Cadiac Axis Determination – Part 1

Few subjects related to 12 lead ECG interpretation provoke more controversy (or anxiety) than axis determination.

It is controversial in that not everyone agrees it is a necessary skill for prehospital providers to learn. It is anxiety provoking in that it can be difficult to understand, especially when taught poorly.

I am of the opinion that axis determination is a critical skill to master. I would even go so far as to say that you cannot be competent at 12 lead ECG interpretation if you don’t understand the heart’s electrical axis.

In many classes, to the extent that axis is discussed at all, the instructor goes straight to providing a cheat sheet for axis determination. The most commonly taught method is the quadrant method that uses leads I and aVF. I don’t think this holds much value for the student. On the one hand, it’s perfectly true that leads I and aVF can place the QRS axis into one of four quadrants in the frontal plane. On the other hand, it leaves the student with a feeling of “so what?” The axis becomes a piece of “gee whiz” information that doesn’t lend itself to a deeper understanding of the 12 lead ECG.

I do teach the quadrant method (and other speed methods for axis determination), but only after I teach the hexaxial reference system, and my students can place the QRS axis within 10 to 15 degrees. This is not particularly difficult, and once it is well understood, it’s the gift that keeps on giving for the rest of your career. It is similar to using the large block method for rate determination in this respect. Once you know it, you know it, and you can estimate the heart rate at a glance. And yet, most paramedics have never bothered to commit this simple method for calculating the heart rate to memory, so they are dependent on the computer, or they have to count out the QRS complexes in a 6 second strip and multiply by 10.

Before we begin looking at the hexaxial reference system, there’s a man we need to discuss, and his name was Willem Einthoven, winner of the Nobel Prize in Physiology or Medicine in 1924 for his invention of the string galvanometer, which was the first reliable electrocardiograph.

You’ll notice in the image to the right that Einthoven’s arms and his left leg are immersed in buckets of salt water. At the time, this was the only way to obtain a signal for the electrocardiograph. Even after the invention of the electrode, they continued to be placed on the subject’s arms and legs. From this configuration, leads I, II, and III were born, and they are called the “limb leads” to this day.

Leads I, II, and III have been around for a long time (over 100 years). I always laugh when I hear people suggest that using leads I, II, and III to estimate the heart’s electrical axis is somehow a new thing! It’s been happening long before any of us were born.

These first 3 leads of the 12 lead ECG form what came to be known as Einthoven’s Triangle or Einthoven’s Equilateral Triangle.

Einthovens Triangle Anatomical_wmIf you’re like me, you’re reading this and it sounds very confusing. After all, if you look at the image on the left, it’s clear that anatomically, leads I, II, and III form a scalene triangle, not an equilateral triangle. So what in the world was Einthoven talking about?

Einthoven meant that electrically speaking, leads I, II, and III form an equilateral triangle. He expressed this with Einthoven’s Law, which states:

I + III = II which can also be written I + (-II) + III = 0

I know what you’re thinking. This equation is scary. I’ve just lost you. Take a deep breath! Everything is going to be okay.

What is lead I? It is a dipole, with the negative electrode at the right arm (white electrode) and the positive electrode at the left arm (black electrode).

What is lead III? It is a dipole with the negative electrode at the left arm (black electrode) and the positive electrode at the left leg (red electrode). Sometimes I wonder why Einthoven didn’t call this lead II.

What is lead II? Continuing clockwise as you look at the patient, you’d think it would be a dipole with the negative electrode at the left leg (red electrode) and the positive electrode at the right arm (white electrode), but it’s not. For reasons known only to Einthoven (perhaps because he liked to view upright QRS complexes), he made lead II a dipole with the negative electrode at the right arm (while electrode) and the positive electrode at the left leg (red electrode).

Had Einthoven not switched the polarity of lead II, Einthoven’s Law would be written like this:

I + II + III = 0

But he did, and there’s no point in crying over spilled milk.

I still know what you’re thinking. You’re feeling anxious because you still don’t understand what the equation is referring to! That’s okay. We’re getting there. Take another deep breath and relax. Everything is still going to be okay.

Rather than explain to you why Einthoven’s Law works, I’m simply going to prove to you that it does work.

Look at the image to the right and come up with a numerical value for the signal recorded in lead I. The R wave is about 7 1/2 mm tall, and the S wave is about 2 1/2 mm deep. Subtract the S wave from the R wave, and you come up with 5 mm.

Let’s do the same thing for the signal in lead II. This is easier, because it’s essentially a monophasic QS complex. It’s about -10 mm.

Do you see where this is going?

Now how about lead III? There’s a little nub of an R wave that is about 1 mm high, and the S wave is about 16 mm deep. Subtract the R wave from the S wave, and you get a complex that measures approximately -15 mm.

Now let’s plug these values into the equation for Einthoven’s Law.

I + (-II) + III = 0

5 + 10 -15 = 0

As you can see, when you plug in the measurements, you end up with an electrical value of zero.

You can try this trick on virtually any ECG.

Because this is true, leads I, II, and III can be represented as an electrically equilateral triangle.

As you will see in Part 2, this is the key to understanding the formation of the hexaxial reference system, and understanding the heart’s electrical axis in the frontal plane.

See also:

Cardiac Axis Determination: Part 1

Cardiac Axis Determination: Part 2

Cardiac Axis Determination: Part 3

Cardiac Axis Determination: Part 4

Cardiac Axis Determination: Part 5

Cardiac Axis Determination: Part 6


  • Tom,Thanks for the blog. Some of that is starting to make sense becuase I know nothing about axis determination and have had a difficult time understading it. Your blog will be passed on to those I teach. Thanks again.

  • e says:

    Please keep going with your posts. I am a paramedic and in my paramedic school they did not teach anything at all about 12 leads. Now I currently work for a service that is really big on 12 leads and I could use all the help I can get.

  • Anonymous says:

    Hey, thanks for your helped me a lot with my lab :-)

  • omeroglu says:

    Hi,What I didn’t understand ,according to equation :I+(-II)+III=0And we have two negative value : -10,-15 ,and you summiting all three :+5,-10,-15, and the result will be 0,and should be 5+(-25)=-20,please explain this and thanks

  • Tom B says:

    omeroglu –

    It would look this way: 5 + -(-10) + (-15) = 0

    which can be re-written: 5 + 10 – 15 = 0

    It may help you to think of the equation this way: I + III = II or 5 + (-15) = -10

    What makes it confusing is the fact that the polarity of lead II is reversed, so you have to add the opposite of the value for lead II.

    Clear as mud?


  • TeePee says:

    Hi TomThink your blog on cardiac axis was excellent – I teach cardiology here in the UK and have struggled for yrs to find an easy way to explain the hexaxial reference system to my students.I will be pointing my class to your blog.Many thanks

  • Tom B says:

    Thanks, TeePee!

    That's the highest compliment I could receive.


  • marianne murphy says:

    I have been acutely involved in ECGs for over 30 years whether in ICU, the EKG dept. or in the electrophysiology lab and have never understood axis determination. Your overview has helped me alot except for one thing that bothers me. I teach the staff in our facility how to do ECG's and the placement of the electrodes on the extremities has always been the most controversial. My understanding is the standard, universal placement is between the elbow and wrist and knee and ankle. How does this fit in with Einthovens theory? Does the different placement change the angle? Thanks for your assistance in clearing up an extremely confusing issue. mamurf2001

  • Tom B says:

    marianne murphy –

    Thank you for the feedback! Usually the argument is whether or not the limb leads need to be placed on the patient's limbs or if they can be placed on the patient's chest.I'd love it if the argument was between the distal extremities or the proximal extremities! It would mean that everyone was using the limbs.

    I honestly don't think it matters as long as the electrodes are on the limbs, although there is a modified placement called the Mason-Likar that is often used in stress testing. My understanding is that this modified lead placement has been well validated.

    I’m sorry I can’t answer your specific question.


  • Hassan Zaghnoun says:

    thanks it so easy explanations

  • Amrit says:

    Sinus rhtyhm without ectopy ~65 bpm, PRi 0.18, QRSd of 0.10, QTc of 410ms. aVL is concerning with a qr complex and ST-elevation. The inferior leads have subtle ST-depression, most visible in III. The precordials display some U-waves, a poor R-wave progression, and peaking in the T-waves.A cold read would have me saying STEMI.

  • rashy says:

    Thank you soooo much!!!! Keep on the good work! Never have I seen a better explanation!!

  • Thanks, Hassan Zaghnoun and rashy!

  • Janelle says:

    Thanks for this! The only thing I don't get is why you sebtract S from R in lead I but R from S in lead III.

  • Dr Muhammad Fayyaz says:

    Beautiful. Thanks a lot, I donot have to open book to refresh my graduate knowledge.

  • Tommi says:

    Finnish paramedic student here.

    Thank you for this explanation, I’ve read quite plenty of books about ECG and always failed understanding heart axis – nobody just haven’t been this clear about it. Also thanks for highlighting the importance of axis determination – I’ve been wondering, why ER-docs always pay that much attention to it and most of the paramedics just say that it doesn’t add up anything useful for diagnostics. As I’m slowly reaching understatement of it, I’m getting more and more of my interpretations right as I gain knowledge about it.

    I’ll tell my fellow students to pay a visit here on your blog! Keep on posting!


  • I agree, axis is an essential measurement of injury and must be taught, but I’ve discovered an easier way.

    Totally free…

    The Star Method of Axis Determination provides specificity necessary for accurate axis evaluation.

    If you check out my Star Method, you’ll see how easy it is to calculate axis by degree in 2 or 3 seconds.

    While quadrant axis will identify gross deviation, more subtle deviation is important too. 90 degrees to an 80 year old is extreme deviation, although still falling within what might be considered normal.

    Anyway, hope you like the Star Method as much as my students and thanks so much for posting all the fantastic materials. Never fail to learn in your company 😀

  • juhi patel says:

    Hey.. it’s clear cut.. thank u .. my concepts are brighter now.. keep helping! :-)

  • juhi patel says:

    why lead 2 is taken more in consideration? Why it’s taken as rhythm strip?

    • Sam Holkar says:

      lead 1+ lead 3= lead 2 that is one answer and when you study Einthoven’s triangle the position of lead 2 is at +60 degree and because of that QRS is more prominant than 1 and 3

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