How does a pilot use maths?

Quick answer

Pilots use maths every day to work out how fast to fly, how far they've gone, how high they are, and which direction to go. They also use maths to plan their flights, check fuel, and make sure they arrive safely on time.

Learning outcome

By the end of this page, you will understand how pilots use maths to plan and fly safe flights, and you'll be able to solve simple problems about speed, distance, time, and direction.

• You can calculate how far a plane travels in a certain time.
• You can work out how long a flight will take using speed and distance.
• You can use simple maps and directions to understand where a plane is going.
• You can solve problems about time zones and how they change when flying.

Why this matters

Maths helps pilots keep passengers safe and on time. When a pilot plans a flight, they use maths to make sure the plane has enough fuel, knows where it’s going, and arrives at the right time. Even if you don’t become a pilot, understanding how pilots use maths helps you see how useful maths is in the real world. You might even become a pilot one day!

How it works

When a pilot flies, they use maths in many ways. Let’s look at some of the main things:

1. Speed and Distance: Pilots need to know how fast their plane is going and how far it has to travel.
2. Time Zones: When flying across countries, pilots must adjust their watches and plan for time zones.
3. Height and Altitude: Pilots must know how high they are flying to avoid other planes and stay safe.
4. Navigation: Pilots use maps, compasses, and GPS to find their way through the sky.

Examples you can see

Let’s look at some real examples that show how pilots use maths:

Speed and Distance Example

Imagine a plane is flying at 500 km/h. If it flies for 2 hours, how far does it go?

Use this formula: Distance = Speed × Time

So, 500 km/h × 2 h = 1,000 km

The plane flies 1,000 kilometres.

Time Zone Example

Let’s say it’s 10:00 in London, and the pilot is flying to New York, which is 5 hours behind.

When it’s 10:00 in London, it’s 5:00 in New York.

So, if the pilot wants to land at 3:00 in New York, they need to plan to arrive at 8:00 in London time.

Height Example

A pilot is flying at 30,000 feet. If they climb 2,000 feet higher, what is their new height?

30,000 + 2,000 = 32,000 feet

The pilot is now flying at 32,000 feet.

Navigation Example

A pilot is flying from London to Paris. They use a compass to find direction. If they fly 200 km due east, then 150 km due north, how far are they from their starting point?

This is a bit more advanced, but we can use a simple idea: if they go 200 km east and 150 km north, they make a right-angle triangle. The distance is the hypotenuse of that triangle.

Using the Pythagorean theorem: Distance² = 200² + 150²

Distance² = 40,000 + 22,500 = 62,500

Distance = √62,500 = 250 km

So, the pilot is 250 km away from where they started.

Try it as a mini adventure

Imagine you are a pilot flying from London to Tokyo. You start at 10:00 in London and the flight is 13 hours long. Tokyo is 8 hours ahead of London.

1. What time will it be in Tokyo when you land?
2. If your plane flies at 900 km/h, how far will it go?
3. How high will you be if you climb from 30,000 feet to 35,000 feet?

Answers:

1. 10:00 + 13 hours = 23:00 in London. Tokyo is 8 hours ahead, so 23:00 + 8 hours = 7:00 in Tokyo.
2. 900 km/h × 13 h = 11,700 km
3. 30,000 + 5,000 = 35,000 feet

Common mistakes

• Mistake: Forgetting to adjust for time zones when planning a flight.
  Why it happens: Not thinking about how time changes when crossing countries.
  Fix: Always check the time difference between where you are and where you’re flying to.
• Mistake: Mixing up speed, distance, and time in calculations.
  Why it happens: Confusing the formula for speed, distance, or time.
  Fix: Remember: Distance = Speed × Time, Speed = Distance ÷ Time, Time = Distance ÷ Speed
• Mistake: Thinking that flying north and then east means flying in a straight line.
  Why it happens: Not understanding that the Earth is round and directions change.
  Fix: Use maps or compasses to check direction, or use simple geometry to find the actual path.

Parent and carer guide

Helping your child understand how pilots use maths can be fun and exciting. Here are some tips:

• Ask your child to imagine they are a pilot and plan a short flight. They can use a map, a clock, and a ruler to work out distance and time.
• Use a real-world example like a trip to the park. If you walk 500 metres in 10 minutes, how far would you walk in 20 minutes?
• Encourage them to ask questions about how pilots use maths. You can look up real flights together or watch short videos about how pilots work.
• Make it fun by playing a game: "If we fly from London to Paris, how long will it take?"
• Remember that mistakes are part of learning. If your child gets a calculation wrong, help them understand why, not just tell them the right answer.

Practice questions

1. A plane flies at 600 km/h for 3 hours. How far does it go?
2. If a flight takes 4 hours and covers 2,400 km, what is the speed of the plane?
3. If it’s 12:00 in London and Tokyo is 8 hours ahead, what time is it in Tokyo?
4. A pilot climbs from 25,000 feet to 30,000 feet. How high is the plane now?
5. If a plane flies 1,000 km in 2 hours, what is its speed?

Answers:

1. 600 km/h × 3 h = 1,800 km
2. 2,400 km ÷ 4 h = 600 km/h
3. 12:00 + 8 hours = 20:00 (8:00 PM)
4. 25,000 + 5,000 = 30,000 feet
5. 1,000 km ÷ 2 h = 500 km/h

FAQ

How do pilots know which direction to fly?

Pilots use compasses, GPS, and maps to know where they are going. They also use navigation systems to help them fly straight.

Why do pilots need to know about time zones?

Because when you fly across countries, the time changes. If a pilot doesn’t adjust for time zones, they might arrive at the wrong time or confuse passengers.

How does maths help pilots land safely?

Maths helps pilots calculate how fast to slow down, how far to go before landing, and how high to fly to avoid obstacles.

Do pilots use maths every day?

Yes! Pilots use maths to plan flights, check fuel, calculate speed, and make sure they arrive safely and on time.

Can I become a pilot if I’m good at maths?

Yes! Being good at maths is very helpful for pilots. You also need to be brave, calm, and good at problem-solving.