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Logarithm Calculator

Logs to any base, with natural log and log base 10 together.

Math Calculators Free, no sign-up Runs in your browser

2, 10 and e (2.71828) are the usual ones.

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Log to your base
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Natural log (ln)
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Log base 10
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Log base 2
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Antilog of the result

About the Logarithm Calculator

Logarithm Calculator answers the question a logarithm asks: this base, raised to what power, gives this number? Log base ten of a thousand is three, because ten cubed is a thousand. The page shows that reading explicitly, because it is the one that makes logs make sense.

All three common bases are shown at once. Base ten is the one used for orders of magnitude, decibels and pH; base two for anything to do with doubling, halving or information; and the natural log, base e, for continuous growth and most of calculus. Having them side by side saves re-entering the number three times.

The change of base formula is printed with your figures in it because it is the trick that makes an arbitrary base possible at all. Any log can be computed as the natural log of the number divided by the natural log of the base, which is exactly what the calculator does internally.

The page shows its working, not just its answer. Where there is a formula it is printed with your own numbers substituted in, so you can check the result rather than take it on trust -- which is the difference between a calculator you can use for something that matters and one you cannot.

Everything runs inside your browser. What you type is never uploaded, never logged and never stored, and the calculator keeps working if your connection drops after the page has loaded.

Looking for something this does not cover? FreeToolsHub.org is another hub of free online tools that need no account, and it is worth a look if logarithm calculator is only part of what you are working on.

How to use the Logarithm Calculator

  1. Enter number and baseDecimals are fine, and thousands separators are accepted and ignored.
  2. Read the log to your base, natural log (ln) and log base 10The figures update as you type. The Calculate button is there if you would rather press something, but nothing waits for it.
  3. Copy or check the resultCopy the summary with the copy button, or read the formula with your own numbers in it.

Features

  • Shows log to your base, natural log (ln), log base 10, log base 2 and antilog of the result together, so you are not running it twice
  • Prints the formula with your own figures substituted in
  • Updates as you type, with no button to press and no page reload
  • Copy the result in one click
  • Free, no sign-up, and it runs entirely in your browser

Who uses this tool

The logarithm calculator is used by writers, developers, students, marketers and anyone else who needs the job done once without installing software. Common cases include:

  • Finding how many doublings fit into a growth factor
  • Converting between log bases
  • Working out an order of magnitude
  • Solving an equation where the unknown is an exponent

Frequently asked questions

What is the difference between log and ln?

log usually means base 10 and ln means base e, about 2.71828. Both are shown here, along with base 2 and whatever base you enter.

Why can I not take the log of a negative number?

Because no real power of a positive base gives a negative result. Logs of negatives exist in the complex numbers but not in real arithmetic.

What is an antilog?

The reverse operation: raising the base to the power of the log, which gets your original number back. It is shown as a check.

If the logarithm calculator is not quite what you need, these other free tools solve closely related problems, and there are 25 more in math calculators.

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Checked and rebuilt on 2026-10-14. The method this calculator uses is described in the section above, and corrections go through the contact page.