About this tool
Logarithm Calculator is a free, in-browser tool for logarithms and their inverses to any base. In Logarithm mode it returns log to the base you choose and also shows the common (base-10), natural (base-e) and binary (base-2) logs together. In Antilog mode it raises the base to your exponent to recover the original value. Everything is computed locally — nothing is uploaded.
Logarithms are computed with the change-of-base rule: log_b(x) = ln(x) / ln(b), where natural log uses ln(x) directly. The base can be 10, e, 2 or any custom positive value other than 1. The antilog is the inverse: for base b and exponent y the result is b^y (or e^y for the natural base), so antilog undoes the logarithm.
Use it for pH, decibels, Richter magnitudes, information theory or any exponential relationship. The value must be positive in Logarithm mode because the log of zero or a negative number is undefined; the tool flags that instead of returning an error value.
Frequently asked questions
How is a log to an arbitrary base computed?
By the change-of-base formula log_b(x) = ln(x) / ln(b). The natural log (base e) is taken directly, base-10 and base-2 use their dedicated functions, and any custom base greater than zero and not equal to 1 is supported.
What is an antilogarithm?
The antilog is the inverse of the logarithm: if log_b(x) = y then the antilog of y is b^y = x. In Antilog mode you enter the exponent and base, and the tool returns the original number by raising the base to that power.
Why must the value be positive for a logarithm?
The logarithm is only defined for positive numbers — there is no real power to which a positive base can be raised to give zero or a negative result. If you enter zero or a negative value the tool shows an invalid-input message.
Does the calculation happen online?
No. Every logarithm and antilogarithm is computed in your browser using standard math functions; no values are sent to a server.
More tools