Natural Logarithm Calculator
Calculate the natural logarithm of any positive number — the logarithm to base e — alongside its base-10 and base-2 equivalents.
How to use it
- Enter a positive number — the natural log appears immediately.
- The other tiles show the same number in base 10 and base 2 for comparison.
- ln(1) is always 0 and ln(e) is always 1.
Examples
| ln(1) | 0 |
| ln(10) | 2.302585093 |
The natural logarithm is the logarithm to base e (≈2.71828), and it is the one that shows up whenever something grows or decays at a rate proportional to its current size — money under continuous compounding, radioactive decay, bacterial growth, drug elimination from the bloodstream.
Worked example — continuous compounding
Money growing continuously at 5% follows A = Pe^(rt). To find how long £1,000 takes to reach £2,000 at that rate, solve 2 = e^(0.05t), so t = ln(2) ÷ 0.05 ≈ 13.86 years. That ln(2) ≈ 0.6931 constant is also why the 'rule of 69.3' is the continuous-compounding version of the more familiar rule of 72.
Reading the result
ln(1) is always 0, because e⁰ = 1. Values under 1 give a negative natural log, and the natural log of a negative number or zero is undefined — there is no real power of e that produces a non-positive result.
Questions people ask
Why is e used as a base?
Because the function eˣ is its own derivative, which makes e the natural choice anywhere growth is proportional to current size — compound interest, radioactive decay, population models.
Is anything sent to a server?
No. Every calculation runs in your browser, so nothing you type is uploaded and the page keeps working offline once it has loaded.
Last updated 17 August 2026