Skip to content

Significant Figures Calculator

Type a number exactly as it was written and see which digits are significant, round it to any number of significant figures, or combine two measurements with the rules chemistry and physics classes use. Unlike a general calculator, it works on the digits you typed, so 1500 and 1500. are treated differently.

What do you want to do?

Type it as written, e.g. 0.004050, 1500., 1.50e3 or 1.50 × 10^3.

Result

Significant figures

4

0 (Leading zeros (not significant)).0 (Leading zeros (not significant))0 (Leading zeros (not significant))4 (Nonzero digits)0 (Zeros between digits)5 (Nonzero digits)0 (Trailing zeros after the point)Nonzero digitsZeros between digitsTrailing zeros after the pointLeading zeros (not significant)

Nonzero digits
2
Zeros between digits
1
Trailing zeros after the point
1
Leading zeros (not significant)
3
Decimal places
6
Scientific notation
4.050 × 10⁻³
Show the working
  1. Nonzero digits4 5 = 2
  2. Zeros between significant digits0 = 1
  3. Trailing zeros after a decimal point0 = 1
  4. Total2 + 1 + 1 = 4

Which digits are significant

The significant figures of a measurement are the digits that carry information about its precision: every digit you are sure of, plus the last, estimated one. These are the conventions taught in chemistry and physics courses:

  1. Nonzero digits always count. 4.56 has three.
  2. Zeros between significant digits count. 10.203 has five; these are sometimes called captive zeros.
  3. Leading zeros never count. In 0.004050 the three zeros in front of the 4 only place the decimal point.
  4. Trailing zeros after a decimal point count. The final zero of 0.004050 says the value was measured to the millionths, so 0.004050 has four significant figures.
  5. Trailing zeros in a whole number without a decimal point are ambiguous. 1500 could have two, three or four. The calculator shows the range and marks those zeros with a dashed underline.

To remove the ambiguity, write a decimal point after the last significant zero (1500. has four) or use scientific notation, where every digit of the number in front counts: 1.5 × 10³ has two, 1.50 × 10³ three and 1.500 × 10³ four. For writing and reading numbers in that form, see the scientific notation calculator.

Counted and defined values are exact and have unlimited significant figures: 12 eggs, 100 cm in a meter, or constants fixed by definition such as the Avogadro constant, 6.02214076 × 10²³ per mole.

The rounding and arithmetic rules

Rounding to n significant figures. Start at the first nonzero digit, keep n digits and look at what is dropped. Below 5, keep the digits as they are; above 5, add one to the last kept digit. Then put the digits back in their place, filling with zeros if needed.

When the dropped part is exactly 5 (2.345 to three figures), two rules are in use. Most schools round up, giving 2.35. NIST’s Guide to the SI instead keeps the last digit even, giving 2.34, so that exact halves are rounded up and down equally often. The calculator lets you choose and shows the other answer when they differ.

The calculator rounds the digits you typed, not a floating-point approximation of them. That matters for numbers such as 1.005: a computer stores it as slightly less than 1.005, so ordinary software rounds it to 1.00, while as written it is an exact tie and rounds up to 1.01.

Multiplying and dividing. The answer keeps as many significant figures as the operand with the fewest:

figures in the answer = fewest figures among the measurements

Adding and subtracting. What matters is the decimal place, not the number of figures. Round the answer to the last place that every measurement reaches:

last place of the answer = coarsest last place among the measurements

In a calculation with several steps, keep all the digits until the end and round once. Rounding at every step lets the errors add up.

Worked examples

Counting 0.004050. The three leading zeros are not significant. The 4 and 5 are, the zero between them is, and the final zero after the decimal point is. That makes 4 significant figures, or 4.050 × 10⁻³ in scientific notation.

Counting 1500. The 1 and 5 are significant; the two zeros may or may not be, so the answer is 2 to 4. As 1.5 × 10³ it has two; written 1500. it has four.

Rounding 1234.5678 to 3 significant figures. Keep 123, drop 45678. The first dropped digit, 4, is below 5, so the digits stay 123 and move back into place: 1230. The final zero is only a placeholder, so to show that the answer has three significant figures, write it as 1.23 × 10³.

Multiplying 12.52 × 3.1. The exact product is 38.812. 12.52 has four significant figures and 3.1 has two, so the answer keeps two: 39.

Adding 12.52 + 3.1. The exact sum is 15.62. 12.52 reaches the hundredths but 3.1 only the tenths, so the answer is rounded to the tenths: 15.6, which has three significant figures, more than 3.1 has. In addition the decimal place decides, not the count.

Things to watch

  • Significant figures are a rule of thumb for precision. They track uncertainty roughly. A lab report that states an uncertainty (for example 9.81 ± 0.02 m/s²) says more; to see how far a result is from a reference, use the percent error calculator.
  • An average can keep more figures than single readings in careful work, because averaging reduces random error; course rules differ, so follow the one you are given. The average calculator keeps full precision for you to round.
  • Logarithms follow a different rule. For pH and other logs, the number of decimal places in the result equals the significant figures of the input. This calculator does not apply it.
  • Exact numbers never limit the answer. Multiplying a measured 2.5 cm by the exact 10 in “10 identical pieces” gives 25 cm with two figures, not one. Leave exact numbers out of the rule.

When a whole number ends in zeros

The calculator reads ambiguous zeros as placeholders when it calculates, which is the cautious reading most textbooks use. If the zeros were measured, type the number with a decimal point (100.) or in scientific notation (1.00e2).

Frequently asked questions

How many significant figures does 0.0050 have?

Two. The zeros before the 5 only locate the decimal point, so they don’t count. The zero after the 5 is a trailing zero after a decimal point, so it does count: 5.0 × 10⁻³.

Are trailing zeros significant?

After a decimal point, yes: 2.50 has three significant figures. In a whole number without a decimal point, such as 2500, it is ambiguous. Writing 2500. or 2.500 × 10³ shows that all four digits are significant.

How do you round to 3 significant figures?

Start at the first nonzero digit and keep three digits. If the next digit is 5 or more, add one to the third digit; otherwise leave it. Then fill with zeros to keep the place value: 1234.5678 becomes 1230, or 1.23 × 10³.

Why does adding use decimal places instead of significant figures?

In a sum, the uncertainty comes from the least precise decimal place, not from the number of digits. 12.52 + 3.1 can only be known to the tenths, because 3.1 is, so the answer is 15.6.

What is round half to even?

A rule for exact ties: when the dropped part is exactly 5, round so the last kept digit is even. 2.345 becomes 2.34 and 2.355 becomes 2.36. NIST’s Guide to the SI uses it because it rounds ties up and down equally often.

Sources

Last reviewed September 19, 2026