Sig Fig Calculator
Count the significant figures in a number, round to a chosen number of sig figs, or add, subtract, multiply and divide with the rounding rule shown. How it works
Use the Sig Fig Calculator
About the Sig Fig Calculator
0.00450 has 3 significant figures: the leading zeros do not count and the trailing zero after the decimal point does. This sig fig calculator counts the significant figures in a number, rounds a number to as many as you choose, and does arithmetic on two numbers or a whole chain with the matching rule applied (12.5 × 3.2 = 4.0 × 10^1).
How many significant figures: worked examples
| Number | Significant figures | Why |
|---|---|---|
| 0.00450 | 3 | Leading zeros do not count; the trailing zero after the decimal point does |
| 0.0001 | 1 | Leading zeros do not count |
| 1002 | 4 | Zeros between non-zero digits count |
| 12.50 | 4 | The trailing zero counts because there is a decimal point |
| 5000.0 | 5 | Every trailing zero counts because there is a decimal point |
| 100. | 3 | The decimal point makes both trailing zeros count |
| 100 | 1 to 3 | Trailing zeros with no decimal point are ambiguous |
| 1200 | 2 to 4 | Trailing zeros with no decimal point are ambiguous |
| 1.20e3 | 3 | The trailing zero counts because the mantissa has a decimal point |
| 6.022e23 | 4 | The zero between non-zero digits counts; the exponent adds nothing |
For an ambiguous number the tool shows the range and uses the lower count in arithmetic. Type 100. or 1.00e2 to make the zeros count.
Sig fig arithmetic: which rule applies
| Calculation | Exact value | Rule | Answer |
|---|---|---|---|
| 12.5 × 3.2 | 40 | Fewest significant figures (2) | 4.0 × 10^1 |
| 4.56 × 1.4 | 6.384 | Fewest significant figures (2) | 6.4 |
| 0.0821 × 298 | 24.4658 | Fewest significant figures (3) | 24.5 |
| 8.314 × 298 | 2477.572 | Fewest significant figures (3) | 2.48 × 10^3 |
| 15.00 ÷ 4.0 | 3.75 | Fewest significant figures (2) | 3.8 |
| 5.00 ÷ 2.5 | 2 | Fewest significant figures (2) | 2.0 |
| 12.11 + 18.0 | 30.11 | Least precise decimal place (tenths) | 30.1 |
| 2.5 + 1.25 | 3.75 | Least precise decimal place (tenths) | 3.8 |
| 1200 + 34.5 | 1234.5 | Least precise decimal place (hundreds) | 1.2 × 10^3 |
| 101.3 − 2.57 | 98.73 | Least precise decimal place (tenths) | 98.7 |
| 28.9 − 0.31 | 28.59 | Least precise decimal place (tenths) | 28.6 |
The exact value is the unrounded result as the tool prints it, without trailing zeros. Multiplication and division count figures; addition and subtraction look at decimal places.
Rounding to significant figures
| Number | Figures kept | Rounded |
|---|---|---|
| 2.675 | 3 | 2.68 |
| 1.005 | 3 | 1.01 |
| 0.004567 | 2 | 0.0046 |
| 0.000123456 | 3 | 0.000123 |
| 3.14159 | 4 | 3.142 |
| 45.678 | 4 | 45.68 |
| 9.995 | 3 | 10.0 |
| 0.99996 | 4 | 1.000 |
| 5 | 3 | 5.00 |
| 123456 | 3 | 1.23 × 10^5 |
| 299792458 | 4 | 2.998 × 10^8 |
| 6.02214076e23 | 4 | 6.022 × 10^23 |
Halves round up: 2.675 becomes 2.68 and 1.005 becomes 1.01, because the rounding is done on the decimal digits you typed.
How to use this tool
- Pick a mode: Calculate with sig figs, Chain of operations, Count sig figs or Round to N sig figs.
- Type the number as a plain decimal or in scientific notation such as 1.20e3. Trailing zeros you type are kept, so 2.50 is read as 3 significant figures.
- In Calculate mode choose the operation, type the second value and tick a value that is exact. In a chain type the whole expression, and mark an exact number with an exclamation mark after it, as in 2.54!. In Round mode enter how many figures to keep.
- Read the result and, under it, which rule was applied and which value limited the answer.
Frequently asked questions
- How many significant figures does 100 have?
- Between 1 and 3. Trailing zeros in a whole number without a decimal point are ambiguous, and the tool says so. Written as 100. it has 3, and written as 1.0e2 it has 2.
- Do zeros count as significant figures?
- Only some do: 1002 has 4 and 0.0001 has 1, while 5000.0 has 5 and 12.50 has 4. Where a zero sits decides it, and the first table above gives the rule for each case. Count mode marks which digits of your own number count.
- What is the sig fig rule for multiplying and dividing?
- Keep as many significant figures as the input with the fewest. 4.56 × 1.4 = 6.384, and 1.4 has only 2 figures, so the answer is 6.4. An exact number, such as a count or a defined constant, never limits the answer: with Value 2 is exact ticked, 12.5 × 3.2 gives 40.0, kept to the 3 figures of 12.5.
- What is the sig fig rule for adding and subtracting?
- Round to the last decimal place that both numbers reach, however many figures that leaves. 12.11 + 18.0 = 30.11, and 18.0 stops at the tenths place, so the answer is 30.1. The same rule covers whole numbers: 1200 + 34.5 is 1.2 × 10^3, because 1200 is known only to the hundreds place.
- How do I round to 3 significant figures?
- Find the third digit that counts and round there, with halves going up. 2.675 becomes 2.68, 0.000123456 becomes 0.000123 and 123456 becomes 1.23 × 10^5.
- How do I use sig figs with several operations?
- Type the whole calculation in Chain of operations, such as (4.56 + 1.2) × 3.0 ÷ 2.00. Each step is carried unrounded with its precision: 4.56 + 1.2 = 5.76 to the tenths place, then × 3.0 = 17.28 and ÷ 2.00 = 8.64, both to 2 significant figures. Only the final answer is rounded, to 8.6, so rounding at every step cannot shift the last digit. An exclamation mark after a number marks it exact, as in 12 × 2.54!.
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