About the Significant Figures Calculator
This significant figures calculator (sig fig counter) tells you how many significant figures a number has and which of its digits count, then rounds the number to any number of significant figures you choose. It reads the number exactly as you type it, so 2.50 is treated as three significant figures and 2.5 as two — the trailing zero matters.
It is built for chemistry and physics students, lab reports and anyone recording measurements, where the number of significant figures shows how precise a value is. Type decimals, whole numbers or E notation (such as 6.020e5) and you will also get the rounded result in scientific notation (decimal places are counted for the number written out in full, so 6.02e23 has none), which is the unambiguous way to show significant figures in large numbers.
Rounding is done on the decimal digits you enter (not on a binary approximation), using the common school rule of rounding 5 upward, so 2.675 rounds to 2.68. Whole numbers with trailing zeros and no decimal point, like 1500, are ambiguous; the calculator follows the usual convention that those zeros are not significant and flags it.
With the default inputs, the significant figures is 4. Change any value above to recalculate instantly.
How to use the significant figures calculator
- 1Type the number exactly as it was measured or given, including any trailing zeros.
- 2Read how many significant figures it has and which digits are significant.
- 3Enter how many significant figures you want to round to.
- 4Copy the rounded value, or use the scientific-notation form to show trailing zeros clearly.
Formula and method
The standard rules are: (1) all non-zero digits are significant; (2) zeros between non-zero digits (captive zeros) are significant; (3) leading zeros, before the first non-zero digit, are never significant — they only place the decimal point; (4) trailing zeros are significant when the number contains a decimal point; (5) trailing zeros in a whole number without a decimal point are ambiguous and are treated here as not significant.
To round to n significant figures, keep the first n significant digits and look at the next one: if it is 5 or more, increase the last kept digit by one (carrying if needed); otherwise leave it. Digits to the left of the decimal point that are dropped become zeros so the magnitude is unchanged. Scientific notation removes any ambiguity because every digit in the coefficient is significant.
- Leading zeros
- 0.00|45 — never significant
- Captive zeros
- 4|0|5 — always significant
- Trailing zeros
- 4.50 — significant with a decimal point; 450 — ambiguous without one
Worked examples
Leading and trailing zeros: 0.004050
The three leading zeros are not significant. The digits 4, 0 (captive) and 5 are, and the final 0 counts because the number has a decimal point — so 4 significant figures. Rounded to 3 it becomes 0.00405.
Ambiguous whole number: 1500
Without a decimal point the trailing zeros of 1500 are treated as placeholders, giving 2 significant figures. Rounded to 3 figures the plain number still reads 1500, so the scientific form 1.50 × 10³ is the clear way to show it.
Round 12.3456 to 3 significant figures
All six digits are non-zero, so there are 6 significant figures. Keeping three gives 12.3; the next digit is 4, so nothing rounds up.
Rounding a 5 up: 2.675
To keep 3 significant figures we look at the fourth digit, 5, and round up: 2.675 → 2.68. The calculator works on the digits you typed, so binary floating-point quirks do not turn this into 2.67.
Carry into a new digit: 1995 to 2 s.f.
The third digit is 9, so 19 rounds up to 20 and the dropped places become zeros: 2000. Written as 2.0 × 10³ it clearly shows the two significant figures.
E notation: 6.02e23
Every digit in the coefficient 6.02 is significant, so the value has 3 significant figures, and rounding to 3 leaves it unchanged. Written out in full it is 602,000,000,000,000,000,000,000 — a whole number, so it has 0 decimal places even though the coefficient shows 2.
Frequently asked questions
How many significant figures does 100 have?+
Written as 100 with no decimal point, it is ambiguous and is usually counted as 1 significant figure. Writing 100. (with a point) means 3, and 1.00 × 10² also clearly shows 3 significant figures.
Are zeros significant?+
It depends on where they are. Zeros between non-zero digits are significant (405 has 3), leading zeros are not (0.0045 has 2), and trailing zeros are significant only when the number has a decimal point (4.50 has 3).
How do significant figures work in multiplication and division?+
The answer should have as many significant figures as the measurement with the fewest. For example 4.56 × 1.4 = 6.384, which is reported as 6.4 because 1.4 has only two significant figures.
How do significant figures work in addition and subtraction?+
For adding and subtracting, round the answer to the fewest decimal places among the inputs rather than the fewest significant figures. So 12.11 + 0.3 = 12.41, reported as 12.4.
Do exact numbers have significant figures?+
Counted values and defined constants (12 eggs, 100 cm in a metre) are exact and are considered to have unlimited significant figures, so they never limit the precision of a calculated result.