I posed a question a few days ago: “How many area codes do we need in Canada?” Here are some of my thoughts. I don’t think this is a complete answer (you’ll see why at the end), but I do think it’s a good back-of-the-napkin attempt. I also think it’s worth considering this problem from the point of view of younger students, who won’t have a lot of math in their pockets yet.

Canada has about 33.5 million people. How many phones should each person have? Well, some of those people are children, some are parts of families, some work, some have cell phones… it’s not simple, is it?

Well, let’s assume most children under 10 years of age don’t need a phone to themselves (I sincerely hope that’s true). I estimate (but haven’t bothered confirming) that there are about 5 million such children in Canada. That leaves 30 million potential phone owners.

Let’s suppose that every one of those individuals has a personal phone (like a cell phone), and that every one of them also has an organization phone (e.g. for a business, church, club, etc.). This isn’t realistic, since most churches don’t have a phone for each member, but also most church-going folks also work, so I’m hoping for some balance here.

That’s a ballpark of around 60 million phone numbers so far.

Also, I’ll guess there are something like 15-20 million families who probably have another shared phone line (like a “landline”), so we’re rounding upwards to 80 million.

Okay, let’s step back and consider the numbers themselves.

Looking at the last 7 digits, they’re broken into the exchange (3 digits) and the end part (4 digits – see my technical jargon there?).

Exchanges can’t start with 0 or 1, so that leaves 800 possible exchanges. The end parts can be anything, so there are 10000 possibilities there. Multiplying those two values gives us 8000000 (8 million) phone numbers per area code.

(Yes, there are a few other exchanges you can’t have, like 555 and so on. They’re small potatoes in this calculation. I’m sure my rounding up other stuff overwhelms them).

All right, so now we have 8 million numbers per area code and a need for 80 million numbers. That means we can have 80 million / 8 million = 10 area codes, right? Hey, that’s just about one per province/territory!

Except the population isn’t evenly distributed across the country. There are 12.8 million people in Ontario and 3.6 million in Alberta. How to resolve this?

Well, let’s round our 80 million up some more to make the numbers nicer. Let’s say we want to future-proof this a bit in case there’s a sudden population increase. Let’s bump it up to 3 phone numbers per person, which is just north of 100 million numbers total. Then we can distribute numbers based on the populations in each region, taking care to not let area codes cross provincial/territorial boundaries for convenience (thank you to Wikipedia for the numbers):

Province/Territory | Population | Phone Numbers Needed |
---|---|---|

Ontario | 12851821 | 38555463 |

Quebec | 7903001 | 23709003 |

British Columbia | 4400057 | 13200171 |

Alberta | 3645257 | 10935771 |

Manitoba | 1208268 | 3624804 |

Saskatchewan | 1033381 | 3100143 |

Nova Scotia | 921727 | 2765181 |

New Brunswick | 751171 | 2253513 |

Newfoundland and Labrador | 514536 | 1543608 |

Prince Edward Island | 140204 | 420612 |

Northwest Territories | 41462 | 124386 |

Yukon | 33897 | 101691 |

Nunavut | 31906 | 95718 |

Okay, so that leaves Ontario with 5 area codes, Quebec with 3, BC with 2, etc., until we arrive at a minimum of 21 area codes for the country. If I’ve counted correctly there are currently 37 in use, which is quite a bit more than my napkinning would suggest is necessary.

Of course, there are other factors I haven’t considered here. How many devices have phone numbers attached that are not for humans talk with? For example, what about automated calling systems? How many people acquire new phone numbers in a given time period? It would be nice to prevent numbers from being reused for a long time (say, a year), which would increase amount of available phone number space needed.

There are probably some other things I haven’t considered – anything come to mind?