# Most basic equation: Heart rate is in units of bpm. What are the units of "b"?

This is the most simple question in the world, but it is surprisingly difficult to explain to a student. The heart rate is measured in bpm, beats per minute. Minutes are a true unit. Beats are not a true unit. However, we are using beats as if it where a unit. I'm not sure how to explain this to a student, and I'm confusing myself. Please help.

• It's a dimensionless quantity. Thus the dimension of "beats per minute" is $\frac 1{\text{time}}$.
– lulu
Commented Dec 11, 2020 at 22:42
• How do you reckon a beat is not a unit? Sure, it is not one of the standard SI/imperial units, but it is clear enough what it refers to and is measuring/describing, surely? Commented Dec 11, 2020 at 22:43
• @lulu But in the medical world, it is allways written as bpm. If you write it as 1/time, no one will understand. Commented Dec 11, 2020 at 22:45
• Are you familiar with hertz (Hz)? A unit is $s^{-1}$, or in plain English, per second. Commented Dec 11, 2020 at 22:48
• @Eevee I agree that we all clearly understand the concept. However, if a beat is not one of the standard SI/imperial units, then it is not a unit. There are no other units. I applogize if we are going in circles. Commented Dec 11, 2020 at 22:48

BPM means "beats per minute" but that doesn't mean that "beats" is a "unit." Otherwise we could have an infinite number of "units" based on counting other things.

For instance: How many red two-door cars with sagging taillights and broken headlights with expired license plates pass by a point on this road in a minute? Oh, $$7$$, you say? Well I suppose the rate is 7 RTDCSTBHELPPM."

So now "RTDCSTBHELP" is a "unit"?!?!

Insane.

• Thanks for the laugh! Let me please pretend I'm the student. I would say to you that you can treat "beats" mathematically as if they were a unit. All the same operations apply. So, isn't it some kind of effective unit? Commented Dec 11, 2020 at 23:01

@Stork led me to the answer, but he didn't quite get there. A "beat" is a "counting unit". This is the term I've been looking for! A "dozen" is also a counting unit. If you google "counting unit", you will find it is a fairly common term. So, if a "beat" is a counting unit, then what kind of unit is a "second". A "second" is a "measuring unit". This implies that counting and measuring should be treated as distinct activities, which makes sense. I had never really stopped to realize that counting and measuring are distinct.

I do apologize for dwelling on this, but I think this terminology will clarify matters for students.

ps. This ancient paper appears to discuss the distinctions.