Euler's Number Calculator

Calculate Euler's number e using series expansion and limit definition. Explore e^x and related constants.

Settings

Series Terms (precision)

Exponent (for e^x)

Series Definition:

e = ∑(n=0 to ∞) 1/n!

e = 1 + 1 + 1/2 + 1/6 + 1/24 + ...

Limit Definition:

e = lim(n→∞) (1 + 1/n)^n

Euler's Number (e)

2.718281828459045

Series approximation: 2.718281828459046

Error: 4.4409e-16

e^1

2.7182818285

Related Constants

e²

7.389056

√e

1.648721

1/e

0.367879

e×π

8.539734

Limit Approximation Convergence

n=102.59374246

n=1002.70481383

n=1,0002.71692393

n=10,0002.71814593

n=100,0002.71826824

n=1,000,0002.71828047

n	n!	1/n!	Partial Sum
0	1	1.0000000000	1.0000000000
1	1	1.0000000000	2.0000000000
2	2	0.5000000000	2.5000000000
3	6	0.1666666667	2.6666666667
4	24	0.0416666667	2.7083333333
5	120	0.0083333333	2.7166666667
6	720	0.0013888889	2.7180555556
7	5040	0.0001984127	2.7182539683
8	40320	0.0000248016	2.7182787698
9	362880	0.0000027557	2.7182815256
10	3628800	0.0000002756	2.7182818011
11	39916800	0.0000000251	2.7182818262
12	479001600	0.0000000021	2.7182818283
13	6227020800	0.0000000002	2.7182818284
14	87178291200	0.0000000000	2.7182818285