A mathematical constant is a number whose value is fixed by an unambiguous definition and does not change across different problems or contexts. Constants are often represented by symbols (like π or e) or named after mathematicians to facilitate their use in formulas and calculations. They are essential in defining relationships, solving equations, and performing calculations in algebra, calculus, geometry, and number theory,
| Constant | Symbol | Approximate Value | |
|---|---|---|---|
| Pi | π | 3.141592653589793… | The ratio of a circle’s circumference to its diameter, and fundamental in geometry, trigonometry, and calculus. It is an irrational number, meaning it cannot be expressed as a simple fraction, and has an infinite number of decimal places. Pi is used in countless applications, from calculating the area and volume of a circle to analyzing waveforms in physics. |
| Tau | Τ | 6.28318530717958647692… | Ratio of a circle’s circumference to its radius. Equal to 2π |
| Euler’s number | e | 2.718281828459045… | The number e, also known as Euler’s number or the base of the natural logarithm, pops up whenever we examine continuous rates of growth (or decay) that are inherently linked to the amount or size of the thing that we are measuring, e.g., exponential growth, compound interest, and calculus. |
| Imaginary unit | i | √-1 | The imaginary unit, usually denoted by i, is a mathematical constant that is a solution to the quadratic equation x2 = −1, which is not solved by any real number. Any real-number multiple of the imaginary unit is called an imaginary number. |
| Golden Ratio | φ | 1.618033988749895… | In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0, a is in a golden ratio to b if (a + b)/a = a/b = φ |
| Negative one | -1 | -1 | In mathematics, −1 (negative one or minus one) is the additive inverse of 1. That is, the inverse property of addition is a property of real numbers that states that the sum of a number and its negative (the “additive inverse”) is always zero. |
| Zero | 0 | 0 | Additive identity of ℂ |
| One | 1 | 1 | Multiplicative identity of ℂ |
Mathematical constants are used to:
- Solve geometric problems (π in circle calculations)
- Model growth and decay (e in exponential functions)
- Analyze sequences and ratios (φ in Fibonacci-related problems)
- Perform complex number calculations (i in electrical engineering and signal processing)
- Establish reference points in experiments and dimensional analysis. These constants are universal and unchanging, making them foundational tools in both theoretical and applied mathematics.
Types of Constants
- Algebraic Constants: Numbers that are roots of polynomial equations with integer coefficients, e.g., √2
- Transcendental Constants: Numbers not algebraic, such as π and e, which cannot be expressed as roots of any polynomial with integer coefficients
- Proportionality Constants: Used to relate physical quantities in formulas, such as gravitational constant in physics, though mathematically fixed in value
See the below references for an extensive list of mathematical constants.
References
“Constant.” The Story of Mathematics, Accessed July 1, 2026. https://www.storyofmathematics.com/glossary/constant/.
HandWiki. “List of Mathematical Constants.” HandWiki, April 16, 2026. https://handwiki.org/wiki/List_of_mathematical_constants.
Sykora, Stanislav. “Math Constants.” Stan’s Hub, March 31, 2008. http://www.ebyte.it/library/educards/constants/MathConstants.html.
“List of Mathematical Constant.” GeeksforGeeks, May 1, 2024. https://www.geeksforgeeks.org/maths/list-of-mathematical-constant/.
“List of Mathematical Constants.” Wikipedia, May 11, 2026. https://en.wikipedia.org/wiki/Mathematical_constant.
“Mathematical Constant.” Wikipedia, May 27, 2026. https://en.wikipedia.org/wiki/Mathematical_constant.
Weisstein, Eric W. “Constant — from Wolfram MathWorld.” Wolfram MathWorld. Accessed July 1, 2026. https://mathworld.wolfram.com/Constant.html.
The featured image on this page is from the dreamstime website.