5, twenty minutes is one third, fifteen minutes is 0.25.
The answer options are usually written so that the value you get from forgetting this is one of them. If your answer appears in the list, that is not evidence you were right.
Worked example
An aircraft flies at 240 knots for 20 minutes. How far does it travel?
- 20 minutes is a third of an hour.
- 240 ÷ 3 = 80.
Answer: 80 nautical miles
The wrong answer here is 4,800, which is what you get by multiplying 240 by 20. It will be one of the options.
Trap two: mixed units in the question
A question may give you a distance in kilometres and a speed in knots, or a fuel figure per hour when the leg is quoted in minutes. Convert once, at the start, and write the converted figure down. Converting halfway through a calculation is how you end up with an answer that is right for a question nobody asked.
The shortcut that does most of the work
Because there are 60 minutes in an hour, speed in knots divided by 60 gives you nautical miles per minute. That single number turns most of these questions into a multiplication you can do without writing anything down.
- 120 knots is 2 nautical miles per minute
- 180 knots is 3 per minute
- 240 knots is 4 per minute
- 300 knots is 5 per minute
- 360 knots is 6 per minute
Learn those five. Test writers use round speeds, and one of these will cover a surprising share of what you see.
Worked example
How long does it take to cover 105 nautical miles at 180 knots?
- 180 knots is 3 nautical miles per minute.
- 105 ÷ 3 = 35.
Answer: 35 minutes
Arrival times
Once you have a flight time, an arrival time is addition, and addition in base 60 is where tired candidates slip. Add the hours first, then the minutes, then carry.
Worked example
Departure 0940. Flight time 1 hour 35 minutes. What is the arrival time?
- 0940 plus 1 hour is 1040.
- 40 plus 35 is 75 minutes, which is 1 hour 15.
- 1040 plus 1 hour 15 gives 1115.
Answer: 1115
Fuel
Fuel questions are the same arithmetic wearing a different hat. Consumption is usually given per hour, so the same conversion applies, and the same trap with it.
Worked example
Burn rate 480 litres per hour. The leg takes 45 minutes. How much fuel is used?
- 45 minutes is three quarters of an hour.
- 480 ÷ 4 = 120, so three quarters is 360.
Answer: 360 litres
How to actually sit these under a clock
- 1
Read the units first
Before anything else, note what units the question gives and what the answer wants. Ten seconds here saves you from the most common way of losing a mark.
- 2
Estimate before calculating
A rough answer tells you which options are impossible. Often only one option is in the right range, and you are done without doing the sum properly at all.
- 3
Move on at twenty seconds
If you are still working at twenty seconds, guess from your estimate and go. An unreached question scores the same as a wrong one, and there are always more questions than time.
The last one is the hardest to make yourself do and worth more than any arithmetic trick on this page.