Value of e isÂ 2.718281828459045…..(so on). It is described basically under logarithm concepts. â€˜eâ€™ is a mathematical constant, which is basically the base of the natural logarithm. This is an important constant which is used in not only Mathematics but also in Physics. Value of e to the power 1 (e^{1}) will give the same value as e but the value of e to the power 0 (e^{0}) is equal to 1 and e raised to the power infinity gives the value as 0.Â It is a unique and special number, whose logarithm gives the value as 1, i.e.,
Log e = 1
In this article, we will learn to evaluate the value of Euler’s number.
Also, read:
Related Links 

Euler’s Number (e)
The Eulerâ€™s number â€˜eâ€™, is the limit of (1 + 1/n)^{n} as n approaches infinity, an expression that arises in the study of compound interest. It can also be expressed as the sum of infinite numbers.
The value of constant e can be calculated by solving the above expression. This will result in an irrational number, which is used in various mathematical concepts and calculations. The name Eulerâ€™s number is given after the Swiss Mathematician Leonhard Euler. This number e is also known as Napierâ€™s constant and was discovered by Jacob Bernoulli while studying the compound interest.
Similarly like other mathematical constants such as Î²,Ï€, Î³, etc., the value of constant e also plays an important role. The number e, have similar property just like other numbers. We can operate all the mathematical operations, using the value of the logarithm base e.
What is the value of e in Maths?
As discussed earlier, Jacob Bernoulli discovered the mathematical constant e. The expression, given as the sum of infinite for Eulerâ€™s constant, e, can also be expressed as;
Therefore, the value of (1+1/n)^{n} reaches e when n reaches âˆž. If we put the value of n in the above expression, we can calculate the approximate the number e value. So, let’s start putting the value of n =1 to higher digits.
n  (1+1/n)^{n}  Value of constant e 
1  (1+1/1)^{1}  2.00000 
2  (1+1/2)^{2}  2.25000 
5  (1+1/5)^{5}  2.48832 
10  (1+1/10)^{10}  2.59374 
100  (1+1/100)^{100}  2.70481 
1000  (1+1/1000)^{1000}  2.71692 
10000  (1+1/10000)^{10000}  2.71815 
100000  (1+1/100000)^{100000}  2.71827 
Value of Exponential Constant
The exponential constant is a significant mathematical constant and is denoted by the symbol ‘e’. It is approximately equal to 2.718. This value is frequently usedÂ to model physical and economic phenomena, mathematically, where it is convenient to write e. The exponential function can be easily described using this constant, for example, y = e^{xÂ }so as the value of x varies, then we can calculate the value of y.
Full value of e
The value of Euler’s number has a very large number of digits. It can go 1000 digits place. But in mathematical calculations, we use only the approximated value of Euler’s number e, equal to 2.72. The first few digits of e are given here though:
e =Â 2.718281828459045235360287471352662497757247093699959574966967627724076630353………..
How to calculate the value of e?
We have learned till now about the Mathematical constant or Eulerâ€™s constant or base of the natural logarithm, e and the values of e. The expression for e to calculate its value was given as;
\(e = \sum_{n=0}^{\infty }\frac{1}{n!} = \frac{1}{1}+\frac{1}{1}+\frac{1}{1.2}+\frac{1}{1.2.3}+….\)Now, if we solve the above expression, we can find the approx value of constant e.
e = \(\frac{1}{1}+\frac{1}{1}+\frac{1}{1.2}+\frac{1}{1.2.3}+….\) Or
e = \(\frac{1}{1}+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+\frac{1}{5!}….\)
Or
e = 1/1 + 1/1 + 1/2+ 1/6 + 1/24 + 1/120 + ……
Now, taking the first few terms only.
e = 1/1 + 1/1 + 1/2+ 1/6 + 1/24 + 1/120
e = 2.71828
Therefore, the value of e is equal to 2.71828 or e â‰ˆ 2.72.
Learn more about different mathematical constant and get the values for them to solve mathematical problems. Also, download BYJUâ€™SThe Learning App to get learning videos and other learning materials.