Swim Faster By Using Math

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By Joe Petrush and Steve Brodsky 

Today I wanted to share with you the “math” on how to unlock swim speed and provide insight on how to design your own training program. At the end of the article there is an offer to learn, in person, the “how” and “why” of your swim training based on the principals outlined below.




Stroke Rate (SR) and Stroke Length (SL).
These two metrics provide real time data and feedback similar to measuring power when cycling or pace when running. We know that learning to calculate, manipulate and personalize stroke rate and stroke length yields tremendous gains for swimmers. There is no guessing or hoping that you will swim faster! It is a math problem that is solved by using 2 sets of numbers.

Unfortunately there is no proof that swimming 10×100 on a two minute base (or any other standard swim set) will make you any faster. You may get fitter from going back and forth across the pool and have the ability to “grind it out” longer but there is no way to gauge true progress on a stroke by stroke, lap by lap basis.

By collecting the real time data that actually determines swim speed (SR and SL) you can make adjustments to your training to maximize results. You no longer have to hope what you are doing is going to work, you will have the two metrics that guarantee success!


You no longer have to hope you go faster…


Stroke Rate (SR)
SR is a measurement of how many strokes you take in a minute. In other words, it is a measurement of how quickly or slowly your arms turn over. To manipulate stroke rate, swimmers can utilize a tempo trainer (TT), a small swimming metronome that is placed under your cap. The TT beeps at a fixed interval that is chosen by the swimmer. The swimmer adjusts their stroke so that the lead hand reaches maximum extension with each beep. It’s the same concept as keeping track of cadence on the bike.

Stroke Length (SL)
SL is a measurement of how far a swimmer travels with each stroke (also known as Distance Per Stroke or DPS). We typically calculate SL by counting the number of strokes a swimmer takes per fixed distance, usually the length of a pool. Since most of us swim at the same pool with regularity, counting the total amount of Strokes taken Per Length (SPL) becomes a simple way to quantify stroke length. As an example, a swimmer may take 20 strokes per length, where each hand entry equates to 1 stroke.

Stroke length is influenced, primarily, by three factors: your body length, your technique (balance, streamline and timing of movements) and your swim fitness. We’ve learned that the best swimmers in the world cover more distance per stroke (they take fewer strokes per length) and they also maintain that number of strokes as they swim.

A great example of this is Sun Yang’s world record-breaking 1,500-meter swim at the London 2012 Olympic Games. Yang held 26-27 strokes per length (50 meters) for the entire 1500 meter swim (a mere 13 strokes per 25 meters). He also maintains a fixed stroke rate of about .96 for the majority of the swim. When he does increase his rate, his SPL does not change (until the last 50 M). From these ideas, we can focus on two things, how to use stroke rate (SR) and strokes per length (SPL) to manipulate speed.




1) Find the lowest number of strokes per length that you can maintain with consistency at a fixed rate and then work to lower those numbers. For example, if you determine that you can hold 16 strokes per length at a rate of 1.8 seconds (taking 1 stroke every 1.8 seconds) with consistency, work to lower the SPL from 16 to 15 while staying at a rate of 1.8. And, also, work to quicken the SR to 1.7, then 1.6 while consistently holding 16 SPL.

There are also ideal lengths that a swimmer should travel based on their height. A taller athlete would cover a greater distance per stroke than a shorter athlete if everything else is equal.


“If a swimmer is not in their ideal SPL range,
they should focus on that first,
then stroke rate second

Coach Joe


2) Using the SR and SPL you have established, see how far you can swim before you start to add a stroke. In other words, if you are able to maintain 16 strokes per length at 1.8 consistently for a 150 yard swim but it goes up to 17 SPL after that, work on holding the same amount of strokes for a 175, then a 200 etc.

Why do we focus on these goals? Numerous studies (Costill et al. 1985, Craig and Pendergast 1979, Maw and Volkers 1996) and swim experts have established that speed = SR x SPL. In other words, going faster comes out of controlling the metrics just like the bike and the run.




Here’s a simple example:
If you swim 25 yards in 10 strokes at a rate of 1.5 (1 stroke taken every 1.5 seconds) you’ve just covered 25 yards in 15 seconds (this does not include the push off or turns).

10 SPL x 1.5 = 15 seconds

By decreasing the amount of strokes taken per length (10 down to 9) or by increasing stroke rate (1.5 down to 1.4) we change the equation and create a faster (or slower) swim. The key is that one of the metrics stays the same to manipulate speed!

  • 9 SPL x 1.5 = 13 seconds (going faster by decreasing SPL, 10 down to 9, but same SR)
  • 10 SPL x 1.4 = 14 seconds (going faster by increasing SR, 1.5 down to 1.4, but same SPL)

In both examples, a faster swim comes through manipulation of SR or SPL. Speed came from smarter swimming, not by working harder while hoping to go faster. In addition to acquiring easy swim power gains, we have two true measures (SR and SPL) to help quantify progress.



  1. Take less strokes at the same rate and you will swim faster!
  2. Take the same amount of strokes at a quicker rate/tempo and you will swim faster!

By taking less strokes, not more strokes, at the same rate swim speed increases. This happens by increasing the distance covered between strokes (or beeps) on the TT. At a rate of 1.5 every time 1 less stroke is taken the swimmer will go across the pool 1.5 seconds faster. If they took 1 more stroke they would go 1.5 seconds slower. 



  • Rate increases (1.5 down to 1.4) but stroke length does not stay the same, it also increases (10 spl up to 11 spl)
  • 11 SPL x 1.4 = 15.4 seconds
  • Rate stays the same (1.5) but strokes per length increase from 10 to 11
  • 11 SPL  x 1.5 = 16.5 seconds

This is why most swimmers “work harder” but don’t always go faster. If more strokes are taken at the same rate, or stroke length isn’t consistent at a faster rate, speed decreases. Having the arms move faster, pulling with more purpose and increasing the kick does not guarantee swim speed, but it does guarantee you will work harder.

Getting Started
As you begin to train with SR and SPL, start by becoming comfortable counting your strokes for each length of the pool. Each time your hand enters the water and reaches maximum extension, that is one stroke. Once you are comfortable with counting strokes, get comfortable with the tempo trainer. Find a rate that feels smooth and controlled— experiment with rates between 1.1 and 1.8. Now swim at that rate, “matching the beep,” having each hand reach maximum extension with each beep.

After you are accustomed to counting strokes and swimming with your TT on a fixed interval, you can begin to work on the goals mentioned above. Here is one example of how to mix this type of training into your current swim routine.




4×50 with decreasing (fewer) SPL
With your TT at 1.5, swim one 50 at an easy pace with a low rate of perceived exertion (RPE). Count your strokes and try to take one less stroke per 25 for each of the next three 50s. So if you swam each length of your first 50 in 18 strokes per 25, try to swim your second 50 in 17 strokes per length, your third 50 at 16, and your final 50 at 15 SPL.

Variation: Try substituting manipulation of SR instead of SPL. For the second, third, and fourth 50 of the set, maintain your SPL (18) while increasing your SR (faster TT setting) by .05 for each of these 50s. (Your first 50 is done at 1.5, 2nd is done at 1.45, 3rd is done at 1.40, 4th is done at 1.35.)

Ultimately, you should work on increasing the distance you can swim while keeping the metrics the same. If you can hold a combination of SR and SPL for 100 yards before adding any strokes or slipping off the beep, try stretching it out to a 125 then a 150. You’ll find that mental focus and technique are key elements in maintaining the strokes per length and stroke rate combinations. Note your gains and enjoy the process.




To help make the process of learning how to use rate and length as simple and easy as possible I’m offering a 2 hour clinic to everyone who wants to maximize their training time. The cost of the clinic is $245 and includes 2 hours of detailed coaching on how to use the tempo trainer while calculating what rate is the most efficient for your current swim ability. You will also find out what the ideal distance per stroke is based on your height and how to develop swimming “gears”. At the end of the clinic everyone will receive supporting documents on how to build stroke specific power, fluidity and long distance efficiency.

To make an appointment or for more information regarding this or any other offer please email Coach Joe at the studio.
Steve Brodsky is a professional writer, English professor, and avid triathlete. Along with his writing partner, Coach Joe Petrush, he has written articles, newsletters, coaching manuals for USAT, and two chapters in a forthcoming triathlon book for over 50 iron-distance triathletes.

Joe Petrush is a certified USAT Level II coach and Total Immersion swim instructor. Joe has participated in USAT’s elite mentorship program at the Olympic Training Center in Colorado and frequently shares his knowledge at USAT coaching certification clinics. Joe is the founder and head coach of both Bay Shore Swim and Premiere Coaching.