Sig Fig Calculator (Significant Figures)

Formula

Count every digit from the first non-zero digit onward; zeros before it never count; zeros ending a whole number with no decimal point are uncertain

All non-zero digits are significant. Zeros between them (captive zeros) always are. Leading zeros never are — they only place the decimal point. Trailing zeros count when a decimal point is written. For a whole number such as 1500 with no decimal point, whether the final zeros were measured cannot be told from the number alone, so the page reports the range rather than picking one.

Worked example

In 0.004050 the three zeros before the 4 only locate the decimal point. The 4, the captive 0, the 5 and the final 0 are all significant: four figures. Rounded to three it is 0.00405, or 4.05 × 10^−3.

Where this can give the wrong answer

• Type the number exactly as written, trailing zeros included. 0.0120 and 0.012 are the same value but have three and two significant figures — which is why this is a text box, not a number box.
• When the dropped digit is exactly 5 with nothing after it, courses disagree. Most math classes round up; many chemistry courses round to the nearest even digit so errors don't pile up in one direction. Choose the rule your course uses: 2.5 to one figure is 3 under the first and 2 under the second.
• Exact numbers — counted items, or defined conversions such as 12 inches in a foot — have unlimited significant figures and should not limit the precision of a calculation.
• Rounding is done on the decimal digits themselves. A computer stores 0.15 as 0.1499…, and naive rounding turns it into 0.1; here it correctly gives 0.2.

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