Significant figures count the digits that carry real information, starting from the first non-zero digit. Rounding to three significant figures gives 0.00234 from 0.00234567 and 1,230,000 from 1,234,567 — the same three digits of precision at very different magnitudes, which is what makes the convention useful in science.
The distinction from decimal places matters. Decimal places count from the point, so they express absolute precision; significant figures count from the leading digit, so they express relative precision. A measurement good to 1 per cent has about three significant figures whatever its size. This page reports the rounding error alongside the result so you can see exactly what was discarded.
The same values at different precisions table follows the calculator: 6 rows spanning 1.23457e+06 through 45.678, there so the result can be cross-checked against a value you already trust. Nothing has to be entered to see it work: the default for number is 1,234,567, and the output recomputes the moment that changes. The result is also read against 4 bands, from negative at the low end to large magnitude at the high end, each with a note on what that range means in practice. The pages people most often open next are Scientific Notation Converter and Least Common Multiple Calculator.
The formula
x- The original value
s- Significant figures wanted
Error- The difference introduced by rounding
How it works, step by step
- Enter the number you want to round.
- Choose how many significant figures to keep.
- The gauge shows the rounded value.
- The rounding error and implied precision appear below.
Worked examples
1,234,567 to three significant figures
The leading three digits are 1, 2 and 3, and the next digit is 4, so it rounds down to 1,230,000. The error introduced is -4,567.
Small numbers keep the same relative precision
0.00234567 to three significant figures is 0.00235, discarding -4.33e-06. Both this and the million-scale example are precise to about 0.1 per cent.
Checking the 3.14159 row
The reference table lists Value = 3.14159, giving 1 s.f.: 3, 2 s.f.: 3.1, 3 s.f.: 3.14, 4 s.f.: 3.142. Entering that above should reproduce the same figures — if it does not, the input is being read differently to the way the table assumes.
How to read your score
Frequently asked questions
Do leading zeros count?
No. In 0.00456 the significant figures are 4, 5 and 6 — the zeros only place the decimal point.
Do trailing zeros count?
It depends on whether they are measured or padding. In 1,200 the trailing zeros are ambiguous, which is why scientific notation is preferred for unambiguous precision.
How do significant figures work in calculations?
For multiplication and division the result carries the fewest significant figures of any input. For addition and subtraction it is decimal places that limit the answer.
Why not just use decimal places?
Because decimal places express absolute precision, which is misleading across different magnitudes. Three decimal places means something very different for 0.001 than for 10,000.
What do the bands under the rounded value mean?
They label the figure so it can be read without a reference point of your own: Negative up to 0; Small magnitude from 0 to 1,000; Moderate magnitude from 1,000 to 1,000,000; Large magnitude from 1,000,000 upwards. The band is a reading aid only — the number itself is exact, and a value sitting just over a boundary is not meaningfully different from one just under it.
What formula does the Significant Figures Calculator use?
The rule it applies is: Round to the first s digits, counting from the leading non-zero digit — with x is the original value; s is significant figures wanted; Error is the difference introduced by rounding. It is stated on the page above the inputs so the result can be reproduced by hand or in a spreadsheet.
Rounding to significant figures
| Value | 1 s.f. | 2 s.f. | 3 s.f. | 4 s.f. |
|---|---|---|---|---|
| 1.23457e+06 | 1e+06 | 1.2e+06 | 1.23e+06 | 1.235e+06 |
| 0.00234567 | 0.002 | 0.0023 | 0.00235 | 0.002346 |
| 98765 | 100000 | 99000 | 98800 | 98760 |
| 3.14159 | 3 | 3.1 | 3.14 | 3.142 |
| 0.999 | 1 | 1 | 0.999 | 0.999 |
| 45.678 | 50 | 46 | 45.7 | 45.68 |
Note how 0.999 jumps to 1 at one and two significant figures.