Significant figures calculator: count, round and calculate
Count every nonzero digit, every zero between nonzero digits and every trailing zero after a decimal point; leading zeros never count. 0.004500 has 4 significant figures, 1200 has 2 and 1200. has 4. When multiplying or dividing, round the answer to the fewest significant figures in the inputs; when adding or subtracting, round to the fewest decimal places.
Inputs used by this calculator
Significant Figures Calculator uses the fields below. The starting values reproduce the page example; replace them with values from the same units and time period before using the result.
| Input | Starting example | Accepted value | How it is used |
|---|---|---|---|
| What to do | Count significant figures | Count significant figures · Round to significant figures · Calculate with sig fig rules | Selects the unit or conversion path used by Significant Figures Calculator. |
| Number | 0.004500 | Text in the format shown | Supplies the number quantity used by the published equation or result breakdown. |
| Significant figures to keep | 3 | 1 to 30 | Selects the unit or conversion path used by Significant Figures Calculator. |
| First measurement | 12.11 | Text in the format shown | Supplies the first measurement quantity used by the published equation or result breakdown. |
| Operation | Multiply (×) | Add (+) · Subtract (−) · Multiply (×) · Divide (÷) | Supplies the operation quantity used by the published equation or result breakdown. |
| Second measurement | 0.0050 | Text in the format shown | Supplies the second measurement quantity used by the published equation or result breakdown. |
- Leading zeros
- Nonzero and captive digits
- Trailing zeros after a point
The counting rules
Significant figures are the digits that carry meaning about how precisely something was measured. Five rules cover almost every case, and the calculator applies them exactly as typed, so type the number the way it was recorded.
- Nonzero digits are always significant: 457 has 3.
- Zeros between nonzero digits are significant: 4,007 has 4.
- Leading zeros are not significant: 0.0032 has 2.
- Trailing zeros after a decimal point are significant: 3.200 has 4.
- Trailing zeros in a whole number with no decimal point are ambiguous: 1200 has 2 to 4.
The ambiguous trailing zero
Is 1200 measured to the nearest hundred or to the nearest unit? The number alone cannot say. This calculator counts those zeros as not significant and shows the possible range. To make all four digits significant, write a decimal point at the end (1200.) or use scientific notation (1.200 × 10³).
Rounding to significant figures
Start counting at the first nonzero digit, keep the number of digits you need and round the next digit: 5 or more rounds up. Rounding 0.0045678 to 3 significant figures gives 0.00457. A carry can add a digit: 999.6 rounded to 3 becomes 1000, which must be written 1.00 × 10³ to show three significant figures, so the calculator gives the scientific form too.
Multiplying and dividing
The answer keeps as many significant figures as the input with the fewest. 12.11 has 4 and 0.0050 has 2, so 12.11 × 0.0050 = 0.06055 is reported as 0.061. Keep every digit during intermediate steps and round once at the end, or rounding errors build up.
significant figures in a product = fewest in the inputsAdding and subtracting
Here decimal places matter, not significant figures. The answer is rounded to the last decimal place that every input has. 12.11 + 0.0050 = 12.1150, reported as 12.12 because 12.11 is known only to hundredths. Subtracting close numbers can lose many significant figures: 10.52 − 10.49 = 0.03 has just one.
decimal places in a sum = fewest in the inputsExact numbers and real measurements
Counted items (12 eggs) and defined values (1 inch = 2.54 cm exactly, 100 in a percentage) have unlimited significant figures and never limit an answer, so leave them out of the rule. In laboratory work the stated uncertainty is the stronger statement; NIST's guidance on measurement uncertainty explains how to report it.
Examples of counting significant figures
| Number | Significant figures | Why |
|---|---|---|
| 457 | 3 | All nonzero |
| 4,007 | 4 | Captive zeros count |
| 0.0032 | 2 | Leading zeros never count |
| 3.200 | 4 | Trailing zeros after a point count |
| 1200 | 2 (up to 4) | Ambiguous trailing zeros |
| 1200. | 4 | The decimal point marks them |
| 1.20 × 10³ | 3 | Scientific notation is explicit |
| 0.0 | — | Zero alone has no significant digits |
Frequently asked questions
How many significant figures does 0.004500 have?
Four: 4, 5 and the two trailing zeros. The leading zeros only place the decimal point.
How many significant figures does 100 have?
One, if it is written without a decimal point; the zeros are ambiguous. Written 100. it has three, and 1.0 × 10² has two.
Are trailing zeros significant?
After a decimal point, yes: 2.50 has 3. In a whole number without a decimal point, they are ambiguous.
How do you round to 3 significant figures?
Keep the first three digits starting from the first nonzero digit and round the fourth: 0.012345 becomes 0.0123 and 45,678 becomes 45,700.
What is the sig fig rule for multiplication?
Round the product to the fewest significant figures among the numbers you multiplied.
What is the sig fig rule for addition?
Round the sum to the fewest decimal places among the numbers you added.
Do exact numbers affect significant figures?
No. Counted values and defined conversion factors are exact and do not limit the answer.
What to keep in mind
Trailing zeros in a whole number without a decimal point, such as 1200, are ambiguous; they are counted as not significant. Exact counts and defined constants have unlimited significant figures and should not limit a result. Ties round half up.
Results are rounded for display in US format, with money in dollars and cents; CSV exports keep full calculation precision. This is a calculation summary, not an official certificate.