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Log Sig Fig Calculator

Use this free log sig fig calculator to calculate the logarithm of a number with the correct significant figures. The tool applies the special sig fig rule for logarithms: the number of sig figs in the input equals the number of decimal places in the log.

Enter Values

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

Choose log base 10 or natural log

Result

Enter values above and click Calculate to see your result.

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Formula

Decimal places in log(x) = Significant figures in x

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.

Worked Example

Find log(4.52 x 10^3) with correct sig figs Step 1: 4.52 x 10^3 = 4520, which has 3 significant figures. Step 2: log(4520) = 3.65514... Step 3: Rule: 3 sig figs in input = 3 decimal places in log. Step 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.

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Sig Fig for Logs CalculatorSig Fig Rules CalculatorSig Fig Scientific Notation Calculator

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