Ln Calculator

Enter a positive number to calculate its natural logarithm, base e.

How to Use the Ln Calculator

Type any positive number into the field and its natural logarithm appears immediately — there's no base to set, since this calculator is locked to base e specifically.

The site's Log Calculator takes any base you give it — 10, 2, whatever the problem calls for — by running the change-of-base formula underneath. This one skips that step entirely, because e isn't an arbitrary choice among many bases; it's the one where calculus stops needing correction factors.

d/dx eˣ = eˣ

That's the whole reason e matters on its own. Differentiate any other exponential function and a multiplier tags along — d/dx(2ˣ) = 2ˣ × ln(2), for instance — except base e, which differentiates to itself exactly, no multiplier attached. That single property is why continuous growth and decay problems gravitate toward e specifically: compound interest compounded continuously, radioactive half-life, population models that assume growth happening every instant rather than in discrete yearly steps. e ≈ 2.71828 falls out of the math in each case rather than being picked for convenience.

ln(x) asks what power gets e to x. ln(10) works out to roughly 2.303, since e^2.303 ≈ 10.

Zero and negative inputs aren't accepted. No real power of e, positive or negative, ever produces zero or a negative result, so there's no exponent that would solve the equation — the calculator flags this rather than returning a nonsense value.