Significant Figures Calculator
Count the significant figures in a number, with each digit marked and the rule that applies, round to any number of sig figs, or add, subtract, multiply and divide measurements with the sig-fig rules.
How to Use
- Choose Count, Round or Arithmetic.
- Type the number exactly as it was measured. Trailing zeros and the decimal point matter, so 2.50 is not 2.5. Scientific notation such as 1.50 × 10^3 or 1.50e3 works.
- To round, enter how many significant figures to keep. Ties round away from zero, the rule taught in school.
- For arithmetic, type an expression such as
12.11 + 18.0 + 1.013or4.56 × 1.4. x, * and / work too. - Read the answer, the unrounded value and the rule used. The diagram lines the digits up by place value and marks which ones are significant.
Worked Example
Counting 0.004560. The three zeros before the 4 only place the decimal point, so they don’t count. 4, 5 and 6 are non-zero, and the final 0 comes after the decimal point, so it was measured. That makes 4 significant figures: 4.560 × 10⁻³.
Adding 12.11 + 18.0 + 1.013. The exact sum is 31.123. The least precise measurement is 18.0, known only to the tenths place, so the answer is rounded to the tenths: 31.1.
The common mistake: using decimal places for division. 25.0 ÷ 0.012 = 2,083.333… Matching the decimal places of 25.0 would give 2,083.3, which claims five significant figures. Division keeps the fewest significant figures, and 0.012 has only 2, so the answer is 2,100, better written 2.1 × 10³.
Show Work
Formulas
Why the Rules Work
Significant figures are a shorthand for uncertainty. A length written as 12.3 cm says the true value is somewhere around 12.25 to 12.35 cm, and the last digit is the uncertain one. The two rules follow from how uncertainty spreads. When you multiply or divide, relative errors combine, so the answer can only be as good as the input with the fewest figures. When you add or subtract, absolute errors combine, so the answer can only be as fine as the coarsest decimal place.
The rules are an approximation. Laboratories and standards bodies state an explicit uncertainty instead, such as 12.30 ± 0.02 cm, following the Guide to the Expression of Uncertainty in Measurement (GUM), first published in 1993. The trailing-zero problem in numbers like 1500 has several workarounds: a trailing decimal point (1500.), a bar over the last significant zero, or, most clearly, scientific notation.
About This Calculator
This calculator reads a number digit by digit, so it knows that 2.50 and 2.5 are different measurements, and works in exact decimals, so 1.005 is a true tie and 0.1 + 0.2 is exactly 0.3. It counts significant figures with each digit marked and its rule named, flags whole numbers whose trailing zeros are ambiguous, rounds to any number of figures with scientific notation, and applies the sig-fig rules to expressions of up to 12 measurements, including mixed ones such as 2.5 × 3.42 + 1.235.
Everything runs in your browser; nothing is sent anywhere.
Related tools: Rounding Calculator, Scientific Notation Converter, and Percentage Calculator.
Frequently Asked Questions
How many significant figures does 0.004560 have?
Four: 4, 5, 6 and the final 0. The three zeros in front only place the decimal point, which is clear in scientific notation, 4.560 × 10⁻³. The trailing zero after the point counts, because nobody would write it unless it had been measured.
Are trailing zeros significant?
After a decimal point, always: 2.50 has 3 significant figures. In a whole number without a point they are ambiguous: 1500 could have 2, 3 or 4, and the usual reading is 2. Write 1.50 × 10³ for 3, or 1.500 × 10³ (or 1500. with a point) for 4. Scientific notation removes the doubt.
What are the rules for adding and multiplying?
Multiplying and dividing keep the fewest significant figures: 4.56 × 1.4 = 6.384, and 1.4 has 2, so the answer is 6.4. Adding and subtracting keep the fewest decimal places: 12.11 + 18.0 + 1.013 = 31.123, and 18.0 has one decimal place, so the answer is 31.1. Keep every digit until the end and round once.
Do exact numbers limit the significant figures?
No. Counted numbers and defined values, such as 3 trials, the 2 in 2πr or 100 cm in a metre, are exact and have unlimited significant figures. The mean of 12.1, 12.3 and 12.6 is 37.0 ÷ 3 = 12.333…, reported as 12.3, because the 3 is a count. This calculator treats every number you type as a measurement, so leave exact numbers out or type them with extra zeros, such as 3.0000.
Why does this round 1.005 to 1.01 when my spreadsheet gives 1.00?
A computer stores 1.005 in binary as 1.00499999999999989341858963598497211933135986328125, just below the tie, so float-based rounding goes down. In the same way 0.1 + 0.2 comes out as 0.30000000000000004. This calculator reads what you type as an exact decimal, so 1.005 to 3 significant figures is 1.01 and 0.1 + 0.2 is 0.3.
How do I use the Significant Figures Calculator?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Do I need to install or sign up for anything?
Not at all — it runs in the browser with nothing to install and no account. After it loads once, it even works without an internet connection.
Is my information private?
Yes. Everything happens in your browser. Nothing you type is sent to a server or saved anywhere.
Common Use Cases
Chemistry labs
Density from 12.5 g and 4.2 mL: 12.5 ÷ 4.2 = 2.976…, reported as 3.0 g/mL.
Physics homework
9.81 m/s² × 3.5 s = 34.335, reported as 34 m/s.
Adding lengths
12.11 + 18.0 + 1.013 cm = 31.1 cm, limited by the 18.0.
Reporting constants
299,792,458 m/s to 3 significant figures is 3.00 × 10⁸ m/s.
Checking answers
See whether 1500 has 2 or 4 significant figures before you divide by it.
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