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Significant Figures Calculator

Enter a number – also as 1.20e3 or 1.20 × 10³. The calculator highlights the significant digits, flags ambiguous trailing zeros, rounds exactly and applies the sig fig rules to products and sums.

e.g. 0.00450, 1200, 1200. (with a trailing point), 1.20e3 or 1.20 × 10³
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Result

Result
3 significant figures
Significant digits [highlighted]
0.00[450]
Scientific notation
4.50 × 10⁻³
Step-by-step
  • Leading zeros never count – they only fix the position of the decimal point (3 zeros).
  • Trailing zeros after the decimal point count – they were measured (1 zero).
  • Significant in [ ], ambiguous in ( ): 0.00[450]

How it is calculated

Which digits are significant?

Significant figures (sig figs) are all the digits of a measured value that were actually measured – from the first non-zero digit to the last measured digit. They express precision: 2.5 m and 2.50 m are the same length, but 2.50 m is precise to the centimetre.

How to find significant figures

  1. Under “What do you want to do?” choose count, round to n significant figures or calculate with two measurements.
  2. Enter the number, also as 1.20e3 – for rounding add n and the rule for an exact 5, for calculating the operation and the second value.
  3. Read the highlighted digits, the result as a decimal and in scientific notation, and the full working.
RuleExampleSig figs
Non-zero digits always count[22.3]3
Leading zeros never count0.00[450]3
Captive zeros always count[1002]4
Trailing zeros after a decimal point count[2.50]3
Trailing zeros without a decimal point are ambiguous[12](00)2 to 4
A trailing decimal point makes them count[1200.]4

Scientific notation removes the ambiguity of 1200: 1.2 × 10³ has 2, 1.20 × 10³ has 3 and 1.200 × 10³ has 4 significant figures. The power of ten never counts.

Rounding to n significant figures

Count n digits from the first non-zero digit and look at the next digit: 0 to 4 → round down, 5 to 9 → round up. Example: 0.0012345 to 2 sig figs → 0.0012|345 → 0.0012.

For an exact 5 there are two conventions. Round half up always rounds up: 2.345 → 2.35. Round half to even, the rule given in the NIST Guide to the SI (Appendix B.7), keeps an even preceding digit: 2.345 → 2.34, but 2.355 → 2.36. Negative numbers are rounded by magnitude: −2.345 → −2.35.

Carry: 99.96 to 3 sig figs gives 99.9|6 → 100.0. That is four digits; with three significant figures the result is 100 – written unambiguously as 1.00 × 10². That is why the calculator switches to scientific notation whenever trailing zeros would otherwise be ambiguous.

Calculating with significant figures

Internally the calculator works exactly with integers (no floating-point errors) and rounds only at the end – which is also how to do it by hand: don’t round intermediate results.

Related tools: the scientific notation converter, plus lab calculations with the density calculator and the molar mass calculator.

Frequently asked questions

How many significant figures does 0.00450 have?

Three: 4, 5 and the final 0. The leading zeros only locate the decimal point and do not count. The trailing 0 counts because it comes after the decimal point and was therefore measured.

Do trailing zeros in a whole number count?

Not necessarily: 1200 may have 2, 3 or 4 significant figures. Write it in scientific notation (1.20 × 10³ = 3 sig figs) or with a trailing decimal point (1200. = 4 sig figs) to make it unambiguous.

What is the difference between significant figures and decimal places?

Decimal places count only the digits after the point; significant figures count every measured digit from the first non-zero one. 0.0045 has four decimal places but two significant figures; 45.0 has one decimal place and three significant figures.

How do I round 2.345 to three significant figures?

Round half up gives 2.35 because the dropped digit is a 5. Round half to even (NIST) gives 2.34 because the preceding 4 is even. You can switch between both rules in the calculator.

What is the rule for adding measurements?

For addition and subtraction the last common decimal place counts: 12.11 + 0.3 = 12.41 is rounded to tenths, giving 12.4. For multiplication and division the smallest number of significant figures counts instead.

Do exact numbers have significant figures?

Counted or defined values – 3 trials, or the factor 2 in 2πr – are exact and do not limit precision. The rules apply to measured values only, so do not enter exact numbers as the second value.

Sources and legal basis

As of:

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