Natural Log Calculator

About this calculator

The natural logarithm, written ln(x), answers the question “e to what power gives x?” where e ≈ 2.71828 is Euler's number. It's the inverse of the exponential function eˣ, and it shows up naturally wherever continuous growth or decay is involved — compound interest compounded continuously, radioactive decay, and the growth curves in calculus and differential equations.

Because different fields prefer different bases, this calculator also converts to base-10 (common, used in engineering and pH/decibel scales) and base-2 (used throughout computer science, e.g., for measuring algorithmic complexity) using the change-of-base formula, log_b(x) = ln(x) / ln(b). Scientists, engineers, and students use ln both as a standalone tool and as a building block inside larger formulas like the Black-Scholes option pricing model.