Significant Figures Calculator
Count, round and calculate with sig figs, plus scientific notation. Runs in your browser.
About this significant figures calculator
This significant figures calculator counts the sig figs in any number, rounds a number to the sig figs you choose, and does arithmetic with measured values using the precision rules from chemistry and physics class. It also writes every answer in scientific, E and engineering notation.
The counter highlights each significant digit and explains, digit by digit, which rule applies: non-zero digits, zeros trapped between them, leading zeros and trailing zeros. Numbers like 1500, where the trailing zeros are ambiguous, are flagged instead of quietly guessed.
Rounding is done on the exact decimal digits you typed, not on a binary floating point copy, so 2.45 really is a tie and rounds the way the rule says.
Features
Digit-by-digit highlighting
Significant digits are marked in yellow, placeholder zeros in grey and ambiguous trailing zeros with a dotted underline, with a plain-English reason for each group.
Rounding with a choice of tie rule
Round half up, the school rule, or round half to even, used in some labs and as the IEEE 754 default. The result keeps any significant trailing zeros, like 12.00.
Arithmetic with the correct rule per step
Addition and subtraction keep the fewest decimal places. Multiplication and division keep the fewest significant figures. Mixed calculations follow both, step by step.
Guard digits carried
Full precision is carried between steps and only the final answer is rounded, so rounding errors don't pile up through a long calculation.
Every notation
Decimal, scientific (6.02 × 10²³), E notation (6.02e23) and engineering notation with exponents in multiples of three.
Flexible input
Type 6.022e23, 6.022 × 10^23, 6.022*10^23 or use superscript digits. Thousands commas like 1,500,000 are read correctly.
How to use the significant figures calculator
- 1Choose Count, Round or Calculate.
- 2Type the number exactly as written, or a calculation with measured values.
- 3Read the count with highlighted digits, the rounded value or the answer with steps.
When to use it
Chemistry homework
Multiply 0.0250 mol by 6.022 × 10²³ and get 1.51 × 10²² with three significant figures, plus the step that explains why.
Lab reports
Find the mean and SD of your readings with the statistics calculator, then round them here to match the precision of your instrument.
Physics problems
Check that 4.56 m × 1.4 m is reported as 6.4 m², not 6.384 m². For the conversions in between, use the unit converter.
Engineering values
Turn 0.000047 F into 47e−6 F, ready to read as 47 µF, with the engineering notation output.
What are the rules for significant figures?
Significant figures are the digits that carry meaning about how precisely something was measured. Five rules cover almost every case:
- Non-zero digits are always significant: 4.56 has 3.
- Zeros between non-zero digits are significant: 1002 has 4.
- Leading zeros are never significant: 0.0045 has 2. They only place the decimal point.
- Trailing zeros after a decimal point are significant: 100.00 has 5. Someone measured those zeros.
- Trailing zeros in a whole number without a decimal point are ambiguous: 1500 could have 2, 3 or 4. Write 1500. (with a point) for 4, or use scientific notation.
How many significant figures does 0.004050 have?
Four. The three zeros before the 4 are leading zeros and don't count. The 4 and 5 are non-zero. The zero between them is a captive zero and counts. The final zero comes after the decimal point, so it counts too. That gives 4, 0, 5 and 0, which is four significant figures, or 4.050 × 10⁻³ in scientific notation.
How do significant figures work in addition and multiplication?
For addition and subtraction, look at decimal places, not significant figures. The answer can't be more precise than the least precise term. 12.11 + 18.0 + 1.013 = 31.123, but 18.0 only goes to tenths, so the answer is 31.1.
For multiplication and division, count significant figures. The answer keeps as many as the input with the fewest. 4.56 × 1.4 = 6.384, and 1.4 has two significant figures, so the answer is 6.4.
In a mixed calculation, apply each rule at its own step but round only at the end. (12.11 + 18.0) × 2.5: the sum is 30.11, good to tenths, which is 3 significant figures. Then 30.11 × 2.5 = 75.275, limited to 2 significant figures by the 2.5, so the answer is 75.
How do you round to significant figures?
Start counting at the first non-zero digit and keep as many digits as you need. Look at the next digit. If it is 5 or more, round up. If it is less, leave the last kept digit alone. Fill dropped whole-number places with zeros and drop decimal places entirely.
1234.5678 to 3 significant figures is 1230, or 1.23 × 10³. 0.0045678 to 2 is 0.0046. When rounding up adds a digit, as with 9.96 to 2 significant figures, the answer is 10. with a decimal point, so the trailing zero counts.
Why use Mavros
| Mavros | Typical upload sites | |
|---|---|---|
| Counting | Highlights each digit and explains the rule used | A number only |
| Ambiguous zeros | Flagged with the possible range, like 2 to 4 | Silently treated one way |
| Rounding | Half up or half to even, on exact decimal digits | Half up only, floating point |
| Arithmetic | Expressions with brackets, rules shown per step | Two numbers and one operator |
| Notation | Scientific, E and engineering | Scientific only |
| Privacy | Runs in your browser | Ad-heavy pages |
Tips
- Type the number exactly as it was recorded. 2.50 and 2.5 are different measurements: the first has 3 significant figures, the second has 2.
- Exact numbers, such as counted items or defined conversions like 100 cm in 1 m, have unlimited significant figures. In the Calculate mode, enter them with extra zeros so they don't limit the answer.
- If an answer like 1000 hides its precision, the calculator warns you and gives the scientific form to report instead.
- Don't round intermediate results in a long calculation. Carry at least one or two extra digits and round once at the end.
- For the plain arithmetic behind the steps, the scientific calculator handles logs, powers and trigonometry.
Questions
How many significant figures are in 100?
One, by the usual convention, because trailing zeros in a whole number without a decimal point are treated as placeholders. Written as 100. it has three, and 1.00 × 10² also has three.
Are zeros significant?
It depends on where they are. Zeros between non-zero digits always count, leading zeros never count, and trailing zeros count only when there is a decimal point.
How many significant figures does 0.050 have?
Two. The zeros before the 5 are leading zeros and don't count, while the zero after the 5 is a trailing zero after a decimal point, so it does.
What is the rule for adding and subtracting sig figs?
Round the answer to the fewest decimal places among the numbers you added or subtracted. 2.1 + 0.335 = 2.435, which rounds to 2.4 because 2.1 has one decimal place.
What is the rule for multiplying and dividing sig figs?
Round the answer to the fewest significant figures among the inputs. 3.0 × 4.123 = 12.369, which becomes 12 because 3.0 has two significant figures.
Do exact numbers affect significant figures?
No. Counted values and defined constants, such as 12 eggs in a dozen or 2.54 cm in an inch, are exact and have unlimited significant figures, so they never limit the answer.
How do I write a number in scientific notation?
Move the decimal point until one non-zero digit is left of it, then multiply by 10 raised to the number of places moved. 0.004050 becomes 4.050 × 10⁻³, keeping all four significant figures.
Should 2.45 round to 2.4 or 2.5?
With the school rule, round half up, it becomes 2.5. With round half to even, used in some labs and in computing, it becomes 2.4 because 4 is even. Pick whichever your course asks for.