Significant Figures Calculator

How to use the Significant Figures Calculator

1. Choose Count sig figs, Round or Calculate.
2. To count, type a number exactly as written, keeping any trailing zeros and decimal point. Each digit is colored and the rule behind it is explained.
3. To round, enter the number and how many significant figures you want. The answer is shown in standard and scientific notation.
4. To calculate, enter two measured values and pick +, −, × or ÷. The answer is rounded with the decimal-place rule (for + and −) or the significant-figure rule (for × and ÷).
5. You can type scientific notation as 6.02e23, 6.02E23, 6.02 × 10^23 or 6.02x10^23.

Significant figure rules

Significant figures are the digits that carry real information about a measurement's precision. The standard rules: (1) all nonzero digits are significant; (2) zeros between nonzero digits are significant (405 has three); (3) leading zeros are never significant, because they only place the decimal point (0.0034 has two); (4) trailing zeros are significant when the number contains a decimal point (2.50 and 120.0 have three and four); (5) trailing zeros in a whole number without a decimal point are ambiguous. "1200" could have two, three or four significant figures. Writing it as 1.2 × 10³, 1.20 × 10³ or "1200." (with a final decimal point) removes the doubt. In scientific notation, only the digits before the × 10 count.

When rounding, the digit after the last kept digit decides: 5 or more rounds up, less than 5 rounds down (this tool rounds halves away from zero). Rounding 0.0045678 to three significant figures gives 0.00457. If rounding leaves trailing zeros in a whole number, scientific notation is shown so the precision is clear.

For addition and subtraction, the answer keeps the same number of decimal places as the least precise measurement: 12.11 + 18.0 = 30.11, which is rounded to tenths, 30.1. For multiplication and division, the answer keeps as many significant figures as the measurement with the fewest: 4.56 × 1.4 = 6.384, rounded to two significant figures, 6.4. In the calculator, whole numbers with ambiguous trailing zeros (such as 1200) are treated as having only their unambiguous figures, the cautious choice.

Counted quantities and defined constants (12 eggs, 100 cm in a meter) are exact and have unlimited significant figures, so they shouldn't limit an answer. In multi-step problems, keep extra digits along the way and round only the final answer.

Frequently asked questions

How many significant figures does 100 have?
Strictly, it's ambiguous: at least one, and possibly two or three. Written as "100." with a decimal point it has three. In scientific notation, 1 × 10², 1.0 × 10² and 1.00 × 10² show one, two and three.

Do zeros after a decimal point count?
Trailing zeros after the decimal point count (3.40 has three significant figures). Zeros right after the decimal point but before the first nonzero digit do not (0.034 has two).

Why do addition and multiplication use different rules?
When adding or subtracting, uncertainty lives in a decimal place (tenths, hundredths), so the least precise place limits the answer. When multiplying or dividing, uncertainty scales with the size of the numbers, so the relative precision (number of significant figures) is what matters.

How many significant figures does zero have?
A value of exactly zero has no nonzero digits, so the usual counting rules don't apply cleanly. Its precision is shown by its decimal places instead; 0.00 is known to the hundredths place.

Does the tool round 2.5 up or to even?
It rounds halves away from zero (2.5 → 3, 0.125 to two figures → 0.13), the method taught in most science classes. Some statistics and computing contexts round halves to the nearest even digit instead.