Natural Logarithm (ln) Calculator

Instantly calculate the natural logarithm of a positive number. Explore the ln curve visually.

Enter a Positive Number:

Natural Logarithm (ln):

ln() ≈

Visualization

Interactive graph of the natural logarithm function. Hover over the curve to explore values. Your calculated point is highlighted in yellow.

Understanding Natural Logarithm (ln)

The natural logarithm, denoted as ln(x) or log_e(x), is the logarithm to the base e, where e is an irrational and transcendental number approximately equal to 2.71828. It answers the question: "To what power must e be raised to equal x?".

Formula: If y = ln(x), then e^y = x.

Use Cases: Natural logarithms are widely used in mathematics, physics, engineering, computer science, and finance. They appear in problems involving exponential growth and decay, calculus, statistics, and more. For example, they are used in radioactive decay calculations, compound interest formulas, and analyzing algorithms.

Learn more about natural logarithms on Wikipedia.