A Tour de France 2021 bicycle maths quiz

A Tour de France 2021 bicycle maths quiz

The biggest bike race is back - with some Tour de France maths puzzles for you to try!

This year the Tour de France celebrates its 108th anniversary, and that's not the only big number associated with this famous race. With 10 to 12 million spectators by the roadside and an enormous 3.5 billion people watching the race on TV, it beats the World Cup and even the Olympic games for the number of viewers.

Setting off this year from Brest in the north west of France, the 22 teams of eight riders finish up a little over three weeks later in the Champs Elysees in Paris after having cycled for a total of 3,383 kilometres, or 2,102 miles. 

Although the race winds around France, the distance covered by the Tour de France is so long that if they started cycling in Glasgow and travelled the distance of the race in a straight line, they'd make it almost the whole way across the Atlantic ocean to Newfoundland, Canada! 

In the Tour de France, cyclists tackle five different mountain ranges with riders climbing the height of Mount Everest almost four times over the course of the race. Impressive stuff!

Here at Komodo we love our bikes, but could only dream of tackling what these elite riders endure throughout the race. 

Our Komodo Team bikes...

As well as cycling, we also love how much maths can be found in a bike:

  • The angles of the frame change how your bike handles corners, and adapt your position when you ride for speed or comfort

  • The use of triangles - the strongest shape - perfectly calculated to support the wheels on thin spokes to keep them as light as possible 

  • Those circular bicycle wheels, cogs and chainrings - there's just so much maths in a circle! 

Tour de France bike maths

The following Tour de France facts and 'bike maths' questions are great jumping off points to help primary-aged children get a practical understanding of how numeracy and geometry apply to real life. 

Why not spend half an hour together working out how you might answer these maths questions about the bikes you ride...

Most Tour de France bikes have about 20 or 22 gears on them. They are changed depending on how steep or flat the stage is. 

Q1. How many gears do you have on your bike? 

Hint: Use your multiplication skills and multiply your front chainrings by the number of cogs on your back wheel. 

Tour de France cyclists turn their pedals an average of 486,000 times during the race, around 90 times a minute!

Q2. How far do you travel with each turn of your bicycle wheels? 

Check out this video to see how to measure it!


And now here's one to test your division skills:

Q3. How many times do your bike wheels turn if you cycle 100 metres?

Hint: Remember to use the same units (metres) for both measurements!

Your answer will be 100 divided by your answer (in metres) to question 2.

Q4. Can you estimate the angle between each of the spokes on your bicycle wheel? 

How would you measure the actual angle? 

It's good practice to estimate angles, but you could measure the actual angle using a protractor, but if the spokes are evenly spaced like in the wheel above, and you remember that one complete turn of a wheel is 360 degrees, you can divide 360 by the number of spokes to find the angle between each of them!


Q5. What is the diameter of your bike wheel? 

Tip: You'll need a measuring tape (or someone who can interpret your tyre markings!) 

Q6. Take your answer to question 2 and divide it by your answer to question 5 - do you know what is special about this number? 

In mathematical language you've just found out the circumference of your wheel divided by the diameter, which gives a special number called pi, which is 3.14 (and goes on for quite a few more decimal places!) If you got close to this number, you did the calculation correctly - it's hard to be completely precise with measurements. 

You can't eat this kind of pi, but it's a really useful number which you can use to calculate the circumference of a circle if you know the diameter (and the other way round) - now you know the hack you can work out your wheel's circumference without marking and measuring it on the road with chalk! 


About Komodo - Komodo is a fun and effective way to boost primary maths skills. Designed for 5 to 11 year olds to use in the home, Komodo uses a little and often approach to learning maths (15 minutes, three to five times per week) that fits into the busy routine. Komodo users develop fluency and confidence in maths - without keeping them at the screen for long. 

Find out more about Komodo and how it helps thousands of children each year do better at maths - you can even try Komodo for free.

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