Math & Science
Significant Figures Calculator
Count significant figures in any number, and round to the precision you actually need.
Significant Figures Calculator
About the Sig Figs Calculator
Significant figures record how precisely something was measured. A length written as 2.50 m claims more precision than one written as 2.5 m, even though the two numbers are equal. This calculator counts the significant figures in any number and rounds to whatever precision you need.
The hard part is zeros. Leading zeros never count, zeros between digits always count, and trailing zeros count only when a decimal point is present. Those three rules cause most of the confusion, and the tool applies them consistently so you can check your own work against it.
It also shows the result in scientific notation, which removes the ambiguity entirely. Writing 1,500 leaves you guessing whether the zeros are measured or just placeholders; writing 1.50 × 10³ says exactly three.
How to use the Sig Figs Calculator
- Type the number exactly as written — the zeros matter.
- Optionally pick how many significant figures to round to.
- Select Count significant figures.
- Check the scientific notation form, which makes the significant digits unambiguous.
- For an integer like 1200, write 1200. if the trailing zeros are significant.
Rules for determining significant figures
1. Every non-zero digit is significant
2. Zeros between non-zero digits are significant
3. Leading zeros are never significant
4. Trailing zeros count only if a decimal point is present
| Number | Sig figs | Why |
|---|---|---|
| 123 | 3 | All digits non-zero |
| 1,005 | 4 | Zeros sit between non-zero digits |
| 0.0045 | 2 | Leading zeros are placeholders only |
| 4.500 | 4 | Decimal point present, so trailing zeros count |
| 1,500 | 2 | No decimal point — trailing zeros ambiguous |
| 1,500. | 4 | The decimal point makes them significant |
| 0.0230 | 3 | Leading zeros no, trailing zero yes |
| 2.50 × 10³ | 3 | Only the mantissa counts |
Worked example
Round 0.0045678 to three significant figures.
Leading zeros do not count, so the first significant digit is the 4. Counting three from there gives 4, 5, 6, and the next digit is 7.
Seven is 5 or more, so the 6 rounds up to 7.
0.00457 — still three significant figures
Sig fig rules for multiplication and calculations
The rule changes depending on the operation, and this is where marks are most often lost.
| Operation | Rule | Example |
|---|---|---|
| Multiply / divide | Fewest significant figures wins | 2.5 × 3.42 = 8.6 (2 s.f.) |
| Add / subtract | Fewest decimal places wins | 2.5 + 3.42 = 5.9 (1 d.p.) |
| Exact counts | Infinite precision, ignore them | 12 eggs is exactly 12 |
| Constants | Use more digits than you need | π to 6 s.f. in a 3 s.f. sum |
Round once, at the end. Rounding each intermediate step lets small errors accumulate and can shift your final digit. Keep full precision through the working and apply the sig-fig rule only to the answer you write down.
Why scientific notation settles the argument
Consider a measurement of 1,500 metres. Is that precise to the nearest metre, or to the nearest hundred? The digits alone cannot tell you. Scientific notation makes it explicit:
- 1.5 × 10³ — two significant figures, precise to the nearest hundred.
- 1.50 × 10³ — three significant figures.
- 1.500 × 10³ — four, precise to the nearest metre.
Only the mantissa carries significance; the power of ten is just scale. This is why scientific work quotes results this way as a matter of course.
Rounding conventions
- Digit below 5 — round down. 3.44 to 2 s.f. is 3.4.
- Digit above 5 — round up. 3.46 to 2 s.f. is 3.5.
- Exactly 5 with digits after it — round up. 3.451 to 2 s.f. is 3.5.
- Exactly 5 with nothing after — conventions differ. Many labs use round-half-to-even (banker's rounding), making 3.45 become 3.4 and 3.55 become 3.6, because always rounding up biases results upward across many measurements.
For rounding a mark rather than a measurement, the grade scale converter is more useful.
How many sig figs? Common examples
| Number | Sig figs | Why |
|---|---|---|
| 100 | 1 (ambiguous) | Trailing zeros with no decimal point are unclear |
| 100. | 3 | The decimal point makes the zeros count |
| 1000 | 1 (ambiguous) | Write 1.000 × 10³ for four |
| 0.06900 | 4 | Leading zeros never count; trailing zeros after a decimal do |
| 2.009 | 4 | Zeros between non-zero digits count |
| 233.356 | 6 | All non-zero digits count |
Rounding to two significant figures
- 233.356 → 230 (two sig figs: the 2 and the 3).
- 2.009 → 2.0
- 0.06900 → 0.069
Sig fig rules for addition and subtraction
Adding and subtracting follow a different rule from multiplying. Count decimal places, not sig figs.
- Add or subtract: round the answer to the fewest decimal places in the inputs. 12.11 + 3.2 = 15.31 → 15.3.
- Multiply or divide: round to the fewest significant figures in the inputs. 4.56 × 1.4 = 6.384 → 6.4.
In a multi-step problem, keep extra digits until the end and round once.
Other ways to use this calculator
Counting and rounding significant figures.
- How many significant figures calculator — type a number to count its significant figures.
- 3 significant figures calculator — choose “3 significant figures” from the menu; 2 works the same.
- Adding sig figs — see the addition rule above, or our sig fig rules and practice.
- How many sig figs calculator — type any number to count its significant figures.
- How many sig figs in 100? — one, unless written as 100. or 1.00 × 10².
- Adding and subtracting sig figs — keep the fewest decimal places.
- Round to 2 significant figures — set the rounding to 2 in the tool.
Related guides
Frequently asked questions
Significant figures are the digits in a number that carry real information about how precisely it was measured. Writing 2.50 m claims precision to the nearest centimetre, while 2.5 m only claims the nearest ten centimetres — the numbers are equal but the claims differ. All non-zero digits count, zeros between them count, leading zeros never do, and trailing zeros count only with a decimal point present.
Only when a decimal point is present. In 4.500 the trailing zeros are significant, giving four sig figs, because there would be no reason to write them otherwise. In 1,500 they are ambiguous — they might be measured or just placeholders — and the usual convention treats them as not significant. Scientific notation removes the doubt: 1.50 × 10³ is unambiguously three.
Count significant digits from the first non-zero digit, then look at the next digit along. If it is 5 or more, round up; otherwise round down. Rounding 0.0045678 to three sig figs starts at the 4, gives 4-5-6, and the following 7 rounds the 6 up to 457 — so 0.00457. Round only once, at the very end of a calculation.
Because it separates the digits from the scale. In 1,500 you cannot tell whether the zeros were measured or are placeholders. Written as 1.5 × 10³ the number has two sig figs; as 1.50 × 10³ it has three; as 1.500 × 10³ it has four. Only the mantissa carries significance, so the notation states the precision explicitly rather than leaving it to convention.
Written as 100 with no decimal point, it has one certain significant figure; the trailing zeros are ambiguous. Written as 100. it has three, and 1.00 × 10² also has three.
When adding or subtracting, round the answer to the same number of decimal places as the input with the fewest decimal places. 12.11 + 3.2 = 15.31, which rounds to 15.3.
One, as written. Trailing zeros in a whole number without a decimal point are ambiguous, so 100 is usually read as 1 significant figure. Write 100. or 1.00 × 10² to show 3 significant figures.
10.00. In addition the answer keeps the fewest decimal places of the numbers added. Both have two decimal places, so the sum is 10.00, which has 4 significant figures.
Keep the first two significant digits, 2 and 3, then look at the next digit, 3. It is below 5, so round down and replace the remaining whole-number digits with zeros: 230. Rounded to 4 significant figures, 45.5147 becomes 45.51.
Four. Leading zeros never count, so 0.0 is ignored. The 6 and 9 count, and the two trailing zeros after the decimal point count too, giving 6, 9, 0, 0.
Sources and further reading
- NIST — Guide for the Use of the International System of Units — expressing measurement precision and rounding
- NIST/SEMATECH e-Handbook of Statistical Methods — measurement uncertainty and reporting conventions
- Significant figures — the standard counting and arithmetic rules