Euler's Number e Digit Viewer

e, approximately equal to 2.71828, is a fundamental mathematical constant. It is the base of the natural logarithm and is unique in that the function e^x is its own derivative. It appears naturally in processes involving growth, decay, and compound interest.

The constant e was discovered by the Swiss mathematician Jacob Bernoulli while studying compound interest. It was later popularized and denoted by Leonhard Euler, who proved many of its remarkable properties. Euler's choice of the letter e has been used ever since.

Yes, e is both irrational (cannot be expressed as a simple fraction) and transcendental (it is not the root of any non-zero polynomial with rational coefficients). This was proved by Charles Hermite in 1873, making e one of the first numbers proven to be transcendental.

The digits of e are most efficiently computed using its series expansion: e = Σ (1 / n!) from n=0 to ∞. By summing many terms using high-precision arithmetic, computers can calculate billions of digits. Other methods include the continued fraction representation and binary splitting algorithms.

e appears in numerous real-world applications: calculating compound interest, modelling population growth, radioactive decay, heat transfer, and in the normal distribution (bell curve). It is also fundamental in calculus, complex numbers, and engineering.

As of 2024, more than 31 trillion digits of e have been computed, though such extreme precision is mainly used for benchmarking supercomputers. For everyday mathematics, about 15-20 digits are sufficient.

The first 20 decimal places of e are: 2.71828 18284 59045 23536. You can explore many more using our digit viewer above!

Yes! Our tool includes Copy and Download buttons. You can copy the exact digits to your clipboard or download them as a plain text file (.txt) for offline use.