Significant Figures Calculator

How to use the significant figures calculator

1. Type the number in the Number box exactly as it was written or measured. Trailing zeros and the decimal point matter, so 12.0 and 12 do not have the same number of significant figures.
2. The count updates as you type; Count does the same on demand.
3. Read the number of Significant figures, the Decimal places and the value in Scientific notation, written with exactly that many significant digits.
4. Under Which digits count, the significant digits are highlighted. Hover over a digit to see the rule that applies. A dotted underline marks an ambiguous trailing zero.
5. Rules applied lists each rule used and the digits it concerns.
6. To round, enter a value in Number of significant figures under Round to significant figures. The Rounded value appears in standard and scientific notation, and Copy copies it.

Scientific notation can be typed as 1.20e3, 1.20 × 10^3, 1.20x10^3 or 1.2x10⁻³ with superscript digits.

The rules for counting significant figures

1. Nonzero digits are always significant. 123.45 has five.
2. Zeros between nonzero digits are significant (sometimes called captive zeros). 1002 has four, and so does 3.005.
3. Leading zeros are never significant. They only place the decimal point: 0.00340 has three significant figures (3, 4 and the final 0).
4. Trailing zeros are significant when a decimal point is written. 12.00 has four; 1200. (with a final point) has four as well.
5. Trailing zeros of a whole number without a decimal point are ambiguous. 1200 may have two, three or four significant figures depending on how it was measured. By convention this tool counts only the certain ones (two) and tells you the possible range.
6. In scientific notation, only the mantissa counts. 1.20 × 10³ has three significant figures; the power of ten only moves the decimal point.

A value of zero is a special case: a plain 0 counts as one figure, and the zeros written after the decimal point (0.00) show its precision.

Why significant figures matter

Significant figures express how precise a measurement is. Writing 2.50 m says the length is known to the centimetre, while 2.5 m only claims the decimetre. In physics and chemistry, results are rounded so that they do not claim more precision than the data: when multiplying or dividing, keep as many significant figures as the least precise factor; when adding or subtracting, keep as many decimal places as the least precise term.

To remove the ambiguity of 1200, write it in scientific notation: 1.2 × 10³ (two significant figures), 1.20 × 10³ (three) or 1.200 × 10³ (four).

Rounding to significant figures

The rounding uses the usual “round half up” rule: 0.004050 to two significant figures gives 0.0041, and 123456 to three gives 123000, or 1.23 × 10⁵. Trailing zeros that belong to the precision are kept, so 0.002 to three significant figures is written 0.00200. The calculation is done on exact decimals, never on binary floating point.