Significant Figures Calculator
Counts the significant figures in a number and rounds it to as many as you need.
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Your details
Trailing zeros count only when written after a decimal point.
Result
- Significant figures as written
- 5
- Rounded to 3 sig figs
- 0.00123
- In scientific notation
- 1.23 × 10^-3
- Decimal places kept
- 5
Standard form makes the precision unambiguous
0.0012340 to 3 significant figures…
Count from the first non-zero digit
Leading zeros are placeholders and never count
Zeros between digits always count
Trailing zeros count only after a decimal point
0.0012340 → 0.00123
Formula — written step by step
0.0012340 to 3 significant figures…
Count from the first non-zero digit
Leading zeros are placeholders: 0.00 does not count
First significant digit is the 1
Digits: 1, 2, 3, 4, 0 — five in all
The trailing 0 counts, being after the point
0.0012340 has 5 sig figs → 0.00123
Significant figures record how precisely a quantity was measured. The leading zeros only place the decimal point; the trailing zero is a genuine claim that the digit was measured as zero.
A worked example
Multiplying measurements
- Length
- 12.34 m — 4 sig figs
- Width
- 2.1 m — 2 sig figs
- 12.34 × 2.1 = 25.914
- The result cannot be more precise than the weakest input
- The weakest input has 2 significant figures
- Round 25.914 to 2 sig figs
Area = 26 m²
Writing 25.914 would claim five figures of precision from a measurement made to two. The rule for multiplication and division is that the result carries as many significant figures as the least precise input — a different rule from addition, which works in decimal places instead.
How to use this calculator
- Enter the number exactly as it was written or measured — trailing zeros matter, so do not trim them.
- Read the count of significant figures the number carries as written.
- Set how many figures you need and read the rounded value.
- Use the scientific-notation row when the rounded figure ends in zeros, since standard form states the precision without ambiguity.
What significant figures record
Significant figures are a claim about precision. Reporting a length as 2.5 m says it was measured to the nearest tenth of a metre; reporting 2.500 m says it was measured to the nearest millimetre. The two are the same quantity but very different statements about the instrument used.
The rules follow from that idea. Leading zeros never count, because they only position the decimal point and say nothing about measurement. Zeros between digits always count. Trailing zeros count when a decimal point is present, because there would be no reason to write them otherwise.
Carrying precision through a calculation
A result can never be more precise than the measurements it came from. For multiplication and division, the answer takes the significant-figure count of the least precise input. For addition and subtraction the rule is different: the answer takes the decimal places of the least precise input, not the significant figures.
The distinction matters. Adding 12.34 and 2.1 gives 14.44, which rounds to 14.4 — one decimal place, and still three significant figures. Multiplying the same two numbers gives a result limited to two significant figures. Applying the multiplication rule to a sum needlessly throws away real precision.
Round once, at the end
Rounding intermediate results and then continuing compounds the error at every step. Standard practice is to keep guard digits throughout the working and round only the final answer to the appropriate number of significant figures.
Exact values are also exempt. A count of 12 items is exactly 12, not 12.0 or 1.2 × 10¹, and a defined conversion factor such as 2.54 centimetres per inch is exact by definition. Neither limits the precision of a result, and treating them as measurements is a common way to lose figures that were never uncertain.
Formula & methodology
What this calculator assumes
- Rounds half away from zero, which is the convention taught in most textbooks. Software and standards bodies frequently use round-half-to-even instead, and the two disagree on exactly the values that end in a five.
- A trailing zero in a number written without a decimal point is genuinely ambiguous — 1500 may carry two, three or four significant figures — and no rule resolves it. Scientific notation is what removes the ambiguity.
- Significant figures describe how a number was written, not how precise a measurement was. A stated uncertainty says more than a digit count ever can.
Sources
Which digits count
| Number | Sig figs | Why |
|---|---|---|
| 1234 | 4 | All non-zero digits count |
| 1002 | 4 | Zeros between digits always count |
| 0.0012 | 2 | Leading zeros are placeholders |
| 1.200 | 4 | Trailing zeros after a point count |
| 1200 | 2 | Trailing zeros with no point are ambiguous |
| 1.200 × 10³ | 4 | Standard form removes the ambiguity |
The 1200 case is the troublesome one: written plainly there is no way to tell whether the zeros were measured. This is precisely why scientific notation is standard in laboratory reporting.
Frequently asked questions
Is 1200 two significant figures or four?
As written it is genuinely ambiguous, and this calculator reports two. If all four digits were measured, write 1.200 × 10³ or 1200. with an explicit decimal point.
Do significant figures apply to counted numbers?
No. A count of 25 people is exact, not a measurement, and places no limit on the precision of any calculation it appears in. The same holds for defined constants.
What is the rule for addition?
Use decimal places rather than significant figures. The sum carries as many decimal places as the input with the fewest, which can leave more significant figures than any single input had.
Should I round at every step?
No. Rounding intermediate values accumulates error. Carry extra digits through the working and round only once, at the end.