Significant figures calculator: count and round

Significant figures (sig figs) are the digits in a number that carry meaning about its precision. Count from the first non-zero digit: non-zero digits and zeros between them always count, leading zeros never do, and trailing zeros count only after a decimal point. So 0.004506 has 4 significant figures and 1.20 has 3. This significant figures calculator counts them, labels every digit with the rule it follows, and rounds to any number of figures.

It opens on 0.0045060 rounded to 3 significant figures. Type your own number, or open the full significant figures calculator over this page.

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Significant Figures Calculator

Round to any number of significant figures and count them

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How to use the significant figures calculator

1. Type the number in Number, as written, exactly as it appears, trailing zeros included. It reads your digits as text, so 1.20 and 1.2 stay different. Commas, standard form such as 6.02e23, and very long numbers all work.
2. To round, type how many figures you want in Round to (significant figures). Leave it empty to just count.
3. Read the number of significant figures, the rounded number and the same answer in standard form.
4. Look at Digit by digit: each digit is marked as counting or not, with the reason. Underneath, a table shows the number rounded to 1, 2, 3 and more figures.
5. To practise, press Random problem in the Practice section.

Significant figures rules

A whole number like 5600 is ambiguous: the zeros might have been measured, or might only fill the places. The calculator follows the usual convention and doesn't count them, and it also tells you how many figures there would be if they were measured. To show they count, write a decimal point (5600.) or use standard form (5.600 × 10³). The calculator counts 5600. as 4.

Worked examples you can check in the calculator

Example 1: counting and rounding a small decimal

Take 0.0045060, the calculator's opening number. The three zeros before the 4 are leading zeros and don't count. Then 4, 5 and 6 count, the 0 between 5 and 6 counts, and the final 0 is a trailing zero after the decimal point, so it counts too. That makes 5 significant figures.

To round to 3 significant figures, keep 4, 5 and 0 and look at the next digit, 6. It is 5 or more, so round up: 0.00451. In standard form that is 4.51 × 10⁻³.

Example 2: rounding a large number

Round 48,762 to 2 significant figures. Keep 4 and 8, and the next digit, 7, rounds the 8 up to 9. Fill the rest with zeros to keep the size: 49,000. Leaving out the zeros and writing 49 would change the number completely.

Example 3: when rounding up adds zeros you must keep

Round 0.0039961 to 3 significant figures. Keep 3, 9 and 9. The next digit is 6, so round up: 0.00399 becomes 0.00400. Write 0.00400, not 0.004: the two trailing zeros show the answer is good to 3 significant figures. The calculator keeps them.

Example 4: standard form

In standard form, only the number in front of the power of ten matters. 6.02 × 10²³ (type 6.02e23) has 3 significant figures. Rounding 299,792,458 to 3 significant figures gives 300,000,000, and standard form, 3.00 × 10⁸, is the clear way to show that it is exactly 3 figures.

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Significant figures in calculations

An answer can't be more precise than the measurements it came from. The calculator rounds one number at a time, so do the calculation first, then round its answer with these rules:

In the first example, 2.4 has only 2 significant figures, so the answer gets 2. In the second, 0.3 has only one decimal place, so the answer gets one. Keep every digit through a multi-step calculation and round only at the end, or the rounding errors build up. A result like 9.81 × 2.0 = 19.62 rounds to 2 significant figures as 20, best written 2.0 × 10¹ so nobody wonders whether the zero counts.

Common mistakes

• Counting leading zeros. 0.0056 has 2 significant figures, not 4 or 5.
• Dropping trailing zeros after rounding. 0.00400 to 3 s.f. needs both zeros.
• Forgetting to keep the size of a large number. 48,762 to 2 s.f. is 49,000, not 49.
• Typing 1.2 when the measurement was 1.20. Type numbers exactly as written, or the count is wrong.
• Mixing up the calculation rules. Multiplying and dividing go by significant figures; adding and subtracting go by decimal places.

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