What the Significant Figures Calculator does
This calculator counts the significant figures in a number and marks every digit as significant, not significant or ambiguous, with the rule that decides each one. It also rounds a number to any number of significant figures and adds, subtracts, multiplies or divides two measured values while keeping the right precision in the answer.
Significant figures (sig figs, s.f.) are the digits that carry real information about how precisely a quantity is known. 0.00450 has three: the leading zeros only place the decimal point, while the final zero says the measurement was good to the hundred-thousandth. The calculator works on the exact decimal you type rather than a binary floating-point copy of it, so it gets the textbook answer in cases where an ordinary calculator or spreadsheet does not, such as rounding 2.675 to 2.68.
How to use it
- Choose Count, Round or Calculate at the top.
- Type the number as you would write it: 0.00450, 1500, 1500. (with a point), 6.02e23 or 1.50 x 10^-3. Commas are read as thousands separators, so 1,234.5 works.
- To round, enter how many significant figures you want. Open "Rounding rule" if your course or standard uses round-half-to-even instead of the usual round-half-up.
- To calculate, enter both numbers and the operation. Tick a box if a number is exact - a count of 12 objects or a defined factor like 100 cm in a metre - so it does not limit the precision of the answer.
- Read the answer, the marked digits and the notes. The notes explain trailing zeros, the trailing decimal point and when scientific notation is the only unambiguous way to write the result.
Reading the results
Green digits are significant. Grey digits are placeholders. Dashed amber digits are trailing zeros in a whole number with no decimal point, such as the zeros in 1500: they might be measured or might only show the size of the number, so the honest count is a range, 2 to 4.
A trailing decimal point is a signal, not a typo. "1500." says all four digits were measured; it is how a rounded answer like 1499.7 to 4 s.f. is written. Scientific notation (1.500 × 10^3) says the same thing more clearly and is the safest form for any answer that ends in zeros.
For addition and subtraction the answer is limited by decimal places, not by significant figures: 12.11 + 18.0 = 30.11, but 18.0 is only known to the tenth, so the answer is 30.1. For multiplication and division the answer keeps as many significant figures as the least precise number: 2.5 × 3.42 = 8.55, which becomes 8.6 because 2.5 has two.
Worked example: the area of a measured rectangle
A card is measured as 12.5 cm by 4.2 cm. The exact product is 12.5 × 4.2 = 52.5 cm². The lengths have three and two significant figures, so the area keeps two: 53 cm², because the dropped part is exactly a half and the school rule rounds it up. With round-half-to-even it would be 52 cm², since 2 is the even neighbour.
Adding a border makes each side 0.70 cm longer (2 × 0.35 cm, where the 2 is exact). 12.5 + 0.70 = 13.20, rounded to the tenths place of 12.5, gives 13.2 cm; 4.2 + 0.70 = 4.90 gives 4.9 cm. The new area, 13.2 × 4.9 = 64.68, keeps two figures: 65 cm².
Rounding only at each step is what the rules describe; in a longer calculation keep a guard digit or two and round once at the end, which here gives the same 65 cm².
Formulas and scoring rules
- Counting rules
R1 non-zero digits count; R2 zeros between them count; R3 leading zeros never count; R4 trailing zeros after a decimal point count; R5 trailing zeros in a whole number without a point are ambiguousIn scientific notation the mantissa follows the same rules; the power of ten never counts.- Round to n significant figures
keep the first n digits from the first non-zero digit; look at the rest: more than half rounds up, less rounds down, exactly half follows the chosen rule- Round half up (school rule)
exactly half -> away from zero: 2.25 -> 2.3, -2.25 -> -2.3- Round half to even
exactly half -> the even neighbour: 2.25 -> 2.2, 2.35 -> 2.4The rule given in ISO 80000-1 Annex B; it avoids a small upward bias when many values are rounded.- Addition and subtraction
answer rounded to the least precise decimal place among the measured numbers- Multiplication and division
answer rounded to the fewest significant figures among the measured numbersExact numbers - counts and defined values - have unlimited significant figures and never limit the answer.
Why significant figures matter
A measurement is only as good as the instrument and the person using it. If a ruler is read to the nearest millimetre, writing 12.5 cm is honest and 12.50 cm claims a tenth of a millimetre nobody measured. Significant figures are a quick way to carry that precision through a calculation without a full uncertainty analysis, which is why they are taught in school chemistry and physics and used on lab reports.
They are a rule of thumb, not a substitute for uncertainty. Metrology guides such as the GUM state results as a value with an explicit uncertainty - 12.5 ± 0.05 cm - and that is the right approach once accuracy really matters.
Why an ordinary calculator sometimes rounds wrongly
Most software stores numbers in binary, where 2.675 cannot be held exactly; the nearest binary value is a little below 2.675, so rounding it to two decimals gives 2.67. This calculator keeps the digits you typed as an exact decimal and does all the arithmetic on that, so the rules are applied to the number as written.
Limitations: what the result does not prove
- Ambiguous trailing zeros are read conservatively: in a calculation, 1500 is treated as having two significant figures. Write 1500. or 1.500e3 if all four were measured.
- Significant-figure rules approximate uncertainty and can mislead in long calculations, subtractions of nearly equal numbers, and functions such as logarithms, which have their own conventions not covered here.
- It cannot know whether a number is exact or measured. Tick the exact box for counts and defined values, otherwise they will wrongly limit the answer.
- Only one operation at a time is calculated. For a chain of steps, carry the unrounded result forward and round the final answer.
Privacy: where your data goes
Everything you paste, type or drop is processed in this browser tab. It is not uploaded, logged, stored or sent to analytics. Session recording and tag-manager scripts are switched off on this page.
Standards and sources
- NIST Special Publication 811 - Guide for the Use of the International System of Units (rounding, Appendix B)
- ISO 80000-1:2022 - Quantities and units, Part 1: General (Annex B, rounding of numbers)
- JCGM 100:2008 (GUM) - Evaluation of measurement data, Guide to the expression of uncertainty in measurement
- LibreTexts Chemistry - Significant Figures
Frequently asked questions
How many significant figures does 0.00450 have?
Three: 4, 5 and the final 0. The three zeros before the 4 only show where the decimal point is, so they never count; the zero after the 5 sits after the decimal point at the end of the number, so it was measured and does count.
Are trailing zeros significant?
After a decimal point, yes: 2.50 has three significant figures. In a whole number without a decimal point they are ambiguous: 1500 could have two, three or four. A trailing point (1500.) or scientific notation (1.50 × 10^3) removes the doubt.
How do you round to 3 significant figures?
Start counting at the first non-zero digit, keep three digits and look at what follows. 0.004567 becomes 0.00457 and 123,456 becomes 123,000, best written 1.23 × 10^5 so the zeros are not mistaken for measured digits.
How many sig figs should the answer to a multiplication have?
The same number as the measured value with the fewest significant figures. 2.5 × 3.42 is 8.55 on a calculator, but 2.5 has two significant figures, so the answer is 8.6. Exact numbers, such as the 2 in a diameter of 2 × radius, do not count.
What is the sig fig rule for adding and subtracting?
Round to the least precise decimal place, not to the fewest significant figures. 12.11 + 18.0 = 30.11 is rounded to the tenths because 18.0 is known only to the tenth, giving 30.1. Subtracting close numbers can therefore leave very few significant figures.
Is zero a significant figure?
It depends where it is. Zeros between non-zero digits (1002) and trailing zeros after a decimal point (3.40) are significant; leading zeros (0.07) never are; trailing zeros in whole numbers like 300 are ambiguous unless a decimal point or scientific notation shows they were measured.
Why does my calculator round 2.675 to 2.67 and not 2.68?
Because it stores 2.675 in binary as a number very slightly below 2.675, so the dropped part is less than half. Worked on the decimal as written, 2.675 to three significant figures is 2.68, which is what this tool and the textbook give.
Last reviewed by the A2Z.Tools team against the sources listed above.
