What Is a Significant Figures Calculator?
This tool rounds any number to a chosen number of significant figures (sig figs). Significant figures are the digits in a number that carry meaningful information about its precision — every non-zero digit counts, as do zeros between significant digits and trailing zeros after a decimal point. Reporting a measurement to the correct number of sig figs communicates how precisely it was measured.
How to Use It
Enter the number you want to round and the number of significant figures you want to keep (between 1 and 15). The calculator returns the rounded value. For example, rounding 12345.678 to 3 significant figures gives 12300.
The Formula Explained
First find the magnitude of the number using \(p = \lfloor \log_{10}|x| \rfloor - (s-1)\), where \(s\) is the desired number of significant figures. This \(p\) is the power-of-ten place value of the last digit you want to keep. Divide the number by \(10^{p}\), round to the nearest whole number, then multiply back by \(10^{p}\). This shifts the number so the rounding boundary lands exactly between the kept and dropped digits.
$$\text{result} = \text{round}\!\left(\frac{x}{10^{\,p}}\right)\times 10^{\,p}, \quad p = \lfloor \log_{10}|x| \rfloor - (s-1)$$
Worked Example
Round 0.0045678 to 2 significant figures. Here \(\log_{10}(0.0045678) \approx -2.34\), so \(\lfloor -2.34 \rfloor = -3\) and \(p = -3 - (2-1) = -4\). Factor \(= 10^{-4} = 0.0001\).
$$0.0045678 / 0.0001 = 45.678, \quad \text{rounded} = 46, \quad 46 \times 0.0001 = 0.0046$$So the answer is 0.0046.
FAQ
Are leading zeros significant? No. Zeros before the first non-zero digit (like in 0.0045) only set the decimal place and are never significant.
What about the number zero? The value 0 has no defined order of magnitude, so this calculator returns 0 for any number of sig figs.
Does it use standard rounding? Yes — it rounds half values up (round-half-away-from-zero on the scaled integer), the most common convention.
