Stamford Spinnakers
The Girls Ice Hockey Association   
of Stamford, Connecticut

High School (U19) Team - Math on Ice


You can't play this game without mathematics, whether you know it or not.

Let's say you're playing defense and an opponent with the puck breaks past your partner across the ice.  Do you skate right to where you see the attacker?  Of course not, because she won't be there when you arrive.  You have to assess her speed, your speed, and her angle of attack, then calculate an angle on which you can intercept her.  Angling is a key ingredient of hockey defense.  It's amazing how well you do it, considering that none of us can easily explain the underlying math!


Which fraction is largest: 5/4, 4/3, 3/2 or 2/1?
If your team has a 5 on 4 advantage, and you have to decide whether to draw an opponent away from the play, it's important to know that 4/3 is a larger fraction (i.e., the numerator is larger in relation to the denominator) than 5/4.  Math tells us that 4 skaters have a better advantage over 3 than 5 skaters have over 4.  


You're the center, preparing for a face-off.  The referee drops the puck.  How soon and how fast do you go for it?  You estimate the time it will take for the puck to reach the ice, where it will land, when you have to start moving your stick and how fast you have to move it.  Thanks to your math skills, you win another face-off!


Your teammate is chasing the puck into her corner of the attacking zone.  You're just entering the left side of the zone at full speed.  When your teammate gets the puck, she has to evaluate your speed and adjust both the speed and direction of her pass to put the puck on your stick when you're in shooting position.  You have to read what she's doing, factor in her passing ability, and adjust your speed to make sure you're there when the puck arrives.  (You can bring a graphing calculator to the SAT, but not to hockey.  Imagine trying to use one with those gloves!)


You know your 6th and 7th teammates on the ice are the boards, right?  But how do you know where on the boards to hit the puck?  Mathematically, of course.  You know the angle of incidence equals the angle of reflection.  That's why your give-and-go with these "teammates" always works so well.


Math is involved in your skating and stick handling, too.

The skater who rolls her ankles has more edge control.  Why?  Because of the ANGLE of her blades against the ice.


The skater who keeps her knees bent controls more ice with her stick.  Why?  Because she understands triangles!


The skater who keeps her hips low* gets longer strides.  How do we know?  More triangles!

*We say it that way because some benefits of staying low are not obtained by bending at the waist.


Why do crossunders help us skate faster while turning?  The reason is that, during a turn without crossunders, the interior skate has less skating to do than the exterior skate.  If the interior skate is fully extended in the usual way, it works against the turn.  (It's like trying to turn a canoe with paddles working at full force on both sides.)  Instead of taking short strides with the interior skate, we convert the interior skate into a second exterior skate, crossing under and making full strides on its outside edge.  What keeps you from falling into the circle when you use both skates externally?  Well, that's getting into Physics, which is interesting, but not on the SAT.  

C = ΠD.  If you skate around a face-off circle without crossunders, your outside skate travels about 13 feet further than your inside skate.
That's not efficient.


How do you aim a one-timer on a puck
passed from the corner?
Vector sums may not be on the SAT,
but you need to compensate for them
if you want to score this goal.



Goaltending and shooting involve lots of math.

When a goalie faces an attacker on a breakaway, she comes out just enough to "cut off the angles."  That requires fast math.  It's shown in two-dimensions below, but it actually involves three.


By the way, that goalie had 14 saves on 15 shots in her last game, a save percentage of 93.33%.  Her team won their 28th game out of 39.  That's hard to compare with another team's record until you mathematically convert it to an impressive 71.8%.

Did we mention dimension?  Math teaches you about length (one dimension), area (two dimensions), and volume (three dimensions).  Consider the dimensions of hockey.  When a brand new hockey player gets the puck on her stick, all she can think about is carrying it toward the other team's goal, and all the other team has to do is stand in her way.  She's thinking about the length of the rink, but not the width (its second dimension).  After a month of Girls Spring Hockey, she will be looking for cross-ice passing opportunities.  Does the rink have a third dimension?  Just ask Spinnakers defenseman Kylee Ruther, who loves to loft the puck over an opponent's head.  One of the first things she checks when we travel to a new rink is the height of the ceiling!  


So, after all these years of getting up early on weekends to practice your mathematics, there's no reason you shouldn't get a perfect score on the Math section of your SAT.  Good luck to our Juniors and Seniors!


Can you think of other applications of math in hockey?  Check out the goalie reaction time calculations at, where you'll also read that Skating, according to physicist Thomas Humphrey, is "the fastest way to travel on the surface of the earth on your feet."  (It doesn't say how he excludes downhill racing.)

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