First N Digits Of E

What this calculator does

This shows the first however many digits of e (Euler's number) you ask for, up to 1,000. Enter a number of digits and it lists them.

Choose how many digits you want, and the tool produces them.

Using the calculator

1. Enter how many digits you want, up to 1,000.
2. Press Calculate.

The result is e written out to that many digits.

What e is

e, known as Euler's number, is one of the most important constants in mathematics, roughly 2.71828. It is the base of the natural logarithm, and the number that describes smooth, continuous growth. It appears in compound interest, in growing populations, in radioactive decay, and all through calculus. It is the base that the natural log calculator is built around.

Digits that never end

Like π, e is irrational: it cannot be written as an exact fraction, and its decimal digits carry on forever without repeating. It begins 2.718281828, and there is a memorable quirk right at the start, the block "1828" appears twice in a row. That is pure coincidence, though, and the pattern does not continue.

Why e matters

What makes e special is a property from calculus: the function e raised to the power x is the one function that is exactly its own rate of change. That is why it sits at the heart of anything growing or shrinking smoothly over time, and why the natural logarithm, which is its inverse, earns the name "natural".

A worked example | the first 10 digits

Ask for the first 10 digits of e.

1. The tool returns 2.718281828.

As with π, a few digits is plenty for real calculations. The rest are there for reference and curiosity.

Questions people ask

What is e?

Euler's number, about 2.71828, the base of the natural logarithm and the constant of continuous growth.

What are the first 10 digits of e?

2.718281828.

Do the digits of e ever end?

No. e is irrational, so its digits go on forever without repeating.

What is e used for?

Continuous growth and decay, compound interest, calculus, and the natural logarithm.

References

A note on the idea behind it. Euler's number e is approximately 2.71828, the base of the natural logarithm and of continuous growth. It is irrational, so its decimal expansion never ends or repeats, and the function e to the power x is its own derivative. For further reading, see E (mathematical constant).

1. Euler's number e, the base of the natural logarithm, an irrational constant near 2.71828.