Logarithm calculator: find the log of any number in any base, including natural log, with the formula shown. Runs entirely in your browser, no signup.
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Every figure above is calculated locally in your browser from the assumptions shown. No inputs are sent anywhere. See the methodology section below for the formulas used.
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BoringToolsKit. “Logarithm Calculator.” boringtoolskit.com/log-calculator/ (reviewed August 2026). Free to reference in articles, syllabi, and answer posts with a link.
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Worked example: one input, three bases
Enter 2500 and switch the base selector. With base 10, the calculator returns 3.39794, because 2500 sits between 1000 (10^3) and 10000 (10^4), so the answer must land between 3 and 4. Formally, log10(2500) = log10(25) + 2 = 1.39794 + 2, which is a quick mental check of the displayed value.
Switch to natural log and the same input gives 7.824046. That is ln(2.5) + ln(1000) = 0.916291 + 6.907755. Switch to base 2 and you get 11.287712, which makes sense: 2^11 = 2048, and 2500 is only about 22% larger, so the answer is just past 11. The three results differ only by a constant factor (dividing by ln of the chosen base), which is exactly what the change-of-base formula says.
A useful sanity habit: the integer part of a base-10 logarithm tells you the digit count. A result of 3.39794 means 2500 has 4 digits. For pH-style work or decibel work, where log10 dominates, that one rule catches most input mistakes instantly.
Edge cases the calculator handles, and where logs still surprise you
The input rejects zero and negatives with an explicit error message rather than failing silently. That is mathematically required: no real exponent turns 10, e, or 2 into a non-positive number. Inputs between 0 and 1 do work and return negative values; log10(0.0001) = -4 exactly, because 10^-4 = 0.0001. If you need logs of negative magnitudes, compute the log of the absolute value and carry the sign question separately, since complex logs are out of scope here.
Display precision is capped at 6 decimal places, so log2(3) shows as 1.584963 rather than the full repeating expansion. For chained calculations this rounding can compound: multiplying three 6-decimal values can drift in the 7th place, which matters for unit conversions but not for typical order-of-magnitude work.
Floating-point quirks also apply. Math.log10 returns exactly 9 for log2(512), but for values very close to powers of the base, the last displayed digit may differ from a hand derivation by 1 unit in the last place. When an exact power matters (sample sizes, binary capacity, half-life steps like 512 = 2^9), verify by exponentiating the result rather than trusting the final digit.
