Opinion, arguments & analyses from the editors of Scientific American

# Metrocard Mathematics: Are Unlimited Subway Passes a Good Deal?

The views expressed are those of the author and are not necessarily those of Scientific American.

Unlimited, or Pay-Per-Ride? That’s the question posed by the New York Times City Room blog this morning, as New Yorkers confront the great algebraic unknown of August: are unlimited subway passes still a good value even if you’re going out of town on vacation?

Perhaps the author, reporter Clyde Haberman, has been reading too much of his paper’s misguided screeds against mathematics education (nicely rebutted by my colleague Evelyn Lamb), but the column, titled “Doing the Metrocard Math,” never does the math.

This is a shame, because the math is not all that difficult to do (despite the Metropolitan Transit Authority’s bizarre decision two years ago to change the base bonus from a nice, even 20 percent to an ungainly 7 percent). The base fare for a subway or bus ride is \$2.25. Any Metrocard purchase of at least \$10 qualifies for the 7 percent bonus, lowering the net base fare to \$2.10.*

Beyond that, you have two choices: An unlimited 7-day card for \$29 or an unlimited 30-day card for \$104. Cost per ride is simply this cost divided by the number of rides. Here I plugged a few numbers into a spreadsheet. For simplicity I based the calculations on the number of rides a passenger expects to take per week.

Rides per week Cost per ride
7-day card 30-day card
8 \$3.63 \$3.03
9 \$3.22 \$2.70
10 \$2.90 \$2.43
11 \$2.64 \$2.21
12 \$2.42 \$2.02
13 \$2.23 \$1.87
14 \$2.07 \$1.73
15 \$1.93 \$1.62
16 \$1.81 \$1.52
17 \$1.71 \$1.43
18 \$1.61 \$1.35
19 \$1.53 \$1.28
20 \$1.45 \$1.21

As we can see, a 7-day unlimited pass only makes sense if you’re planning to take 14 or more rides a week—twice a day, weekends included. A 30-day unlimited pass works out after 12 rides a week, just in case you prefer to spend Sundays at home. To my surprise, a standard 10-ride-a-week commuter should always pay by ride. (Indeed, Haberman quotes Gene Russianoff, the staff attorney for the Straphangers Campaign, a riders’ advocacy group, as saying that a quarter of all 30-day unlimited buyers “don’t use them often enough to get their discount value.”)

But back to our original question: Should the summer jet-setter still buy a 30-day pass? Depends, obviously, on the jet-setter. But unless they’re a three- or four-trip-a-day rider, they may want to consider going à la carte even after August comes to an end.

*: Update 7/31/12 5:46pm: To my shame, I mistakenly said the MTA provides a 7 percent discount on Metrocards over \$10. They give a 7 percent bonus. (So \$10 in the machine nets you a \$10.70 card.) This changes the net base fare from \$2.09 to \$2.10. The rest of the calculations (and the conclusions) remain unchanged.

Update 8/6/12 6:52pm: Here’s a link to a Google Doc of the spreadsheet I made for the calculations, for anyone who’s interested (or would like to play with the values for their home transit system).

Photo by cfarivar on Flickr

About the Author: Michael Moyer is the editor in charge of space and physics coverage at Scientific American. Follow on Twitter @mmoyr.

The views expressed are those of the author and are not necessarily those of Scientific American.

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Rights & Permissions

1. 1. Courtney-Ostaff 6:23 pm 07/31/2012

Which is great, but there’s also the intangible of not waiting in line to renew your card. OTOH, can you get them by mail, or auto-renewed? Then that’d take that away. Ooh, I know, you should pay every time you swipe your metro card, instead of buying, and then swiping. Like those Easy Pass things…

2. 2. JHSmith 7:02 pm 07/31/2012

According to your table, which I recreated myself, you should never buy the 7-day pass. A 30-day pass will always be cheaper than the 7-day.

However, for travelers who will only be in town for 1-2 weeks, they should buy the 7-day pass if, as you alluded to, they travel at least 12 each week. No sense in them paying \$104 when they could pay \$29 or \$58.

3. 3. JHSmith 7:11 pm 07/31/2012

EDIT: Sorry, I forgot the premise of a local taking a vacation and not being able to use all of the 30-day pass (i.e. – 1 week vacation, 3 weeks of work, 1 week of vacation). In that case they should opt to buy 7-day passes if they travel 14 times a week.

4. 4. Forsythkid 7:52 pm 07/31/2012

I’ll do whatever the government tells me to do.

5. 5. Cramer 12:57 am 08/1/2012

Courtney-Ostaff, you must not live in NYC.
1. I have never waited in line for MTA vending machine. There are many, many machines.
2. You can buy as many rides as you want. You are not limited to \$10 or \$20. You can buy \$100 in rides if you like, which should last a month.

6. 6. jeremynyc 2:18 pm 08/1/2012

Huh. This has always been obvious to me–those bonuses are pretty big. The one thing that’s not factored in here is loss–you can get a refund for a lost unlimited card, but not for one with \$100 on it (which is how I usually purchase), and those bonuses mean that you end up with funny amounts on your cards, leaving some amount left over. Reusing a card is fine, but then big brother knows even more about you (not that this is a huge concern for me, just gives me the heebeejeebees.)

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