Math calculator
Logarithm Calculator
Calculate logarithms in various bases.
About the logarithm calculator
The logarithm calculator computes log base 10, natural log (ln), or log base 2 of any positive number.
How to use this calculator
- 1
Enter number
Enter a positive number.
- 2
Choose base
Select base 10, e (natural), or 2.
- 3
View results
See the logarithm value.
How the calculation works
log_b(x) = ln(x) ÷ ln(b). Natural log uses base e ≈ 2.71828.
Example: log₁₀(1000) = 3. ln(e) = 1. log₂(256) = 8.
When to use a calculator vs. mental math
Simple operations like percentages and proportions are great for mental math. Complex problems — quadratic equations, standard deviation, and base conversions — benefit from calculator precision. Always estimate the answer first to catch input errors, and verify results with a second method when possible.
Important limitations
This tool provides a mathematical estimate based only on the values entered. It does not account for regulations, taxes, lender fees, market conditions, or individual circumstances. Results are for planning purposes only — consult a qualified professional for regulated, medical, financial, or construction decisions.
Frequently asked questions about logarithm calculator
How accurate is the logarithm calculator?+
The calculation follows the displayed formula and retains full numeric precision before formatting the result.
Can I use the result professionally?+
Use it as a planning estimate. Confirm regulated, medical, financial, or construction decisions with a qualified professional.