Math calculators

Sig Fig Calculator

Updated Sep 1, 2026 By Jehan Wadia
Rate Formulas
Overline Notation: To mark a trailing zero as significant using overline, append ~ after the zero. For example, 5200 has 2 sig figs, but 52~00 means the first trailing zero is overlined (3 sig figs), and 52~0~0 means both trailing zeros are significant (4 sig figs).
Supports decimals, scientific notation (e.g. 4.50e-3), and overline (~) notation.
= 0.00450
3
Significant
Figures
Digit Analysis
Significant
Not Significant
Rules Applied
    Scientific Notation
    Number Properties
    Supports +, -, *, /, ^, parentheses, sqrt(), log(), ln(), sin(), cos(), tan(), abs(), exp(), pi, e

    Introduction

    Significant figures (or "sig figs") are the digits in a number that actually matter and carry meaning. They help us show how precise a measurement really is. For example, saying a rope is 5.00 meters long is more precise than saying it is 5 meters long, because it has more significant figures. Scientists, engineers, and math students use sig figs every day to keep their answers honest and accurate.

    This sig fig calculator makes it easy to count the number of significant figures in any number you type in. It also shows you which digits are significant and which are not. This tool rounds a number to the sig figs you choose, so you can also use it to check your homework. Simply enter your number and get your answer right away.

    How to use our Sig Fig Calculator

    Enter a number or math expression, and this calculator will tell you how many significant figures it contains and which digits are significant.

    Number or Expression: Type in any number (like 0.00340 or 1500) or a math expression (like 3.14 × 2.0). The calculator accepts whole numbers, decimals, and numbers in scientific notation (like 2.50 × 10³).

    What Are Significant Figures?

    Significant figures (often called "sig figs") are the digits in a number that carry meaning and tell you how precise a measurement is. When you measure something in science class (like the length of a table or the mass of a rock), you can only be so exact. Significant figures are how we show that level of exactness. The more significant figures a number has, the more precise the measurement is.

    The Rules for Counting Significant Figures

    There are a few simple rules that determine which digits in a number are significant:

    • All non-zero digits are significant. In the number 425, all three digits count. That gives you 3 significant figures.
    • Zeros between non-zero digits are significant. These are called "captive zeros." In 3,007, all four digits are significant because the two zeros are trapped between the 3 and the 7.
    • Leading zeros are never significant. These are the zeros that come before the first non-zero digit. In 0.0045, only the 4 and the 5 are significant, giving you 2 sig figs. The leading zeros just show where the decimal point is.
    • Trailing zeros after a decimal point are significant. In 8.500, all four digits are significant. Those trailing zeros tell you the measurement was precise to the thousandths place.
    • Trailing zeros in a whole number without a decimal point are ambiguous. The number 5200 could have 2, 3, or 4 significant figures depending on the measurement. This is why scientific notation is so useful: it makes the number of sig figs clear.

    Sig Fig Rules in Math Operations

    When you do math with measured numbers, your answer can only be as precise as your least precise measurement. The rules depend on what kind of math you're doing:

    • Multiplication and division: Your answer should have the same number of significant figures as the number with the fewest sig figs. For example, 4.56 × 1.4 = 6.384, but since 1.4 has only 2 sig figs, you round the answer to 6.4.
    • Addition and subtraction: Your answer should have the same number of decimal places as the number with the fewest decimal places. For example, 12.11 + 0.3 = 12.41, but since 0.3 has only one decimal place, you round to 12.4.

    Why Significant Figures Matter

    Significant figures keep your results honest. If you measure a room with a tape measure that's only accurate to the nearest centimeter, it wouldn't make sense to report your answer down to the micrometer. Sig figs prevent you from claiming your answer is more precise than your original measurements actually allow. This is especially important in science, engineering, and medicine, where reporting false precision can lead to real mistakes.

    Scientific Notation and Sig Figs

    Scientific notation is a way of writing numbers that makes significant figures perfectly clear. Instead of writing 5200 and leaving people guessing, you can write 5.2 × 10³ for 2 sig figs, 5.20 × 10³ for 3 sig figs, or 5.200 × 10³ for 4 sig figs. Each version tells the reader exactly how precise the measurement is. The calculator above fully supports scientific notation using formats like 4.50e-3 or 4.50 × 10^-3.

    What Is Overline Notation?

    Overline notation is another way to handle the problem of ambiguous trailing zeros in whole numbers. A bar is placed over the last significant trailing zero to show it was actually measured. For example, in 5̄200, the overline on the 2 (and the zeros between it and the non-zero digits before it) tells you the number has 3 significant figures. In this calculator, you can use the tilde symbol (~) after a zero to mark it as overlined. For instance, typing 52~00 means the first trailing zero is significant, giving you 3 sig figs.

    Sig Figs and Logarithms

    Logarithmic functions follow a special sig fig rule: the number of significant figures in the argument determines the number of decimal places in the result, not the total number of significant figures. For example, log(5.00) has 3 sig figs in the argument, so the result should be reported to 3 decimal places as 0.699. This calculator's expression mode handles this rule automatically.

    Formulas used

    Rounding to N Significant Figures
    x_{\text{rounded}} = \frac{\operatorname{round}\!\left(x \times 10^{N - \lceil \log_{10} |x| \rceil}\right)}{10^{N - \lceil \log_{10} |x| \rceil}}
    Scientific Notation
    x = m \times 10^{n}, \quad 1 \le |m| < 10, \quad n = \lfloor \log_{10} |x| \rfloor
    Multiplication / Division Rule
    \text{SF}_{\text{result}} = \min\!\left(\text{SF}_a,\; \text{SF}_b\right)
    Addition / Subtraction Rule
    \text{DP}_{\text{result}} = \min\!\left(\text{DP}_a,\; \text{DP}_b\right)
    Logarithm Sig Fig Rule
    \text{DP}_{\log(x)} = \text{SF}_x
    Exponentiation Sig Fig Rule
    \text{SF}_{a^{\,b}} = \text{SF}_a

    Frequently asked questions

    How many significant figures does 100 have?

    The number 100 written without a decimal point has 1 significant figure. The trailing zeros are ambiguous because there is no decimal point to confirm they were measured. If you write it as 100. (with a decimal point), it has 3 sig figs. Writing it as 1.00 × 10² also makes it clear there are 3 sig figs.

    Does the number zero have any significant figures?

    Yes. A single zero (0) is considered to have 1 significant figure. If you write 0.0, it also has 1 sig fig because the leading zero is not significant and the trailing zero after the decimal shows precision.

    Are trailing zeros before a decimal point significant?

    If a number is written with a decimal point at the end, such as 1500., then all four digits including the trailing zeros are significant (4 sig figs). Without the decimal point, 1500 typically has only 2 sig figs because the trailing zeros are ambiguous.

    What is the difference between significant figures and decimal places?

    Decimal places count how many digits come after the decimal point. Significant figures count all the digits that carry meaning, no matter where they are. For example, 0.0045 has 4 decimal places but only 2 significant figures. The two rules are used in different math operations: decimal places for addition and subtraction, sig figs for multiplication and division.

    How do I use the tilde (~) for overline notation?

    Place a ~ right after the zero you want to mark as significant. For example, type 52~00 to say the first trailing zero is significant (3 sig figs). Type 52~0~0 to make both trailing zeros significant (4 sig figs). The calculator will display those zeros with an overline to show they count.

    How do you round a number to a specific number of significant figures?

    Find the digit at the position of the last sig fig you want to keep. Look at the next digit to the right. If it is 5 or greater, round up. If it is less than 5, keep the digit the same. For example, rounding 0.004536 to 2 sig figs: the first two sig figs are 4 and 5, the next digit is 3 (less than 5), so the answer is 0.0045. This calculator does this for you automatically using the round control.

    Are exact numbers treated differently for significant figures?

    Yes. Exact numbers, like counted items (12 eggs) or defined values (1 inch = 2.54 cm exactly), have infinite significant figures. They never limit the sig figs in your answer. In this calculator, constants like pi and e are treated as exact and will not reduce the sig fig count of your result.

    How many sig figs does 0.010 have?

    The number 0.010 has 2 significant figures. The leading zeros (0.0) are not significant. The 1 is significant because all non-zero digits count. The trailing 0 after the decimal is significant because it shows the measurement was precise to that place.

    Why are leading zeros not significant?

    Leading zeros only serve as placeholders to show where the decimal point is. They do not reflect the precision of a measurement. For example, 0.005 and 5 × 10⁻³ represent the same value and precision. Both have just 1 significant figure. The zeros in 0.005 disappear when you write it in scientific notation, proving they carry no measured meaning.

    How are sig figs handled for logarithms?

    Logarithms follow a special rule. The number of significant figures in the input becomes the number of decimal places in the result. For example, log(5.00) has 3 sig figs in the input, so the answer is written to 3 decimal places: 0.699. The expression calculator applies this rule automatically when you use log() or ln().