Significant Figures / Sig Fig Calculator
The scientist's guide to precision. Count digits, calculate sums, and master the rules of rounding.
Enter a number to begin
Explore More Lab Tools
Why Precision Matters
In math class, 2.0 and 2 are usually the same. In a chemistry lab, they are completely different.
Writing 2 g implies you measured roughly 2 grams (could be 1.5, could be 2.4). Writing 2.00 g implies you used a precise digital scale that usually costs hundreds of dollars. Significant figures (sig figs) are the language scientists use to communicate how good their tools are.
The 4 Golden Rules
- 1-9Non-zeros are always significant. (45 = 2)
- 101Sandwiched zeros are significant. (10.05 = 4)
- 0.01Leading zeros are never significant. They are just placeholders. (0.0002 = 1)
- 1.0Trailing zeros are significant ONLY if there is a decimal. (100 = 1, but 100. = 3)
Math Rules
Two different games, two different rules.
Multiplication / Division
Answer cannot be more precise than the weakest link.4.5 (2) * 2.000 (4) = 9.0 (2)
Addition / Subtraction
Answer depends on decimal places, not count.10.5 (1 dec) + 1.25 (2 dec) = 11.8 (1 dec)
Scientific Notation & Ambiguity
The Problem with "100"
If you write "100", do you mean exactly one hundred, or about a hundred? It's ambiguous. Scientists solved this with Scientific Notation.1 x 10^2 = 1 sig fig.1.00 x 10^2 = 3 sig figs.
Exact Numbers
When you count "6 eggs", that is an exact number. It has infinite sig figs (6.00000...). It does not affect calculations. Defined conversions (12 in = 1 ft) are also exact.
Frequently Asked Questions
What are the rules for zero?
- Leading zeros (0.005) are NEVER significant. 2. Captive zeros (101) are ALWAYS significant. 3. Trailing zeros are ONLY significant if there is a decimal point (100.0 has 4 sig figs, 100 has 1).
How do I multiply with sig figs?
The rule for multiplication and division is: "The answer can have no more significant figures than the measurement with the fewest significant figures." Example: 2.0 (2 sig figs) * 3.00 (3 sig figs) = 6.0 (2 sig figs).
How do I add with sig figs?
The rule for addition and subtraction is different. It relies on decimal places, not total sig figs. You round the answer to the same decimal place as the least precise measurement. Example: 1.2 + 3.05 = 4.25 -> 4.3.
What are exact numbers?
Exact numbers have infinite precision and do not limit your significant figures. Examples include counted objects (3 apples), defined constants (100 cm in 1 m), or integral formulas (radius = diameter / 2).
Why do we use significant figures?
To tell the truth about precision. If you measure a table with a ruler that only has cm marks, you cannot claim it is "150.255 cm" long. You must round to show the uncertainty of your measuring tool.
Does 100 have 1 or 3 sig figs?
It has 1. To show 3, you must write "100." (with a decimal) or use scientific notation: "1.00 x 10^2". This ambiguity is why scientific notation is preferred in science.
How do I round a 5?
Standard rounding says 5 goes up. However, in serious science, many use the "Round Half to Even" rule to prevent statistical bias. If the digit before the 5 is even, keep it. If odd, round up. (e.g., 2.5 -> 2, 3.5 -> 4).
Are constants like Pi exact?
No, Pi is an irrational number. When you use 3.14, you are limiting your precision to 3 sig figs. You should use a version of Pi with more digits than your most precise measurement.
What about pH calculations?
Logarithms are tricky. The number of significant figures in the original number determines the number of DECIMAL places in the log value. log(1.00) = 0.000 (2 decimals for 2 sig figs).
What is scientific notation?
Scientific notation expresses numbers as a product of a coefficient and a power of 10 (e.g., 2.5 x 10^3). All digits in the coefficient are significant.
Do unit conversions affect sig figs?
If the conversion is exact (1 min = 60 sec), it does not. If it is approximate (1 lb = 0.45359 kg), it counts as a measurement and could limit precision if it has fewer sig figs than your data.
What is precision vs accuracy?
Precision is how repeatable a measurement is (sig figs). Accuracy is how close it is to the true value. You can be very precise (2.0000 g) but inaccurate if your scale is broken.
Does the calculator handle scientific notation?
Yes, input numbers like "1.23e-4" and we will correctly count the significant figures in the mantissa (1.23 -> 3 sig figs).
How many sig figs in 0.00?
Zero? No, wait. 0.00 is ambiguous but usually treated as 2 significant figures indicating precision to the hundredth place, though the value is zero.
How do I handle multi-step calculations?
Do not round intermediate steps! Keep all digits in your calculator and only round the very final answer based on the original data's significant figures.