About this logarithm calculator
This free logarithm calculator evaluates a number with base 10, base 2, the natural base e, or your own positive base. Switch to antilog mode when you know the exponent and want the corresponding number instead. Both modes show the inputs, formula, intermediate values and a reverse-operation check rather than giving an unexplained answer.
You can use the tool while practising algebra, checking a spreadsheet formula or comparing two numerical representations. For a broader expression with several arithmetic operations, open the Scientific Calculator. This dedicated log calculator focuses on choosing the base correctly and understanding the relationship between a logarithm and a power.
How to calculate a logarithm or antilog
- Select Logarithm to find an exponent, or Antilog to raise the selected base to an exponent.
- Choose common log (base 10), natural log (base e), binary log (base 2), or Custom base. The custom field appears only for that choice.
- Enter the argument for a logarithm, or the exponent for an antilog. Use a decimal point, not a thousands separator; scientific notation such as 2.5e-6 is accepted.
- Calculate, then review the base, input and calculation steps. Changing any field clears the old result so it cannot be mistaken for the new calculation.
Copy, Download and Print include the working as well as the answer. Reset restores the initial operation and empties the number field. A device purchase is not necessary to use this browser-based tool.
Affiliate disclosure: As an Amazon Associate I earn from qualifying purchases.
For a separate arithmetic check, you may browse scientific calculators (paid link). Check the model’s supported functions; choose a model with the log, ln and arithmetic functions you need; ordinary calculators do not necessarily solve symbolic inequalities. No purchase is required.
Logarithm and change-of-base formulas
The defining relationship is logb(x) = y exactly when by = x. For a real logarithm, x > 0, b > 0 and b ≠ 1. Change of base gives logb(x) = ln(x) / ln(b). Antilog mode calculates by = exp(y × ln(b)).
Base 10 is the common logarithm, while ln uses the constant e. Base 2 is useful when working with powers of two. A custom base between zero and one is also valid; its logarithm changes sign compared with a base above one. You can compare the inverse calculation with the Exponent Calculator, but keep the same base in both tools.
Worked log and antilog examples
Choose base 2 and enter 128 in Logarithm mode. The result is 7 because 2 raised to 7 is 128. Choose base 10 and enter 0.001 instead: the result is −3, corresponding to 10 raised to −3.
For a custom-base example, choose 0.5 as the base and 0.125 as the argument. The answer is 3. In Antilog mode with base 10 and exponent 2.5, the answer is approximately 316.227766017. This example is not a whole-number power, so the display is an approximation.
When studying powers and roots together, the Square Root Calculator offers a separate check for square roots. Keep an original copy of your inputs when comparing rounded results between different tools.
Precision, input limits and domain errors
The tool uses JavaScript double-precision arithmetic and displays up to 12 significant digits. It is not an arbitrary-precision or symbolic log solver. Displayed intermediate values are rounded for reading; the actual operations use unrounded numbers. A reverse-operation check helps spot a mistaken base, but it does not prove the floating-point result is exact.
Number inputs are limited to 48 characters. Nonzero argument and custom-base magnitudes must be between 1e-100 and 1e100. Antilog exponents must additionally be between −1,000,000 and 1,000,000, and the output must lie between 1e-300 and 1e300. Unsupported ranges produce an error instead of infinity or zero.
Zero and negative arguments have no real logarithm here. A base entered so close to one that the browser rounds it to one is rejected. Other bases close to one may amplify input rounding significantly. Fractions, expressions, complex numbers and symbolic equations are not accepted; enter a decimal approximation when appropriate and do not infer extra accuracy from a long display.
Choosing a related math tool
Use this page for a single numeric logarithm or antilog, not for solving a whole equation containing logarithms. The Linear Equation Calculator and Quadratic Formula Calculator address different equation types. Checking which operation a question actually requests is often more useful than switching blindly between calculators.
Try changing only the base while leaving the argument fixed, then compare the resulting exponents. Next use Antilog mode to recover the original argument. These paired calculations provide a practical way to practise the notation without requiring an account or sending your number inputs to the calculator server.
Logarithm Calculator FAQs
Sources and methodology
These educational references explain the mathematical ideas. This independently implemented calculator is not affiliated with their publisher. Its supported methods, exact checks and limits are documented above.