Negative Log Calculator
Use our negative log calculator to calculate negative log values and understand what a negative log means. Includes when logs can be negative, negative natural log (ln), negative log rules, and why you can’t take the log of a negative number in real math (plus what to do instead).
What is a Negative Log?
A negative log means the result of a logarithm is negative. This happens when the input is between 0 and 1. For example, log10(0.1) = −1 and ln(0.5) is negative.
If you’re asking can log be negative or can you have a negative log, yes—the log output can be negative. But there’s an important distinction: you generally cannot take the log of a negative number in real-number math.
This negative log calculator focuses on valid real logs that produce negative outputs (like log(0.01), ln(0.2), etc.), and it explains what to do when someone tries to log negative numbers.
Negative Log Rules
Logs can be negative when the argument is between 0 and 1. Also, a negative sign in front of a log changes the sign of the result.
For any base b > 1, inputs between 0 and 1 produce negative logs.
A negative sign in front just flips the sign of the log result.
A negative natural log is simply ln(x) being negative for x between 0 and 1.
Because 10^-2 = 0.01.
Natural logs are negative for inputs between 0 and 1.
How to Calculate a Negative Log
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Enter the number x (choose a value between 0 and 1 to produce a negative log result).
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Choose the base (b). Use 10 for common log or e for negative natural log (ln).
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The calculator computes log_b(x) or ln(x).
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If you want a “negative log” as -log(x), apply a minus sign to the result.
Frequently Asked Questions
Yes. If 0 < x < 1 and the base b > 1, then log_b(x) is negative.
Yes—negative log results are common for inputs between 0 and 1 (like log10(0.1) = −1).
It’s a logarithm that outputs a negative value, usually because the input is between 0 and 1.
It means the exponent needed to reach the input is negative. Example: log10(0.01) = −2 because 10^-2 = 0.01.
Yes. ln(x) is negative when 0 < x < 1.
Compute log_b(x). If x is between 0 and 1 (and b > 1), the result will be negative. If you mean -log(x), take the log and then apply a negative sign.
Use LOG or LN on a value between 0 and 1 to get a negative result. If you need -log(x), press the negative key (or prefix with −) after getting the log.
In real-number math, log of a negative number is undefined. Some advanced math uses complex numbers (involving i). If you only need real results, you must use a positive input or transform the data.
Because real logarithms require the argument x to be greater than 0.
Common “negative log rule” ideas are: logs are negative for 0<x<1 (base>1), and a leading minus sign just flips the log’s sign: -log(x)=-(log(x)).
People sometimes say “negative log scale” when they mean a log scale applied to small values (between 0 and 1) that produce negative log outputs, or measures like -log10(p) used in stats (e.g., p-values).