Significant Figures Calculator
Find how many significant figures a number has, with every digit marked and the rule explained. Round to a chosen number of sig figs, and do arithmetic that follows the textbook rules.
Count significant figures
Try:
5 significant 0 not significant 0 ambiguous
Round to significant figures
Calculate with significant figures
How to count significant figures
- Type a number in the first box. Standard numbers, numbers with commas and scientific notation (1.20e3 or 1.20 × 10^3) all work.
- Each digit is colored: significant digits are bold, leading zeros are grey, and trailing zeros that might or might not count are underlined. The rules that apply are listed below.
- Use the second box to round any number to the sig figs you need, and the third to add, subtract, multiply or divide two measurements with the answer rounded correctly.
The rules for significant figures
- Non-zero digits are always significant: 452 has 3.
- Zeros between non-zero digits are significant: 4,005 has 4.
- Leading zeros are never significant; they only show where the decimal point is: 0.0072 has 2.
- Trailing zeros after a decimal point are significant: 3.500 has 4.
- Trailing zeros in a whole number with no decimal point are ambiguous: 1,200 could have 2, 3 or 4. Write 1.20 × 10³ for exactly 3, or 1200. (with a decimal point) for 4.
Sig figs in calculations
Multiplying and dividing: the answer has as many significant figures as the measurement with the fewest. 12.11 × 0.31 = 3.7541, but 0.31 has only 2 sig figs, so the answer is 3.8.
Adding and subtracting: the answer is rounded to the least precise decimal place, not the fewest sig figs. 12.11 + 0.3 = 12.41, but 0.3 is only known to the tenths place, so the answer is 12.4.
In a multi-step problem, keep extra digits in the middle steps and round only the final answer, so rounding errors do not build up. Exact numbers, such as counted items or defined conversions (100 cm in 1 m), have unlimited significant figures and never limit the answer.
Rounding
To round to n significant figures, count n digits from the first non-zero digit and look at the next digit: 5 or more rounds up, less than 5 rounds down. This calculator rounds halves up, the way most textbooks teach it, and uses exact decimal arithmetic so values like 2.675 round correctly.
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Frequently asked questions
How many significant figures does 100 have?
Strictly it is ambiguous: at least 1, possibly 3. Most teachers count it as 1. Write 100. or 1.00 × 10² to show 3 significant figures.
Is zero significant?
Zeros are significant when they sit between non-zero digits or at the end of a number with a decimal point. Leading zeros, as in 0.05, are not.
Why does adding use decimal places but multiplying uses sig figs?
When adding, the uncertainty is in the last decimal place of each value, so the least precise place limits the sum. When multiplying, relative uncertainty matters, which depends on the number of significant figures.
Does scientific notation change the number of sig figs?
No. It just makes them clear: every digit in the number before × 10ⁿ is significant.
Is anything sent to a server?
No. Everything is calculated in your browser, and nothing you enter leaves your device.