Calculate with significant figures
Adding and subtracting keeps the fewest decimal places. Multiplying and dividing keeps the fewest significant figures. Uses the Rounding setting above.
About this tool
This significant figures calculator does three jobs. It counts the significant figures in any number you type and colors each digit to show whether it counts, does not count, or is ambiguous, with the reason. It rounds the number to any number of significant figures and shows the answer in standard and scientific notation. And it adds, subtracts, multiplies or divides two measured numbers and rounds the answer by the sig fig rules, step by step.
All arithmetic is done on the digits as text, not on binary floating-point numbers. That matters for rounding. A computer stores 2.675 as a binary number slightly below 2.675 (2.67499999999999982236431605997495353221893310546875), so JavaScript's (2.675).toPrecision(3) and Python's round(2.675, 2) both give 2.67. This calculator works on the digits you typed and gives 2.68, the answer a chemistry or physics class expects.
How to use the sig fig calculator
- Type a number. Plain decimals (
0.00450), whole numbers (1500), a trailing decimal point (1500.), negative numbers and scientific notation all work. Write scientific notation as6.02e23,1.50×10^3,1.50x10^-3or1.50×10³. Commas used as thousands separators, such as12,500, are removed. - Read the count. Highlighted digits are significant, faded digits are not, and digits with a dashed underline are ambiguous. The list underneath names each kind of digit and the rule behind it.
- Pick how many significant figures to keep and a rounding method, then click Count & round. The result appears in standard notation, scientific notation and E notation.
- For a calculation, enter A and B, choose the operation, tick a box if a number is exact, and click Calculate. Every step is listed so you can copy it into your work.
The rules for counting significant figures
Significant figures are the digits in a measurement that carry meaning: every digit you are certain of plus the first uncertain one. The rules below follow the OpenStax Chemistry: Atoms First 2e section on measurement uncertainty and the LibreTexts Chemistry page on expressing numbers.
| Rule | Example | Sig figs |
|---|---|---|
| Nonzero digits always count | 4.56 | 3 |
| Captive zeros (between nonzero digits) count | 1.007 | 4 |
| Leading zeros never count; they only place the decimal point | 0.0045 | 2 |
| Trailing zeros count when there is a decimal point | 0.00450, 2.500 | 3, 4 |
| Trailing zeros in a whole number with no decimal point are ambiguous | 1500 | 2, 3 or 4 |
| A trailing decimal point makes those zeros count | 1500. | 4 |
| In scientific notation, every digit of the number before ×10 counts | 1.500×10³, 1.5×10³ | 4, 2 |
Why 1500 is ambiguous. Written as 1500, the zeros might have been measured or might only show where the decimal point goes. OpenStax notes that the zeros in 1,300 grams could be significant or could just mark place value, and that scientific notation removes the doubt. Many textbooks, including the LibreTexts page above, settle on the convention that trailing zeros count only when the number has a decimal point, which gives 1500 two significant figures. This tool shows the range, for example 2 to 4 (ambiguous), and uses the lower value in calculations. If the zeros were measured, write 1500. or 1.500×10^3.
Negative signs and exponents never change the count. The minus sign and the power of ten only give the size and direction of the value.
Exact numbers have unlimited significant figures
Some numbers are not measurements at all. A count, such as 12 eggs or 3 trials, has no uncertainty, and OpenStax calls counting the only type of measurement that is free from uncertainty. Defined values are exact too: there are exactly 100 centimeters in a meter and exactly 2.54 centimeters in an inch. Exact numbers can be considered to have an unlimited (infinite) number of significant figures, so they never limit the precision of a result. Dividing the total mass of 3 samples by the count 3 keeps the precision of the mass. Tick A is exact or B is exact to have the calculator skip that number when it applies the rules.
How rounding to significant figures works
Keep the first N significant digits and look at the digits you drop. If the first dropped digit is 6 to 9, round up, and if it is 0 to 4, leave the last kept digit alone. If the first dropped digit is 5, the two methods differ only when nothing but zeros follows that 5:
- Round half up, the default here, always rounds a 5 up. It is the rule taught in most US classes, and the one LibreTexts gives: if the first dropped digit is 5 or higher, round up.
- Round half to even rounds an exact half to whichever neighbor has an even last digit, so 2.45 becomes 2.4 and 2.55 becomes 2.6. OpenStax Chemistry uses this rule for a dropped 5 with nothing after it. It avoids a slight upward drift when many values are rounded. If any nonzero digit follows the 5, both methods round up.
Rounding can carry into a new place: 9.996 to 3 significant figures is 10.0, still three figures. When a rounded whole number ends in zeros that are significant, the tool writes a trailing decimal point, such as 1500., and the scientific form always shows the exact count.
Rules for calculations
- Addition and subtraction: round the answer to the same number of decimal places as the input with the fewest decimal places. 12.52 + 3.1 = 15.62, which rounds to 15.6 because 3.1 has one decimal place. The number of significant figures in the answer can go up or down.
- Multiplication and division: round the answer to the same number of significant figures as the input with the fewest significant figures.
For a chain of steps, keep extra digits in the intermediate results and round once at the end. Rounding after every step can shift the last digit.
Worked example
The default number is 0.0402650. The first two zeros, in 0.0, are leading zeros and do not count. The 4, 2, 6 and 5 count, the zero between 4 and 2 is a captive zero and counts, and the final zero is a trailing zero after a decimal point, so it counts as well. That gives 6 significant figures.
Rounded to 4 significant figures, the kept digits are 4026 and the dropped digits are 50. With round half up the 5 rounds up, giving 0.04027, or 4.027 × 10−2. Switch Rounding to round half to even and the answer becomes 0.04026, because the dropped part is exactly a half and 6 is already even.
The calculation section starts with 4.56 × 1.4. The exact product is 6.384. 4.56 has 3 significant figures and 1.4 has 2, so the answer keeps 2: 6.4.
Common mistakes
- Counting leading zeros in a small decimal. 0.0045 has two significant figures, not five.
- Dropping significant trailing zeros. A balance reading of 2.500 g has four significant figures, and writing 2.5 g throws away precision.
- Using the sig fig rule for addition. 100.5 + 2.25 is 102.8, based on decimal places, not on the fewest significant figures.
- Letting a count limit the answer. Three trials is exact and has no effect on the precision.
- Rounding with a spreadsheet or a calculator that works in binary and then wondering why 2.675 became 2.67.
When you need significant figures
- Chemistry and physics lab reports, homework and exams.
- Checking answers in unit conversions, such as with the Unit Converter.
- Reporting measurements in engineering, nursing dosage practice and lab work at a stated precision.
- Writing large and small numbers cleanly in scientific notation.
For other everyday math, try the Percentage Calculator or turn a fraction into a decimal with the Fraction to Decimal Chart.
Frequently asked questions
Written as 100, the number is ambiguous: it has at least one and up to three significant figures, depending on whether the zeros were measured. Under the common classroom convention it has one. Write 100. with a decimal point, or 1.00 x 10^2, to show three significant figures, and 1.0 x 10^2 for two.
It depends on where the zero is. Zeros between nonzero digits always count, zeros at the start of a number never count, and zeros at the end count when the number has a decimal point. A value that is only zeros, such as 0.00, has no nonzero digits, so the usual counting rules do not give it a meaningful count.
It is already one significant figure, because the three leading zeros do not count. Rounding a number such as 0.000548 to one significant figure keeps the 5 and looks at the next digit, 4, so the answer is 0.0005. In scientific notation that is 5 x 10^-4.
Calculators show every digit of the arithmetic result, not the precision of your data. Multiplying 4.56 by 1.4 gives 6.384 on a calculator, but the measurement 1.4 only has two significant figures, so the reported answer is 6.4. The extra digits suggest a precision you never measured.
No. Decimal places count digits after the decimal point, while significant figures count meaningful digits from the first nonzero digit. 0.0045 has four decimal places but two significant figures, and 4500.0 has one decimal place but five significant figures. Addition uses decimal places and multiplication uses significant figures.
Work out the limiting precision for each step but keep one or two extra digits in the intermediate values, then round only the final answer. When a problem mixes addition and multiplication, apply the decimal place rule to the addition part and the significant figure rule to the multiplication part, in the order you calculate them.