About the Euler's Number (e) Digit Generator
Euler's number, written e, is the base of natural logarithms and one of the most important constants in mathematics. It is about 2.71828, and its decimal digits go on forever without repeating. This digit generator calculates e on the spot, up to 5,000 places after the decimal point, and groups the digits in tens so they are easy to read, copy or memorise. You can also type a number, such as a birthday, and see where it first appears among the first 5,000 decimals. The digits are computed from an exact series with big integers, not copied from a table.
Updated October 2026
How to use the Euler's Number (e) Digit Generator
- 1Enter how many digits after the decimal point you want, from 0 to 5,000.
- 2Read the digits, shown in groups of ten after the 2.
- 3Press Copy digits to copy the plain, unbroken string.
- 4Optionally type a number to find where it first shows up in e.
e in everyday life
If you earn interest on a deposit and the bank adds that interest more and more often, your balance grows towards a limit. That limit for a 100 percent yearly rate is e times your deposit. This is why e shows up when interest is compounded continuously, and why it is the natural base for growth that is smooth rather than in steps.
Handy approximations
- 2.718 is enough for most schoolwork.
- 2.71828 works for engineering sketches.
- 2.718281828459 is plenty for calculators and spreadsheets.
- The digits 1828 repeat once at the start, which is a coincidence and not a pattern.
Related tools
Use the Log Calculator for natural logarithms, the Exponent Calculator for powers of e, the Compound Interest Calculator and the Exponential Growth Calculator for continuous growth, and the Pi Digit Generator for the other famous constant. The Rounding Calculator can shorten any long result to the number of digits you need.
Features
- Up to 5,000 decimal places of e
- Digits grouped in tens
- Copy as one plain string
- Search for numbers up to 12 digits long
- Calculated exactly, not looked up
- Digits are cut off, not rounded
- Runs in your browser
Frequently asked questions
What is the value of e?
Euler's number e is approximately 2.718281828459045. Its digits never end and never repeat in a pattern. The first digits are 2.71828 18284 59045 23536 02874 71352 66249 77572 47093 69995.
Why is e important?
It is the base of natural logarithms and appears in continuous growth and decay, compound interest, probability and calculus. The function e to the power x is its own derivative, which makes it central to differential equations. Population growth, radioactive decay and the cooling of hot objects all use it.
How is e calculated here?
The tool adds the series 1 plus 1 plus 1/2 plus 1/6 plus 1/24 and so on, where each term is one over a factorial. Using whole-number arithmetic with extra guard digits, it keeps adding until the terms are too small to matter, so every digit shown is correct.
Is e rational or irrational?
e is irrational, so it cannot be written as a fraction of two whole numbers, and it is also transcendental, so it is not the solution of any ordinary polynomial equation with whole-number coefficients. Euler proved it irrational in the 1700s.
Who discovered e?
Jacob Bernoulli met the number while studying compound interest in 1683. Leonhard Euler later named it e and worked out many of its properties, which is why it is called Euler's number. It is not related to Euler's constant gamma, which is a different number.
Are the digits rounded?
No, they are truncated. Asking for 5 decimals gives 2.71828, although the next digit, 1, would not change a rounded answer anyway. Asking for 3 gives 2.718, while a rounded value would be 2.718 too, and 4 gives 2.7182 where rounding would give 2.7183.