Significant figures calculator — count and round sig figs

How to use the significant figures calculator

1. Type your number in Number, exactly as it was written or measured. Keep any trailing zeros and the decimal point, because they change the count.
2. Set Round to significant figures to the number you need, from 1 to 50.
3. Read Significant figures in the input and the Rules applied note that explains the count.
4. Copy the Rounded value, or the Scientific notation version when the plain form ends in zeros. Very large and very small results are rounded straight to scientific notation.

What it does and when to use it

Significant figures show how precise a measurement is. A length written as 12.0 cm claims more precision than 12 cm. In science and engineering you round your final answer to match the least precise input, so counting and rounding sig figs is a skill tested in chemistry, physics and maths exams.

If you need to round to decimal places instead, or want a different rounding rule, use the rounding calculator. To convert a result into powers of ten with engineering notation too, use the scientific notation converter.

How it works

Counting. The tool reads the number as text, so it sees the zeros you typed:

1. Leading zeros are never significant.
2. Zeros between non-zero digits are significant.
3. With a decimal point, every digit after the first non-zero digit counts, including trailing zeros.
4. In a whole number with no point, trailing zeros are ambiguous, so a range is shown.

Rounding. It finds the exponent e of the first significant digit (the power of ten it sits in), then rounds to sig − 1 − e decimal places with round half up. The number is stored as an exact fraction, so there are no binary rounding errors.

Step by step for 0.004560 to 2 significant figures:

1. The first non-zero digit, 4, is in the thousandths place, so e = −3.
2. Decimal places to keep: 2 − 1 − (−3) = 4.
3. 0.0045|60: the next digit is 6, which is 5 or more, so round up.
4. The answer is 0.0046, or 4.6 × 10⁻³.

The input itself, 0.004560, has 4 significant figures: 4, 5, 6 and the trailing 0.

Worked examples

Small decimal. 0.004560 to 2 s.f. gives Rounded: 0.0046 and Significant figures in the input: 4.

Ambiguous zeros. 1500 to 3 s.f. reports 2 to 4 (ambiguous) and gives 1.50 × 10³. The plain answer 1500 cannot show the third figure.

A tricky half. 2.675 to 3 s.f. gives Rounded: 2.68. Many spreadsheet and code functions show 2.67 here because 2.675 cannot be stored exactly in binary.

Large whole number. 98765 to 2 s.f. gives Rounded: 99000 and Scientific notation: 9.9 × 10⁴.

Limits and tips

• For very large or very small results (10¹⁵ and up, or below 10⁻⁶), Rounded is given in scientific notation, such as 6.0 × 10²³ for 6.022e23 to 2 s.f., and the full digits move to Written out.
• The tool counts figures in one number. For calculations, apply the rules yourself: for × and ÷ keep the fewest significant figures, for + and − the fewest decimal places. The percent error calculator is a common next step in lab work.
• Everything runs in your browser.