Everything is worked out in your browser and saved on this device for next time.
About the sig fig calculator
Significant figures (sig figs) are the digits of a measured number that really carry meaning. A length of 12.30 cm has four: the 0 at the end says the ruler was read to the hundredth. Chemistry and physics classes ask you to count them, round to them, and keep the right number of them after a calculation.
This calculator does all three:
- Count — type a number and see each digit coloured: green when it counts, grey when it does not, orange when it is unclear. The rules that apply to your number are ticked.
- Round — round any number to 1–10 significant figures, with the steps and a table.
- Calculate — add, subtract, multiply or divide two measured numbers and get the answer with the right sig figs.
The number is read as you type it, so 100 and 100. are different (1 and 3 sig figs), and 1.20 keeps its last zero. Scientific notation works too: 1.20e3, 1.20 × 10^3 or 1.20×10³.
Features
- Digit-by-digit colours — see which digits count and why
- The rules ticked — only the rules that apply to your number are marked
- Unclear zeros — 1500 shows "2 – 4" and how to write it clearly
- Scientific and E notation — 0.00450 → 4.50 × 10⁻³ and 4.50e-3
- Round to sig figs — the kept digit, the deciding digit and a table from 1 to 10 figures
- Sig-fig arithmetic — × ÷ by the fewest sig figs, + − by the last shared decimal place
- Exact math inside — no rounding errors before the final rounding
- Saved on your device — your numbers are still there next time
The rules
- Non-zero digits are always significant: 123 has 3.
- Zeros between non-zero digits are significant: 2005 has 4.
- Leading zeros are never significant: 0.0045 has 2.
- Zeros at the end after a decimal point are significant: 4.50 has 3, 0.0800 has 3.
- Zeros at the end of a whole number without a decimal point are unclear and are not counted: 1500 has 2 (but could have up to 4). Write 1500. or 1.500 × 10³ to show 4.
- In scientific notation, only the digits before × 10 count: 6.022 × 10²³ has 4.
| Number | Sig figs | Why |
|---|---|---|
| 0.00450 | 3 | leading zeros do not count; the end zero after the point does |
| 100 | 1 | the end zeros are unclear (1 to 3) |
| 100. | 3 | the decimal point makes the zeros count |
| 1.00 × 10³ | 3 | only 1.00 counts |
| 2005 | 4 | the zeros are between non-zero digits |
| 0.0800 | 3 | 8 and the two end zeros |
| 12.30 | 4 | the end zero after the point counts |
| 6.022 × 10²³ | 4 | only 6.022 counts |
Rounding examples
| Number | Sig figs | Rounded | Scientific |
|---|---|---|---|
| 123456 | 3 | 123000 | 1.23 × 10⁵ |
| 0.004567 | 2 | 0.0046 | 4.6 × 10⁻³ |
| 99.96 | 3 | 100. | 1.00 × 10² |
| 3.14159 | 4 | 3.142 | 3.142 × 10⁰ |
| 1999 | 2 | 2000 | 2.0 × 10³ |
The digit after the last kept one decides: 5 or more rounds up, less than 5 leaves the kept digits as they are. 99.96 to 3 figures is written 100. with a point, because "100" alone shows only 1 figure.
Calculating with sig figs
- × and ÷: the answer keeps as many significant figures as the number with the fewest. 2.50 × 3.1 = 7.75 → 7.8 (2 figures, like 3.1). 9.81 × 12 = 117.72 → 120 (2 figures, like 12), better written 1.2 × 10².
- + and −: the answer keeps the last decimal place that both numbers know. 12.3 + 4.567 = 16.867 → 16.9 (one decimal place, like 12.3). 100.0 − 0.25 = 99.75 → 99.8.
- Exact numbers — counted things (3 apples) and definitions (100 cm in 1 m) never limit the sig figs.
- In a long calculation, keep all the digits until the end and round once.
Frequently asked questions
How many sig figs does 100 have?
One, by the usual school rule: zeros at the end of a whole number without a decimal point are not counted. It could be 1, 2 or 3 — the number does not say. Write 100. or 1.00 × 10² for three.
Are leading zeros significant?
No. In 0.0045 the zeros only show where the decimal point is. The number has 2 significant figures.
How do I round to 3 significant figures?
Start at the first non-zero digit and count 3 digits. Look at the next digit: 5 or more rounds the third digit up. 0.004567 → 0.00457.
Which rule is used for 5?
A 5 rounds up (away from zero), the rule taught in most schools: 2.45 to 2 figures is 2.5.
Why does addition use decimal places and not sig figs?
When you add, the answer can only be as exact as the least exact place. 12.3 is known to the tenths, so 12.3 + 4.567 can only be known to the tenths.
Can I type numbers with commas?
Yes. On this page 1,500 is read as fifteen hundred and 1,5 as one and a half.
Related tools
- Scientific Calculator — powers, logs and roots for your lab sums
- Unit Converter — change units before you calculate
- Standard Deviation Calculator — how spread out your measurements are
- Percentage Calculator — percent error and percent change
- Long Division Calculator — division written out step by step
How to use it
- Choose Count sig figs, Round to sig figs or Calculate
- Type a number as you wrote it — keep the zeros at the end, and the decimal point
- For scientific notation type 1.2e-3 or 1.2 × 10^-3
- Read the answer in the result box, and the coloured digits, rules or steps under the form
- Or tap an example to see how a rule works
