Significant Figures Calculator

What this calculator does

Significant figures are how scientists and engineers say "these are the digits that actually mean something". Rounding a number to a set number of them is a standard step in any measurement or calculation. This rounds a number to the number of significant figures you choose.

Enter a number and how many significant figures you want, and it returns the rounded value. It runs right here in the browser.

Using the calculator

1. Enter the number.
2. Enter how many significant figures to round it to.
3. Press Calculate.

It returns the number rounded to that many significant figures. Reset clears the boxes.

What significant figures are

The significant figures of a number are the digits that carry real information about how precise it is. If a scale reads 4.5 grams, both of those digits mean something: the 4 and the 5 were genuinely measured. Significant figures are just a way of counting how many such meaningful digits a value has, and therefore how trustworthy it is.

The only thing that makes this fiddly is zeros, because a zero sometimes carries real information and sometimes is just holding a place. Sorting out which is which is what the rules below are for.

Which digits count: the rules

There are four rules that settle whether a digit is significant:

• All non-zero digits count. In 4.53 every digit is significant, so it has three.
• Zeros between non-zero digits count. These "sandwiched" zeros are real, so 5008 has four significant figures.
• Leading zeros do not count. Zeros before the first non-zero digit are just placeholders marking the decimal point, so 0.0085 has only two significant figures, the 8 and the 5.
• Trailing zeros after a decimal point count. A zero written at the end of a decimal was measured on purpose, so 3.10 has three significant figures and 12.000 has five.

One trap to watch: trailing zeros in a plain whole number, like 1500, are ambiguous, since it is not clear whether they were measured or are just rounding. Scientific notation, or a written decimal point, is used to make the intent clear.

Rounding to a number of significant figures

To round to a chosen number of significant figures, you keep that many significant digits, counting from the first non-zero digit, and drop the rest. Whether the last kept digit stays or rises depends on the very next digit:

• If the first dropped digit is less than 5, leave the last kept digit as it is.
• If it is 5 or more, round the last kept digit up by one.

Any digits before the decimal that you drop are replaced by placeholder zeros to keep the number the right size. So rounding 12345 to two significant figures gives 12000, where the zeros are just holding the places.

Worked examples

3.14159 to three significant figures. The first three significant digits are 3, 1 and 4. The next digit is 1, which is less than 5, so the 4 stays. The answer is 3.14.

2.7182 to three significant figures. The first three are 2, 7 and 1. The next digit is 8, which is 5 or more, so the 1 rounds up to 2. The answer is 2.72.

0.008765 to two significant figures. The leading zeros do not count, so the first two significant digits are 8 and 7. The next digit is 6, so the 7 rounds up to 8. The answer is 0.0088.

Why they matter

Significant figures are really about honesty. They stop you from claiming more precision than you actually have. If a ruler only measures to the millimetre, reporting a length to the nearest thousandth of a millimetre is a fib, dressed up in extra digits that were never really measured.

This is why 14 and 14.0 are not the same statement, even though they are the same value. Writing 14.0 says you measured down to the tenth and found it to be zero, which is a more precise, more trustworthy claim than plain 14. Keeping the right number of significant figures is how a measurement carries its own honesty about how good it is, which is exactly what matters in science and engineering.

Questions people ask

What are significant figures?

The digits in a number that carry real information about its precision. Counting them tells you how many meaningful digits a value has.

Do zeros count as significant?

It depends. Zeros between non-zero digits count, and trailing zeros after a decimal point count. Leading zeros do not, as they only hold the decimal place.

How do you round to significant figures?

Keep the required number of significant digits and look at the next one. If it is 5 or more, round the last kept digit up; if less, leave it. Fill any gaps before the decimal with placeholder zeros.

Does 3.10 have two or three significant figures?

Three. The trailing zero after the decimal point is significant, because it says the value was measured to the hundredth and found to be zero there.

Why are significant figures important?

They keep a number honest about its precision, preventing you from implying more accuracy than the measurement actually has.

References

A note on where this comes from. Significant figures are the digits of a value that carry meaning about its precision, governed by standard rules for which zeros count, and rounded by the usual round-half-up convention. They are a core part of reporting measurements honestly in science and engineering. For further reading, see Significant figures.

1. The significant figures convention, distinguishing digits that carry measured precision from placeholder zeros.
2. The round-half-up rule for rounding, keeping the last significant digit or raising it according to the first digit dropped.