When scientists report numbers obtained from experimental measurements, it is important to indicate the precision associated with these numbers. That is to say, there must be some level of confidence that the reported number can be reproduced if exact experimental conditions are used to repeat the measurement. This is the purpose of utilizing significant figures (also referred to as significant digits). Significant figures signify the precision in a given number and often note the level of precision for an experimentally measured parameter. For example, 12.0236 has six (6) significant figures and, in this case, indicates that the number has precision to the fourth decimal place. Therefore, if exact experimental conditions are used, repeated measurements should yield numbers that are very close to 12.0236 (to the fourth decimal). Numbers beyond the fourth decimal will vary and are not significant. To obtain better precision beyond the fourth decimal, improved experimental conditions and/or better measurement instrumentation is needed. The image to the left shows a few examples of numbers with the significant figures highlighted. The digits that are not highlighted are not significant.

It is important to note that precision and accuracy are entirely different. As noted above, precision refers to how reproducible a given measurement is, and significant figures are used to indicate the level of precision (i.e., reproducibility) for a measured parameter. Accuracy refers to how close the measured value is to its actual value. It is indeed possible to have very precise (i.e., highly reproducible) measurements that are far from the actual value of the parameter. For example, this could happen if an instrument used for making measurements is not properly calibrated.

Five (5) simple rules help us understand which digits of any number represent significant figures.

This calculator allows you to determine and/or set the significant figures for a number. Numbers may be entered in one of three formats (decimal notation, scientific notation, or exponential notation), and the calculator will output that number in all three formats, with the significant figures highlighted. A decimal is a number expressed in base-ten numeral system. Examples of decimals are 123, 98.69, −659.821, 10359.659586, and 0.0123456789. A decimal, such as 123, expressed in scientific notation has the following format: 1.23 × 10² (assuming 3 significant figures). 123 expressed in exponential (e) notation has the following format: 1.23e2 ( e  may also be capitalized, i.e., 1.23E2).

For the purpose of using the calculator below, it is straightforward to enter numbers in decimal notation and in exponential notation. They may be entered exactly as they appear. Commas may also be entered as thousand separators. For exponential notation, there should not be a space before or after  e . To enter numbers in scientific notation, use the  x  character (letter  x ; lower or upper case) or  *  character (asterisk) for the multiplication symbol, and use the  ^  character (caret) to indicate the power to which 10 should be raised. For example, 1.23 × 10² may be entered as 1.23 x 10^2. Spaces do not make a difference, so this is fine as well: 1.23x10^2. The asterisk character may also be used, so this will also work: 1.23 * 10^2.

For additional significant figures calculators, see our other calculators: Convert Numbers between Decimal, Scientific, and Exponential Notation, and Significant Figures Calculator for handling significant figures in simple mathematical operations such as additions, subtractions, multiplications, and divisions.