Significant Figures CalculatorFree online math calculator — instant results, no sign-up
Round a number to a specified number of significant figures.
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About the Significant Figures Calculator
The Significant Figures Calculator rounds a number to a specified count of significant digits, starting with its first nonzero digit. With the default number 12345.678 and 4 significant figures, it returns 1.235e+4. This tool controls significant digits rather than the number of digits after the decimal point.
- Number
- The numerical value to round, defaulting to 12345.678; it has no required unit, and rounding preserves any units associated with the original value.
- Significant figures
- The desired count of significant digits, defaulting to 4; this is a unitless positive integer.
Formula and method
For x ≠ 0: k = floor(log10(|x|)), s = 10^(p − 1 − k), and y = round(x × s) / s. For x = 0: y = 0. With x = 12345.678 and p = 4: k = 4, s = 0.001, and y = round(12.345678) / 0.001 = 12350 = 1.235e+4.
- xThe input number.
- pThe requested positive integer count of significant figures.
- kThe base-10 exponent locating the first significant digit of the absolute input value.
- sThe scaling factor that places the last digit to retain in the units position.
- yThe rounded output, with the same units as x.
- |x|The absolute value of x.
- floorThe operation that returns the greatest integer less than or equal to its argument.
- log10The base-10 logarithm.
- roundRounding to the nearest integer; exact halfway cases depend on the calculator's tie-breaking rule.
For a nonzero input, determine its magnitude from the base-10 logarithm of its absolute value. Scale the number so that the requested final significant digit occupies the units position, round to the nearest integer, and undo the scaling. For 12345.678, the first four significant digits are 1, 2, 3, and 4; the next digit is 5 with further nonzero digits, so the retained 4 rounds up to 5. The result is displayed as 1.235e+4.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Number12345.678
- Significant figures4
Results
- Rounded value1.235e+4
How to use the Significant Figures Calculator
- 1Enter 12345.678 in the Number field to use the default example.
- 2Enter 4 in the Significant figures field.
- 3Run the calculation to round the input to four significant digits.
- 4Read the Rounded value row: 1.235e+4.
- 5Interpret the result as 1.235 × 10^4, or 12350, rounded to the nearest ten.
Reading your result
The Rounded value row gives the input rounded to the requested significant-digit count. For the default inputs, 1.235e+4 means 1.235 multiplied by 10 to the fourth power, equal to 12350. The coefficient 1.235 explicitly shows four significant figures; the exponent sets the magnitude and does not count as a significant digit.
Limitations
The significant-figure count must be a positive integer, and the number must be finite. Zero needs special handling because log10(0) is undefined; a numerical zero alone does not communicate measurement precision. Exact halfway cases require a tie-breaking convention, which is not established by the supplied example. Finite numerical precision can affect very large or very small inputs and values near rounding boundaries. Rounding does not improve the accuracy of the original number, and plain-number formatting may leave trailing zeros ambiguous.
Common questions
Why does 12345.678 become 1.235e+4 with 4 significant figures?+
The first four significant digits are 1234. The discarded portion is more than halfway to the next multiple of ten, so the result rounds upward to 12350, displayed as 1.235e+4.
Is choosing 4 significant figures the same as choosing 4 decimal places?+
No. Significant figures count from the first nonzero digit, wherever it occurs. For 12345.678, four significant figures require rounding to the tens place, not keeping four places after the decimal point.
Why use scientific notation for the rounded result?+
Scientific notation makes the significant-digit count clear. In 1.235e+4, all four digits of 1.235 are significant, whereas the final zero in the plain form 12350 could be mistaken for an additional significant digit.
Do leading zeros or a minus sign count as significant figures?+
No. Leading zeros only locate the first significant digit, and a minus sign only indicates the sign. Zeros between significant digits count, while trailing zeros must be interpreted using the stated precision or output notation.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.