Constant simply is a fixed value or a value that does not change. A constant always has a known value such as pi(π) whose value is, π = 3.1415… Letter such as a, b, c used as the replacement for a constant.
In this article, we will discuss in detail about Constant in Mathematics.
Table of Content
 What is Constant in Math?
 Constant Term in Algebraic Expression
 How to Recognize a Constant in Algebraic Expression?
 What is the Constant Term?
 What is the Constant Number?
 Difference Between Constants and Variables
 Mathematical Constants
 Constants Written as Variables
 What is Constant Function?
 Graph of Constant Function
 Examples on Constant in Mathematics
 Practice Problems on Constant in Math
What is Constant in Math?
A constant in mathematics refers to a fixed value that remains unchanged throughout a particular context or problem. Constants don’t vary or take on different values and maintain their specific numerical value, providing stability and consistency within mathematical formulations.
Constant Term in Algebraic Expression
In algebraic expressions, a constant term does not contain any variables and represents a fixed value within the expression. For example, in algebraic expression 2x^{2} + 3x – 11, 11 is constant. Constants provide stability and consistency within mathematical formulations serving as fundamental elements in various algebraic expressions, equations and functions.
How to Recognize a Constant in Algebraic Expression?
Identifying constants in algebraic expressions involves looking for terms that do not involve variables and maintain a consistent value regardless of any changes in the variables present in the expression. Constants can be represented using specific numerical values or variables, depending on the context of the problem or equation.
What is the Constant Term?
A constant term in mathematics refers to a part of an algebraic equation that remains unchanged because it does not contain any variables. For instance, in the quadratic polynomial equation 𝑥^{2}+2𝑥+3=0, the number 3 is a constant term.
To illustrate further, take the algebraic expression 2𝑥−5=102x−5=10. In this equation, both 5 and 10 are constant terms.
What is the Constant Number?
Constant numbers are numerical values that do not change and remain constant throughout mathematical operations or equations. Constants are used extensively in various fields such as physics, engineering, economics and computer science to represent fixed values and parameters in mathematical models and calculations.
Examples include integers, fractions, irrational numbers like π (pi), and transcendental numbers like e (Euler’s number).
Arbitrary Constants
Arbitrary constants are constants introduced into mathematical expressions or equations to represent unknown or unspecified values.
Example: They are typically denoted by letters such as “C” or “K” and are used in solving differential equations and other mathematical problems.
Operations on Constants
Mathematical operations, such as
Can be performed on constants like any other numerical values, preserving their constant nature.
Difference Between Constants and Variables
Constants differ from variables in that they maintain a fixed value, whereas variables can vary and take on different values within a given context or equation. Below are the tabular differences between constants and variables:
Constants Vs Variables 


Criteria 
Constant 
Variable 
Definition 
A value that remains unchanged over time or within a specified context 
A symbol or value that can change typically represented by a letter or symbol 
Representation 
Often represented by specific symbols such as π (pi), e (Euler’s number), g (acceleration due to gravity) 
Represented by letters or symbols which can vary in different contexts 
Examples 

x, y, z (commonly used in algebra), a, b, c (coefficients in equations) 
Role in Equations 
Used as fixed values in equations or formulas 
Represent quantities that can change and are manipulated in equations 
Importance 
Fundamental in mathematical calculations and constants in scientific laws 
Important in expressing relationships and solving equations in various fields 
Mathematical Constants
Mathematical constants are specific numerical values that arise frequently in mathematical calculations and theories such as π (pi). Below is the table of Mathematical Constants:
Constant 
Name 
Value 

Archimedes’ Constant 
Approximately 3.14159 . . . 

e (Euler’s number) 
Euler’s Constant 
Approximately 2.71828 . . . 
φ (phi) 
Golden Ratio 
Approximately 2.61803 . . . 
γ (EulerMascheroni) 
EulerMascheroni Constant 
Approximately 0.57721 . . . 
√2 
Square root of 2 
Approximately 1.414 . . . 
√3 
Square root of 3 
Approximately 1.732 . . . 
In some mathematical contexts, constants may be represented using variables, particularly when the exact value is unspecified or unknown. For instance, “k” may represent a constant rate in exponential growth equations.
Constants Written as Variables
Constant sometimes also is used to represent a variable (but a fixed) value when the exact value of that constant is not known in an expression or a word problem. In general term ‘C’ or ‘c’ is used to represent constant variable value.
Here, “c” is the variable, but its value will always be a “fixed number” when actually writing a polynomial or expression.
In quadratic equation, ax^{2} + bx + c = 0 (c is a constant whose value is unknown)
What is Constant Function?
A constant function is a type of function in which the output value remains constant regardless of the input value. It is represented by a horizontal line on a graph.
Definition of Constant Function
Mathematically, a constant function can be represented as:
f(x) = c
Where c is a constant value. This means that no matter what value of x is chosen, the value of f(x) will always be c. For example, if f(x)=5, then for any input f(x) will always be 5.
Graph of Constant Function
This is represented in the image added below as,
Read More,
Examples on Constant in Mathematics
Example 1: Identify the constant term in the given algebraic expression: 3x^{2} + 2xy − 7.
Solution:
Given Expression,
3x^{2} + 2xy − 7
Constant term in the expression is −7
Example 2: Compute the value of the given algebraic expression: 5a + 3 when a = 2.
Solution:
Given Expression,
5a + 3 when a = 2
Substituting a = 2 into the expression,
= 5(2) + 3
= 10 + 3 = 13
Example 3: Solve the equation 2x + 8 = 16 for the value of x.
Solution:
Given Expression,
2x + 8 = 16
Subtracting 8 from both sides,
2x + 8 – 8 = 16 8
2x = 8
Dividing both sides by 2
2x/2 = 8/2
x = 4
Example 4: Evaluate the the given expression: 4×(3+2)−7.
Solution:
Given Expression,
4 × (3+2) − 7
= 4×5 – 7
= 20 – 7 = 13
Example 5: Find the value of the given algebraic expression for a if 3a – 6 = 15.
Solution:
Given Expression,
3a – 6 = 15
Adding 6 to both sides o
3a = 21
Dividing both sides by 3
a = 7
Practice Problems on Constant in Math
Problem 1: Determine the constant term in the given algebraic expression : 2x^{2} + 5x −9.
Problem 2 : Solve the algebraic equation 3y – 7 = 5 for y.
Problem 3: Compute the value of 2b^{2} – 3 when b = 4.
Problem 4: Simplify the algebraic expression 6 + 4x – 2x for x=3.
Problem 5 : Find the value of c in the given algebraic expression if 2c + 10 = 26.
Constant in Math – FAQs
What is a constant in mathematics?
A constant in mathematics refers to a fixed value that remains unchanged throughout a particular context or problem.
How do constants differ from variables?
Constants maintain a fixed value, while variables can vary and take on different values within a given context or equation.
What is a constant term in an algebraic expression?
A constant term in an algebraic expression is a term that consists solely of a constant. It does not contain any variables and represents a fixed value within the expression.
How can I recognize a constant in an algebraic expression?
Identify terms that do not involve variables and maintain a consistent value regardless of any changes in the variables present in the expression.
What are constant numbers?
Constant numbers are numerical values that do not change and remain constant throughout mathematical operations or equations.
What are arbitrary constants in mathematics?
Arbitrary constants in mathematics are constants introduced into mathematical expressions or equations to represent unknown or unspecified values. They are typically denoted by letters such as “C” or “K” and are used in solving differential equations and other mathematical problems.
Can mathematical operations be performed on constants?
Yes, mathematical operations such as addition, subtraction, multiplication, and division can be performed on constants like any other numerical values, preserving their constant nature.
What is a constant function?
A constant function is a type of function in which the output value remains constant regardless of the input value. It is represented by a horizontal line on a graph.
What are mathematical constants?
Mathematical constants are specific numerical values that arise frequently in mathematical calculations and theories such as π (pi), e (Euler’s number) and φ (phi).
How are constants represented in mathematical expressions?
Constants can be represented using specific numerical values or variables depending on the context of the problem or equation.