Maximal vs. Maximum - Difference Explained (Helpful Examples)

The differences between using “maximal” and “maximum” are subtle, but it’s important to know what they are and how they work. This article will look at using both and how you can make sure you don’t make the mistake of confusing them in the future.

What Is The Difference Between Maximal And Maximum?

You should use “maximal” when you want to talk about a general quantity that is greatest or largest amount, though it doesn’t have to refer to the absolute highest number. You should use “maximum” when you want to talk about the highest possible quantity, with no wiggle room.

The definition of “maximal,” according to The Cambridge Dictionary, is “largest or greatest.

The definition of “maximal,” according to The Cambridge Dictionary, is “being the largest amount or number allowed or possible.”

“Maximum” is a specific quantity. It only refers to the absolute largest number possible and nothing more or less than it. “Maximal” is much more general, allowing us to still talk about a large or great quantity, but it’s relative to what the context is rather than an outright value.

Is Maximal Or Maximum Used The Most?

The two words are used in similar ways, though it might help you to visualize which is used more. Generally, with words and phrases like this that only have subtle differences, there’s a clear winner when you look at the popularity of each word in recent times.

According to this graph, “maximum” is used the most and by quite a large margin. It’s rare that native speakers will use “maximal” because there aren’t many situations where it is needed in place of “maximum.”

Generally, we use “maximum” to talk about an absolute amount that’s the largest possible recorded amount. We use this whenever we need to talk about a large quantity of something, which happens more frequently than you might realize.

On the flip side of that, we only use “maximal” when talking about the largest number at that given time. For example, if we are experimenting, we might say:

This only works at a maximal of fifty degrees; otherwise, it fails.

Here, “fifty degrees” is the largest possible number to succeed in the context, but obviously, there are much higher recordable temperatures.

Examples Of How To Use “Maximal” In A Sentence

Let’s go over some examples of how to use each of the words. From there, you might have a much easier time understanding how they work and making a choice to use them yourself.

“Maximal” refers to a general number that is the largest possible number at any given moment. It refers mostly to the context that we require it for.

What is the maximal distance we can run before our legs tire?
This needs to happen at a maximal of fifty degrees, or it dies.
What’s the maximal time it would take to complete this for an unfit person?
The maximal speed is highlighted here.
We strive to achieve maximal privacy for the people while keeping everyone safe.

Examples Of How To Use “Maximum” In A Sentence

“Maximum” is more common. In fact, most native speakers use the two words interchangeably, which is one of the reasons why “maximum” is used so much more frequently than “maximal.”

“Maximum” refers to an absolute amount of something. That amount is the greatest possible number and refers to no more or no less than it.

This microwave’s maximum temperature is 400.
We work with a maximum of six people at a time.
The maximum distance you need to run is three miles.
The maximum time taken to complete this task is sixty minutes. Don’t fail me.
We’ve achieved maximum coverage across all known mediums.

As you can see, “maximum” works much better when referring to the largest possible number of things at a time. We can use it whenever we want to do this, and most people prefer it over “maximal.”

Maximal And Maximum – Synonyms

If you’re struggling with the differences between the two words, it might help you to look at a few synonyms. These will really help you to think outside the box and come up with new words in your vocabulary that mean the same thing.

Highest
Largest
Greatest
Utmost
Biggest
Top
Topmost
Paramount
Extreme
Peak

All of these synonyms work well to replace both “maximal” and “maximum” in sentences. We can use them to talk about the largest possible amount of something.

Highest Vs. Maximum: What Is The Difference?

“Highest” is one of the words we mentioned as a synonym above. In most contexts, the words work really well to replace each other, which is why we think they work so well.

You should use “highest” when talking about the largest possible point or quantity of something. Usually, it refers to vertical distances (like mountains) or numbers (highest number). “Maximum” allows for more general uses, making it more versatile.

We can look at this graph to see how the words differ in use for most native speakers. Both words are almost identical in usage, with “highest” only barely being more popular.

What’s interesting about the above graph is that “maximum” was the most popular choice of the two during the 1900s, but it seems to have fallen out of popularity slightly since then.

What Is Maximal In Math?

We might also hear about the word “maximal” in math. It’s actually more commonly used in mathematic situations because it works as a concept rather than worrying about replacing “maximum.”

In math, “maximal” is an element used in order theory. In order theory, “maximal” is a subset that can’t be smaller than any other subset of a given order or model.

Is “Max” Short For Maximum Or Maximal?

We might also hear the word “max,” but it’s only short for one of the two words.

“Max” is short for “maximum” and refers to the greatest possible number of something. Even though they both start with the same letters, “max” is not short for “maximal.”

We can use both “max” and “maximum” synonymously with each other. We mostly use “max” informally and “maximum” formally.

The max amount I can give you is thirteen coppers.
Your maximum distance covered is recorded here.

What Does “Take It To The Max” Mean?

There are a few phrases and idioms that include the word “max” that we think you should know about. All of these idioms are informal but work well when you know how to use them.

“Take it to the max” means that we should take something to the next level. That means we should put more effort into something and try and get the “maximum” success out of whatever it is.

It’s a saying that was more popular in the late 1900s and rarely gets used today. However, you might come across it in certain situations, as follows:

Take it to the max! Don’t stop until the two of you are married!
We should kick this up a notch and take it to the max!
Give it all you’ve got and take it to the max!

What Does It Mean To Get Maxed?

Another phrase is “get maxed,” which is actually a verb we can use. Again, it’s fallen out of popularity in the last few decades, but it could still be relevant in a few situations.

“Get maxed” is a verb we use to talk about reaching the upper limit or amount of something. If we “max out,” we are said to “get maxed” for doing whatever we’ve reached the limit of (“get maxed on your credit card”).

It’s usually not a good thing to “get maxed” when you look at the context of points on your driver’s license or your credit card debt.

Does Maximum Mean At Most?

Sometimes, people confuse the meaning of “maximum” and “at most.” They are not synonymous, and it’s good to know what each of them means so you can work them into your writing.

“Maximum” and “at most” do not mean the same thing. “Maximum” means the largest possible number, while “at most” means that the specified number is the most allowed, but it would be preferred if less is given.

For example:

I have a maximum of fifteen dollars to spend.

This means that we’re happy to spend “fifteen dollars” on something and don’t mind if we hit that cap.

I want to spend fifteen dollars at most.

This means that, while “fifteen dollars” is okay for us to spend, we’d rather spend a smaller quantity of that and keep some of the rest of it for ourselves.

Quiz: Have You Mastered The Maximal Or Maximum Grammar?

That’s all you need to know about “maximal” and “maximum.” We’ll finish with a quick grammar quiz to see what you’ve picked up from this article. The answers will be in the following section.

What is the (A. maximal / B. maximum) distance I can cover before it breaks down?
The (A. maximal / B. maximum) coefficient doesn’t make sense here.
Why can’t we work with a larger (A. maximal / B. maximum)?
What is the (A. maximal / B. maximum) number of calories I can eat a day?
The (A. maximal / B. maximum) speed of this vehicle is in the documents provided.

Quiz Answers

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