About Significant Figures Calculator
This significant figures calculator is free, needs no sign-up and runs in your browser, so the numbers you type are never uploaded. It does the four jobs students and lab workers need: counting the significant figures of a number, rounding to a chosen number of them, adding, subtracting, multiplying and dividing with the correct precision rule, and writing the number in scientific notation.
The counter does not just give a number. Each digit is coloured and explained: a leading zero is a placeholder, a non-zero digit always counts, a zero between non-zero digits counts, and a trailing zero counts only when the number has a decimal point. Whole numbers ending in zeros, like 1200, are genuinely ambiguous, and the calculator says so and lets you decide.
All the arithmetic is exact. Numbers are held as decimal digits rather than floating point, so rounding a result that lands exactly on a 5 is done correctly, and 2.5 rounded to one figure is 3 every time.
How to use Significant Figures Calculator
- Choose Count, Round, Arithmetic or Scientific notation.
- Type the number exactly as it was measured, keeping any trailing zeros: 0.00450, 1200, 1.20e3.
- For rounding, set how many significant figures to keep. For arithmetic, type the second number and choose the operation.
- Read the answer, then open the digit-by-digit reasons or the steps.
- For a whole number that ends in zeros, use the switch to say whether those zeros were measured.
Features
- Digit-by-digit rule explanation: leading, non-zero, captive and trailing zeros.
- Round to any number of significant figures from 1 to 50, half up.
- Add and subtract by decimal places, multiply and divide by significant figures.
- Scientific notation that keeps exactly the significant figures.
- E-notation input such as 1.20e3 and 4.5 x 10^-3.
- A clear note on the ambiguity of trailing zeros in whole numbers, with a switch.
- Exact decimal arithmetic, no floating-point surprises.
The rules in one place
Counting: every non-zero digit counts; zeros between non-zero digits count; leading zeros never count; trailing zeros count only if the number has a decimal point.
Calculating: when you multiply or divide, the answer has as many significant figures as the input with the fewest. When you add or subtract, the answer has as many decimal places as the input with the fewest.
0.00450 -> 3 significant figures
1200 -> 2 (ambiguous)
1200. -> 4
4.56 × 1.4 = 6.384 -> 6.4 (2 figures)
12.11 + 1.013 = 13.123 -> 13.12 (2 decimal places)Worked examples
Count 0.003040 gives 4 significant figures
The three leading zeros do not count. The 3, the zero between 3 and 4, the 4 and the final 0 after the decimal point do.
Count 1200 gives 2 (ambiguous), or 4 written as 1200.
Trailing zeros in a whole number are not counted unless a decimal point is shown.
Round 34567.89 to 3 significant figures gives 34600
In scientific notation: 3.46 x 10^4. Keep 3, 4 and 5. The next digit, 6, rounds the 5 up to 6.
12.11 + 1.013 gives 13.12
The exact sum is 13.123. The first number is known to the hundredths, so the answer is rounded to the hundredths.
4.56 × 1.4 gives 6.4
The exact product is 6.384. The second number has two significant figures, so the answer has two.
0.00450 in scientific notation gives 4.50 × 10^-3
The trailing zero is significant, so the mantissa keeps three digits: 4.50, not 4.5.
Counting significant figures
| Number | Significant figures | Why |
|---|---|---|
| 4.07 | 3 | The zero is between non-zero digits |
| 0.0072 | 2 | Leading zeros are placeholders |
| 0.0070 | 2 | The final zero after the point counts |
| 3.0 | 2 | A trailing zero after a decimal point counts |
| 500 | 1 | Trailing zeros without a point are not counted |
| 500. | 3 | The decimal point makes them count |
| 5.00 × 10² | 3 | Scientific notation shows exactly which zeros count |
Good to know
Exact numbers and rounding
Counted quantities (12 eggs) and defined constants (100 cm in a metre) are exact. They carry no measurement uncertainty and should not limit the answer, so leave them out of the comparison. This calculator treats every number you type as a measurement.
Rounding is half up: a 5 followed by nothing rounds the previous digit up. Some courses use round-half-to-even for a trailing 5, which would differ in rare cases. Do not round in the middle of a long calculation; round once at the end.
Privacy: how it works
- Everything is calculated by code running in your browser tab. The numbers you enter are not sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- Write whole numbers that end in zeros in scientific notation, 1.20 × 10³, so nobody has to guess how many figures you meant.
- Keep extra digits in intermediate steps and round only the final answer.
- For a mixed calculation, apply the multiply rule and the add rule to each step separately and round at the end.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Numbers are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What are significant figures?
They are the digits of a measurement that carry information about its precision: all the digits you are sure of, plus the first uncertain one.
Do trailing zeros count?
Only if the number has a decimal point. 1.20 has three significant figures, but 1200 has two unless you write 1200. or 1.200 × 10³.
Why are leading zeros not significant?
They only fix the position of the decimal point. 0.0045 and 4.5 × 10⁻³ are the same number, and both have two significant figures.
How do I round to 3 significant figures?
Find the first non-zero digit, keep three digits from there, and round up if the next digit is 5 or more. 34567.89 becomes 34600.
What is the rule for multiplying and dividing?
The answer has as many significant figures as the least precise input. 4.56 × 1.4 = 6.384, which rounds to 6.4.
What is the rule for adding and subtracting?
The answer has as many decimal places as the input with the fewest. 12.11 + 1.013 = 13.123, which rounds to 13.12.
How many significant figures does 100 have?
By the usual convention one, but it is ambiguous. Write 1.00 × 10² for three, or 100. with a point for three. The calculator has a switch to count the zeros.
Popular Significant Figures Calculator pages
- Round to Significant FiguresType a number and how many significant figures to keep.
- Significant Figures AdditionEnter two numbers to add or subtract them and keep the right precision.
- Significant Figures MultiplicationEnter two numbers to multiply them and keep the right significant figures.
- Significant Figures DivisionEnter two numbers to divide them and keep the right significant figures.
- Scientific Notation and Sig FigsType a number and get its scientific notation with the right number of digits.
- Significant Figures in Whole NumbersWhole numbers that end in zeros are ambiguous. See how many figures 1200 has and how to say what you mean.