The Fluency Equation
Breaking Down What It Takes to Speak Effortlessly
In school, I learned a concept that reshaped the way I saw the world: Formulas.
A formula is a delicate balance between the beauty of art and rigor of science. It reassures me that everything can be understood and that everything has a story waiting to be told. Formulas do more than explain; they narrate. As a student of the sciences, I have always leaned into these stories, listening to the way they unfold, uncovering the hidden dramas and triumphs encoded in their lines.
Fluency Formula
Recently, Viktoria Verde, PhD posted a simple conceptual formula for Spoken Fluency that aided me to distill my ideas into a simple form.
Fluency (Spoken) = (Knowledge × Automaticity) ÷ Cognitive Load
This is an interesting formula. It tells a simple story.
Fluency is just how well our brains can deploy what we know under current cognitive constraints.
From a deeper mathematical perspective, this formula tells us:
To improve Fluency, we either increase knowledge or automaticity, or both, or decrease cognitive load.
If Cognitive Load = 0, then Fluency = infinity i.e. we would be Perfectly Fluent. However, perfection doesn’t exist because of the permanent existence of cognitive load which acts as friction.
If Knowledge or Automaticity is 0, then fluency = 0 i.e. there is no fluency. This explains why beginners cannot be fluent: you cannot deploy what you do not know, and you cannot be fluent without automated access to what you know.
This last point reveals something subtle but essential:
Fluency begins at automaticity, not knowledge.
Defining Fluency
This leads to a provocative question:
If someone has internalized a dialogue, and that is the only thing he knows in the language. If he executes it perfectly, is he fluent?
According to the formula, yes—100%. He is fluent because he can perform with the required knowledge and automaticity under low cognitive load to pull off a simple conversation. However, he is fluent in a tiny domain.
I call this Performance Fluency or Acting. This is what happens in many language exams: learners perform well in narrow contexts, then struggle dramatically in the real world. However, what we really want is Functional Fluency, the ability to navigate broad, unpredictable communicative domains without performance breakdown.
Cognitive Load & Working Memory
Viktoria’s equation gave us a simplified guide to Fluency. If you want to get to fluency, just increase knowledge or automaticity. These are the easiest to do. Here is what’s harder to tackle, Cognitive Load.
Cognitive Load is the amount of mental effort being used in working memory at a given moment. It is said that working memory is limited, but Viktoria proposes that training your working memory to handle more complex tasks can make speaking a language feel easier and more automatic.
You can’t dramatically expand your absolute working memory capacity. That’s relatively fixed but you can absolutely train your functional working memory for specific tasks. — Viktoria Verde in The Working Memory “Fitness” Nobody Talks About
This is important as functional working memory is training your brain to handle the mental juggling required to speak a new language. A more efficient working-memory system means lower cognitive load for the same communicative task. However, I approach the problem more broadly: increase the efficiency of the entire system, not just its memory component.
System Efficiency
My desire is simple, to eliminate waste and achieve maximum effect with minimal workload as humanly possible. In thinking back to acquiring our first language, growing up:
We built knowledge, and automaticity developed simultaneously through immersion.
By age 2–3, we began training the brain to support linguistic computation by starting to speak.
Repeated exposure across contexts slowly eliminates situation novelty that reduces cognitive load.
Over time, extremely high efficiency emerges in language production.
We naturally performed all the steps required to create an efficient system for language production. A stealable schema that can be replicated.
As a language learner, if we seek to build this kind of systematic efficiency, we would need to do something similar.
We would need to build knowledge and proceduralize as much of it as possible via input or otherwise.
Then, we would need to train the brain’s capability to handle complexities of speaking the language. (Maxing out functional working memory)
Next, we would need to get massive repeated exposure in as many varied speaking situations as possible either via immersion (in-country) or simulation.
In my system, where I would do activities like, hundreds of hours of pronunciation practice or grammar practice, or internalizing 10,000 real sentences, shadowing a native and having provocative debates, are undoubtedly my attempt to expand the capacity and efficiency of my mental workspace, so I can handle more complex tasks and multitask better and automating my language production, so that it no longer consumes significant working memory, freeing up cognitive resources to deal with more complex elements of communication.
Final Thoughts on the Fluency Formula
What happens to this formula as speaking practice tends to infinity?
In the beginning, knowledge: low, automaticity: low, cognitive load: moderate to high, Fluency: minimal as we are only in the process of building new knowledge and memorizing phrases and new words.
As we move into intermediate levels, automation increases, knowledge increases but cognitive load also increases as we learn more complex structures, …attempt to communicate in a more complex fashion.
In advance levels, we still have high knowledge and high automation, but the cognitive load is reduced as our interlanguage starts to stabilize thus making Fluency more robust and reliable.
For Native Speakers. Automaticity will be practically maxed out for most core language structures thus Fluency will come to depend largely on how much new vocabulary can be integrated without overloading working memory.
So hence why final formula I believe would be for near-native speakers:
With context familiarity behaves like:
Cognitive Load = Base Load – Familiarity Effects
Familiarity effects act as a load regulator, reducing the mental cost of handling new contexts and maintaining fluent speech even under complex conditions.
The New Story of Fluency
By combining both formulas, we arrive at a more detailed story of fluency:
Fluency is the automatic, low-effort deployment of an expanding active vocabulary in real-world contexts, made possible by minimized cognitive load through familiarity and practice.
However, does this paint the complete picture of fluency? I have no idea. I am not a linguist nor am I fluent in an excess of 4 languages. Just a regular guy trying to learn a few languages thoughtfully.
Thanks for joining me on this thought provoking journey through the idea of Fluency!
You can see some of latest article here:
OMB! I have just realized I was not following the greatest guy in Substack:)
I’ve just remembered…I have a friend who teaches, she might be interested in your substack, Shamar.
“If Knowledge or Automaticity is 0, then fluency = 0 i.e. there is no fluency.” Ha, this could be a real polite way to tell someone spouting opinions and ignorance.