Logarithm Calculator

Calculate a logarithm using a chosen base. Enter your own values below to see logarithm and check the method behind it.

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Your inputs

Change the example values to match your situation.

Your result

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Fill in your inputs and select Calculate.
Your result and breakdown will appear here.

How this calculator works

log base b of a = ln(a) ÷ ln(b). Both inputs must be positive and b ≠ 1.

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What is Logarithm Calculator?

Logarithm Calculator helps you calculate a logarithm using a chosen base.

The main result is logarithm. The formula, example and assumptions below explain how to interpret it.

How to use Logarithm Calculator

Use the example to get familiar with the form, then enter your own figures. Any rates in the example are illustrative. Check the field labels and units before calculating.

  1. Gather number and logarithm base. Use values from the same situation or reporting period.
  2. Replace the example number with your own value, then complete the other fields. Check the displayed units.
  3. Select Calculate and read logarithm. Change one input and calculate again to compare a second scenario. Reset restores the original example.
  • Enter number, at least 1e-9. Decimals are accepted.
  • Enter logarithm base, at least 1e-9. Decimals are accepted.

Logarithm Calculator: a worked example

With the inputs below, the result is 2 (logarithm). Follow the example, then replace these illustrative values with your own.

Example inputs and output
Input or outputExample value
Number100
Logarithm base10
Logarithm2

Understanding the Logarithm result

The main output is logarithm. It applies to the inputs and operation you selected.

Displayed results use a readable number of decimal places. When checking a result by hand, keep extra precision until the last step. To compare scenarios, change one input at a time and keep the others fixed.

Logarithm Calculator: assumptions and common mistakes

A useful estimate starts with the right inputs. Check the following assumptions and limits before applying the result to your situation.

  • Check the base value, sample definition and chosen operation. Display rounding should come after the calculation.

For wider guidance, visit NIST statistical handbook. The formula and scope of this specific tool are stated on this page.

Logarithm Calculator FAQs

What does Logarithm Calculator calculate?

Logarithm Calculator helps you calculate a logarithm using a chosen base. Its main output is logarithm.

What inputs do I need for Logarithm Calculator?

You need number and logarithm base. Use the field labels and units to match your figures to the formula.

Which formula does Logarithm Calculator use?

log base b of a = ln(a) ÷ ln(b). Both inputs must be positive and b ≠ 1.

What is a worked example for Logarithm Calculator?

Example inputs: Number: 100; Logarithm base: 10. The result is 2 (logarithm).

How should I enter number?

Enter number, at least 1e-9. Decimals are accepted.

How do I choose logarithm base?

Enter logarithm base, at least 1e-9. Decimals are accepted. The example uses 10; replace it if your circumstances differ.

How should I read logarithm?

The main output is logarithm. It applies to the inputs and operation you selected.

Why might my Logarithm Calculator result differ from my records?

Check the base value, sample definition and chosen operation. Display rounding should come after the calculation. Differences in entered values, units or rounding can also change the comparison.

Can I compare two scenarios in Logarithm Calculator?

Yes. Note your first logarithm, change number or another input, and select Calculate again. Editing a field clears the old result so it is not mistaken for a new calculation.

Is Logarithm Calculator free, and where are my inputs calculated?

This calculator is free to use without signing in. Its formula runs in your browser; calculator inputs are not sent to a calculation API. The inputs reset to the example values when you reset the form or start a fresh page.