Some things in life never change, like the number of days in a week, your birthday each year, or how homework always seems to find you.
The same goes for constants in math. While math often teaches us that numbers and values can change, constants are the fixed parts that always stay the same.
And once you understand them, a lot of math starts to make more sense.
In this guide, we’re focusing on what constants are, where they appear in math, and how to recognize them. Plus, you’ll get to test your skills with a fun quiz at the end.
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In math, a constant is a quantity that does not change in value. This could be a number, a term, or even a mathematical object that remains fixed within a particular context.
Think about your birthday. The date of your birthday never changes — it’s the same every single year. For example, if your birthday is February 25th, it will always be February 25th, no matter what.
Now, let’s say you’re making a plan for your birthday party. The number of friends who can come to your party can change depending on who is available.
Maybe 10 friends can make it one year, only 5 friends the next year, and maybe 12 friends the year after that. The number of friends keeps changing.
But the date of your birthday? That’s a constant!
We'll explore different types of constants next, including constant numbers, constant terms, and constant functions.
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If a constant is something that doesn’t change, let’s ask ourselves: can a number ever change its value?
Is 4 ever not 4? Can the number 12 suddenly become 9 just because we want it to? Of course not!
That’s because numbers represent fixed values. A constant number is exactly that — a number whose value does not and cannot change.
A constant number is a fixed value that never changes.
In math, all numbers are considered constant numbers because their values remain the same, no matter where or how they are used.
Real numbers, natural numbers, whole numbers, and integers are all examples of constant numbers.
Let’s take a look at a few more examples:
If the number 7 is always 7, what happens when we place that number inside a math expression, like 3x + 7? Does it still count as a constant?
Let’s think about that expression for a moment. One part of it, 3x, can change depending on what value x takes.
So the 3x part of the expression varies because it changes depending on the value of x.
But what about the 7?
No matter what x is, that 7 in our expression doesn’t budge. It stays the same every time. That’s why we call it a constant term.
A constant term is a number that doesn't change in a mathematical expression or equation.
It isn’t multiplied by a variable and doesn’t depend on anything else to define its value. Whether it’s +2 in 3x + 2 or –5 in 4y – 5, a constant term always holds its value.
Let’s take a closer look at how constant terms fit into expressions by breaking down our example: 3x + 7
This expression has three important parts:
We’ve seen constants as standalone numbers and within expressions. But what if the outputs of a function have the same value every time?
A constant function is a function that satisfies the rule f(x) = k, where k is a constant.
What do we mean by this?
Suppose you let x = 1, and you get 2. Then let x = 5 — still get 2. Let x = –10 and, yep, the result is 2 yet again.
So, a constant function means that no matter what value you plug in for x, the output will always be the same.
The graph of a constant function is a horizontal line with a slope of zero, like so:
Let’s say we have the function f(x) = 2.
Notice that for any value we substitute for x, the value of the function stays 2.
Now let’s plot those points on a graph. Since the output is always 2, the graph forms a horizontal line made up of points where y = 2.
This shows that a constant function has no slope — it stays flat no matter what x-value you choose.
Here’s another way to think of it. Imagine a vending machine where every snack costs $2. Whether you press button 1 for chips, 2 for candy, or 3 for cookies, the price is always $2.
This can be written as a constant function: f(x) = 2.
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From geometry to calculus, mathematical constants are the building blocks that help us solve problems and make sense of how math works. Let’s take a look at some of the most recognizable ones:
Pi is one of the most well-known constants in math. It represents the ratio of a circle’s circumference to its diameter, and its value is approximately 3.14.
The golden ratio is a fascinating constant that appears in nature, art, architecture, and even seashells!
Euler’s number is a special constant used mainly in higher-level math, like algebra, calculus, and statistics.
Ready to put what you’ve learned to the test? Try these questions and see how well you understand constants and their different types!
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Learning about constants can sometimes feel confusing, and that's okay! At Mathnasium, we often hear certain questions from curious students. Let’s clear up some of the most common dilemmas.
Students typically start learning about constants in elementary school when they work with numbers that never change, like 0, 1, or 7. As they move on to middle school, they learn about constant terms in algebraic expressions and explore constant functions later on.
Yes, absolutely! A constant can be positive or negative. For example, in the expression 2x - 5, the constant term is -5. Its value is fixed and doesn’t change, even though it’s a negative number.
Yes! The number 0 is a constant because it always represents nothing or no quantity. It’s also important in math because it acts as the starting point on the number line and follows special rules for addition, subtraction, multiplication, and division.
Constants are everywhere! Examples include:
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