Significant figures calculator
Type a number, get its significant figures — and round it if you need.
How do I count significant figures?
All non-zero digits count, and so do zeros between them (105 has 3). Leading zeros never count (0.0045 has 2). Trailing zeros count only if there is a decimal point: 0.00450 has 3, 12.0 has 3.
How many significant figures does 1200 have?
It is ambiguous: at least 2, and up to 4 if the zeros were measured. Write 1200. (with a point) for 4, or use scientific notation — 1.20 × 10³ has 3.
How do I round to significant figures?
Keep that many digits from the first non-zero one and round the last: 1,234.5 to 3 significant figures is 1,230, and 0.0012 to 3 is 0.00120.
How many significant figures in a multiplication answer?
As many as the input with the fewest: 2.5 × 3.42 = 8.55, but 2.5 has only 2 significant figures, so the answer is 8.6.
And for addition?
Round to the fewest decimal places instead: 12.11 + 0.3 = 12.41 → 12.4, because 0.3 is only known to one decimal place.
Do exact numbers count as significant figures?
No. Counted items (5 eggs) and defined values (12 inches = 1 foot) are exact, so they have no limit on their significant figures and never restrict an answer. Only measured values do (OpenStax Chemistry 2e, section 1.5).
How does the calculator round a lone 5?
Up: 2.5 to one significant figure is 3. OpenStax Chemistry 2e rounds an exact 5 with nothing after it to the even digit instead, which would give 2. When a nonzero digit follows the 5, every rule rounds up. If your course uses round-half-to-even, apply it by hand to exact ties.
The counting rules
NIST SP 811 (section 7.9) calls a digit significant if it is required to express the numerical value of a quantity. In practice (OpenStax Chemistry 2e, section 1.5) all nonzero digits count, zeros between them count, leading zeros never count (0.00832407 has 6), and trailing zeros after a decimal point count (55.0 has 3). Trailing zeros of a whole number such as 1300 are ambiguous, which is why the calculator shows 2–4 for it. Scientific notation settles the question: 1.3 × 10³ has 2, 1.30 × 10³ has 3 and 1.300 × 10³ has 4, which is why NIST writes 1.200 km when both zeros of 1200 m are measured.
Worked example: the bathtub
OpenStax multiplies 13.44 dm, 5.920 dm and 2.54 dm, which have 4, 4 and 3 significant figures. The raw product is 202.09 dm³, but the fewest figures win, so it is rounded to 3: 202 dm³, or 202 L. Subtraction follows the decimal-places rule instead. In 486 g − 421.23 g the first number has no decimals, so 64.77 becomes 65 g, not the 64.8 that the three figures of 486 would suggest.
Common mistakes
Applying the multiplication rule to sums and differences, as in the 64.8 g above. Treating the zeros of 1300 as measured claims a precision the writer may not have; write 1.30 × 10³ when they are. Rounding at every step lets small errors pile up, so carry extra digits through the calculation and round the final result, as the OpenStax examples do. And exact numbers such as 12 inches per foot should never be the number that sets the rounding.
Sources: NIST Special Publication 811, “Guide for the Use of the International System of Units”, section 7.9; OpenStax, Chemistry 2e, section 1.5 “Measurement Uncertainty, Accuracy, and Precision”. Related tools: rounding calculator, scientific notation calculator, percent error calculator and standard deviation calculator. How we check our calculators.