Significant Figures Calculator
Count the significant figures in any number with each digit highlighted and the rule that applies, round to any number of sig figs with exact decimal math, and add, subtract, multiply or divide with the correct sig fig rules. It all works privately in your browser.
Accepts 1200, 1200., 0.00450, 4.50e-3, 4.50 × 10^-3 or 4.50×10⁻³.
How to use the Significant Figures Calculator
- Type a number on the Count tab, such as 0.004050, 1200 or 6.02e23. The count updates as you type.
- Read the breakdown: green digits are significant, grey ones are placeholders and orange trailing zeros are ambiguous.
- Round a number on the Round tab: enter the value and the number of sig figs, then press Apply rounding.
- Calculate with sig figs on the Arithmetic tab: enter two numbers, choose +, −, × or ÷ and press Calculate to get the correctly rounded answer with steps.
- Tick Exact number for counted values (like 3 trials) or defined conversions so they do not limit the answer.
Significant figures rules
| Rule | Example | Sig figs |
|---|---|---|
| Non-zero digits are always significant | 4.56 | 3 |
| Zeros between non-zero digits (captive zeros) are significant | 1.0203 | 5 |
| Leading zeros are never significant | 0.0045 | 2 |
| Trailing zeros after a decimal point are significant | 2.500 | 4 |
| Trailing zeros in a whole number with a decimal point are significant | 1200. | 4 |
| Trailing zeros in a whole number without a decimal point are ambiguous (usually not counted) | 1200 | 2 (2–4) |
| In scientific notation only the coefficient counts | 1.200 × 10³ | 4 |
| Exact numbers (counts, definitions) have unlimited sig figs | 12 eggs, 100 cm/m | ∞ |
Sig figs in calculations: worked examples
Multiplication and division keep the smallest number of significant figures:
- 4.56 × 1.4 = 6.384 → 6.4 (1.4 has 2 sig figs)
- 12.11 × 0.0230 = 0.278530 → 0.279 (0.0230 has 3 sig figs)
- 25.0 ÷ 3.0 = 8.333… → 8.3 (3.0 has 2 sig figs)
Addition and subtraction keep the least precise decimal place:
- 12.11 + 18.0 = 30.11 → 30.1 (18.0 is known to tenths)
- 1.0023 − 0.12 = 0.8823 → 0.88 (0.12 is known to hundredths)
- 1200 + 34.5 = 1234.5 → 1200 (1200 is known only to hundreds)
In multi-step problems, keep at least one or two extra digits in intermediate results and round only the final answer, otherwise rounding errors build up. When a calculation mixes both rules, such as (2.31 + 4.1) × 1.25, apply the addition rule to the bracket first (6.41 → 6.4, 2 sig figs), then the multiplication rule to the product.
Why this calculator is exact
Ordinary calculators store numbers in binary floating point, which cannot represent most decimals exactly; that is why 2.675 can round to 2.67 in some software. This tool treats every number as a string of decimal digits and rounds it with whole-number arithmetic, so 2.675 to 3 sig figs is always 2.68, and very large or very small values such as 6.02214076 × 10²³ or 1.6 × 10⁻¹⁹ keep every digit. To convert between notations, use the scientific calculator or the exponent calculator for powers of ten.
Frequently asked questions
How many significant figures does 0.004050 have?
Four. The leading zeros (0.00) only place the decimal point and are not significant. The 4, the captive 0 between 4 and 5, the 5 and the trailing 0 after the decimal point are all significant.
Are trailing zeros significant?
Trailing zeros are significant when the number contains a decimal point, as in 2.50 (3 sig figs) or 1200. (4 sig figs). In a whole number without a decimal point, such as 1200, they are ambiguous and are usually not counted, giving 2 sig figs. Write 1.200 × 10³ to show four.
How do you round to significant figures?
Start counting at the first non-zero digit, keep the number of digits you need, and look at the next digit: 5 or more rounds up, less than 5 rounds down. Then replace dropped digits left of the decimal point with zeros. For example 123,456.789 to 3 sig figs is 123,000, or 1.23 × 10⁵.
What are the sig fig rules for addition and subtraction?
The answer is rounded to the least precise decimal place of the numbers, not to the fewest significant figures. 12.11 + 18.0 = 30.11, which is rounded to the tenths place because 18.0 is only known to tenths: 30.1.
What are the sig fig rules for multiplication and division?
The answer has as many significant figures as the input with the fewest. 4.56 × 1.4 = 6.384, and because 1.4 has only two significant figures, the answer is 6.4.
Do exact numbers affect significant figures?
No. Counted quantities (12 eggs, 3 trials) and defined values (1 m = 100 cm exactly) have unlimited significant figures, so they never limit the precision of a result. Tick Exact number for them.
What is round half to even?
Also called banker's rounding, it rounds a digit followed by exactly 5 to the nearest even digit, so 2.45 becomes 2.4 and 2.55 becomes 2.6. It avoids an upward bias over many roundings. Most chemistry classes use round half up, the default.