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Log Sig Fig Calculator

Free log and pH sig fig calculator that applies the special logarithm rule: significant figures in the input become decimal places in log(x), ln(x), or pH. Solve pH from [H+], pKa from Ka, and any other log calculation with correct precision.

Enter Values

Number

The number to take the log of (must be positive)

Log Base

Choose log base 10 or natural log

Result

Enter values above and click Calculate to see your result.

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Formula

Core Formula

\text{Decimal places in } \log(x) = \text{Sig figs in } x

How it works: When taking a logarithm, the number of significant figures in the original number determines the number of decimal places (not sig figs) to keep in the result.

Review and Methodology

Updated Apr 28, 2026

This calculator runs locally in your browser. Inputs are converted into the units required by the formula, and the result is paired with supporting references so you can verify the method before using it for planning or estimates.

Worked Example

Find log(4.52 x 10^3) with correct sig figs

1Step 1: 4.52 x 10^3 = 4520, which has 3 significant figures.

2Step 2: log(4520) = 3.65514...

3Step 3: Rule: 3 sig figs in input = 3 decimal places in log.

4Step 4: Round to 3 decimal places: 3.655

Result: log(4520) = 3.655

Sig Fig Rules for Logarithms

Logarithms have a special sig fig rule that differs from standard arithmetic. In a logarithm like log(x) = y, the integer part of y (called the "characteristic") is determined by the order of magnitude, while the decimal part (called the "mantissa") carries the precision. Because of this, the sig figs of x correspond to the decimal places of log(x), not the total sig figs of log(x).

The characteristic (integer part) of a log gives the order of magnitude, not precision information
The mantissa (decimal part) of a log carries all the precision, so sig figs map to decimal places
log(3.45 x 10^2) = 2.538, keeping 3 decimal places because 3.45 has 3 sig figs
This rule applies to both common logs (base 10) and natural logs (ln)

This rule is essential in chemistry (pH calculations, equilibrium constants), physics, and any field where logarithmic scales are used. Getting it wrong can lead to over- or under-reporting precision.

You can also calculate changes using our Sig Fig for Logs Calculator, Sig Fig Rules Calculator or Sig Fig Scientific Notation Calculator.

Frequently Asked Questions

Why are sig figs handled differently for logs?

Because the integer part of a log (the characteristic) only indicates the power of 10, not precision. For example, log(1000) = 3.000 and log(9999) = 3.9999, so the "3" part just means "thousands." All the precision is in the decimal part (mantissa).

What is the characteristic and mantissa?

For log(x) = y, the characteristic is the integer part of y (the digit(s) before the decimal) and the mantissa is the decimal part. In log(350) = 2.544, the characteristic is 2 and the mantissa is .544.

Does this rule apply to natural log (ln)?

Yes. The same rule applies: the number of sig figs in the input equals the number of decimal places to keep in ln(x).

How does this apply to pH calculations?

pH = -log[H+]. If [H+] = 2.5 x 10^-4 (2 sig figs), then pH = 3.60 (2 decimal places). The "3" is the characteristic and ".60" has the 2 significant decimal places.

What about negative log inputs?

You cannot take the log of a negative number or zero in real number arithmetic. The input must be a positive number.

Can I use this Log Sig Fig Calculator on my own web page?

You can. Look for the "Embed" button near the top of this calculator. It lets you pick a size, border style, and color palette, then gives you an iframe tag to paste into any webpage. The widget is responsive, loads fast, and costs nothing. More details at calculory.com/services/embed-calculators.

AI Assistant

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I can help you understand the log sig fig calculator formula, interpret your results, and answer follow-up questions.

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