Log Calculator – Calculate Logarithms with Any Base
Compute log and antilog in any base.
About the Log Calculator
What is the Log Calculator?
A log calculator finds the logarithm of a number in any base, or reverses it with the antilog.
Why use this calculator?
Logs turn multiplication into addition, which is how they once powered slide rules and how they still describe earthquakes, sound and pH today.
How to use it
- Choose logarithm or antilog mode.
- Enter the number (and base) for a log, or the exponent for an antilog.
- Read the answer plus common-base conversions.
Formula
log_b(x) = ln(x) ÷ ln(b); antilog_x(b) = b^x.
Logs of zero and negative numbers are undefined; antilogs always exist.
Frequently Asked Questions
What is the natural log?
The logarithm to base e (≈2.718), written ln, used in growth, decay and continuous compounding.
Why are logs undefined for negatives?
No real exponent of a positive base gives a negative result, so the inverse function has no real value there.
What order of operations does this use?
It follows standard PEMDAS/BODMAS rules: parentheses, exponents, multiplication and division, then addition and subtraction.
How precise are the answers?
The calculator uses double-precision floating-point math (about 15 significant digits) and rounds the display. For exact symbolic results use dedicated algebra software.
Can I enter negative numbers or decimals?
Yes. Negative values, decimals and very large or small numbers are all supported unless a field says otherwise.
What does it mean if I get an error?
Errors usually mean an invalid input, such as division by zero or a negative value where only positives make sense. Check your entries and try again.
Is this calculator free to use?
Yes. Every calculator on this site is completely free, with no hidden fees, no subscriptions and no limits on how many times you can use it.
How accurate are the results?
We use standard, widely accepted formulas and calculate in your browser using double-precision arithmetic. Results are rounded for readability, so treat them as reliable estimates rather than a guarantee. Real-world factors can vary the true figure.
Can I add this calculator to my own website?
Yes. Open this calculator page and use the "Add to your website" box in the sidebar to copy a ready-made iframe snippet, then paste it into any HTML page.
Does it work on a phone or tablet?
Yes. The layout is fully responsive, so it works on desktops, laptops, tablets and mobile phones, and every input adapts to touch screens.