Digits of e (Euler's Number) Calculator
Explore, search, and analyze the first 1000 decimal digits of e ≈ 2.71828…
e = 2.71828182845904…
Searches within the first 1000 decimal digits after the decimal point
Occurrences in e (first 1000 digits):
Frequency of each digit (0–9) in the first 1000 decimal digits of e
| Digit | Count | % | Bar |
|---|
digits
e vs π — Key Differences
| Property | e | π |
|---|---|---|
| Value | 2.71828… | 3.14159… |
| Irrational | ✓ | ✓ |
| Transcendental | ✓ | ✓ |
| Named after | Leonhard Euler | Greek letter π |
| Key application | Growth, e^x, ln(x) | Circles, geometry |
| Euler's identity | e^(iπ) + 1 = 0 | |
About Euler's Number (e)
Euler's number e (approximately 2.71828) is the base of the natural logarithm and is one of the most important constants in mathematics. It appears naturally when studying growth processes, compound interest, and probability.
One of the most beautiful results in mathematics is Euler's identity: e^(iπ) + 1 = 0, which connects five fundamental constants.
Key definition: lim(n→∞) (1 + 1/n)^n = e
This arises from continuous compounding: if you compound 100% interest n times per year, as n→∞ you get e times the principal.
Frequently Asked Questions
Why is e called Euler's number?
Leonhard Euler popularized the constant and introduced the letter "e" for it in the 18th century, though Jacob Bernoulli first encountered it while studying compound interest. The constant has since been named in Euler's honor.
Is e normal like π is conjectured to be?
Like π, e is conjectured to be a normal number (all digits equally frequent), but this has not been proven. Statistical tests on billions of digits show near-uniform distribution of all ten digits.
What is e used for in practice?
e is fundamental to: natural logarithms, exponential growth/decay, compound interest, probability distributions (normal distribution uses e), calculus (d/dx[e^x] = e^x), and complex numbers via Euler's formula e^(ix) = cos(x) + i·sin(x).
How was e first discovered?
Jacob Bernoulli discovered e in 1683 while studying compound interest. He noticed that as compounding frequency increases, the growth approaches a limit. Later, Euler fully developed its properties and notation.
What is the series definition of e?
e = 1/0! + 1/1! + 1/2! + 1/3! + … = Σ(n=0 to ∞) 1/n! = 1 + 1 + 1/2 + 1/6 + 1/24 + … This series converges very quickly, which is why e can be computed efficiently.
How many digits of e have been computed?
Over 1 trillion digits of e have been computed. The series definition (1/n!) converges much faster than π algorithms, making e easier to compute to high precision than π.
Is e connected to π?
Yes! Euler's identity e^(iπ) + 1 = 0 is the most famous connection. Also, Stirling's approximation uses both: n! ≈ √(2πn) · (n/e)^n. The Gaussian integral ∫e^(-x²) dx = √π connects them geometrically.
What is the "e day" equivalent of Pi Day?
In the US, "e Day" is celebrated on February 7 (2/7, representing 2.7…). In Europe, it is sometimes celebrated on January 8 (because e ≈ 2.71828… and 1/8 = 0.125, close to the third digit). Neither has the widespread recognition of Pi Day.