Value of e

Value of e is described basically under logarithm concepts. ‘e’ 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. e1 will give the same value as e but the value of constant e0 is equal to 1 and e raise to the power infinity gives the value as 0. It is a unique and special number, whose logarithm gives the value as 1, i.e.,

Log e = 1

The Euler’s number ‘e’, 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.

Value of e

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 Euler’s number is given after the Swiss Mathematician Leonhard Euler. This number e is also known as Napier’s constant and was discovered by Jacob Bernoulli while studying the compound interest.

Similarly like other mathematical constants such as β,π, γ, 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?

As discussed earlier, Jacob Bernoulli discovered the mathematical constant e. The expression, given as the sum of infinite for Euler’s constant, e, can also be expressed as;

What is the Value of e

Therefore, the value of (1+1/n)n reaches e when n reaches ∞. 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

How to calculate the value of Euler’s Number e?

We have learned till now about the Mathematical constant or Euler’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 = \(\frac{1}{1}+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}+\frac{1}{5!}….\)


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 ≈ 2.72.

Learn more about different mathematical constant and get the values for them to solve mathematical problems. Also, download BYJU’S-The Learning App to get learning videos and other learning materials.


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