Significant Figures Calculator

About Significant Figures Calculator

The Significant Figures Calculator is a comprehensive tool that helps you count, round, and perform arithmetic with the correct number of significant figures. Whether you are a chemistry student checking lab results, a physicist analyzing measurements, or an engineer verifying precision, this calculator provides digit-by-digit visual analysis and step-by-step explanations for every calculation.

What Are Significant Figures?

Significant figures (also called significant digits or "sig figs") are the digits in a measured or calculated number that carry meaningful information about its precision. When scientists report a measurement like 4.50 grams, the three significant figures tell others that the measurement is precise to the hundredths place. Understanding sig figs is essential for properly reporting scientific data and performing calculations that don't overstate precision.

The Rules of Significant Figures

How to Use This Calculator

This calculator offers three modes to handle all your significant figures needs:

Count Sig Figs

Enter any number — including scientific notation like 5.020e3 — and the calculator instantly shows how many significant figures it contains. Each digit is displayed as a color-coded card: teal cards for significant digits and gray dashed cards for non-significant digits. Hover over any card to see which rule applies.

Round Number

Enter a number and the desired number of significant figures. The calculator rounds the number correctly and shows both the original and rounded versions side-by-side as digit cards, so you can see exactly which digits were kept or changed. The scientific notation equivalent is also provided.

Arithmetic

Enter two numbers and select an operation (+, −, ×, ÷). The calculator performs the operation and applies the correct sig fig rule automatically. For addition and subtraction, it uses the decimal places rule. For multiplication and division, it uses the sig figs rule. The step-by-step breakdown explains the reasoning.

Significant Figures in Arithmetic

Addition and Subtraction

The result should have the same number of decimal places as the measurement with the fewest decimal places. For example: 12.5 + 1.27 = 13.77, rounded to 1 decimal place gives 13.8.

Multiplication and Division

The result should have the same number of significant figures as the measurement with the fewest sig figs. For example: 3.20 × 4.1 = 13.12, rounded to 2 sig figs gives 13.

Frequently Asked Questions

What are significant figures?

Significant figures (sig figs) are the digits in a number that carry meaningful information about its measurement precision. They include all non-zero digits, zeros between non-zero digits (captive zeros), and trailing zeros after a decimal point. Leading zeros are never significant.

How many significant figures does 100 have?

The number 100 written without a decimal point has 1 significant figure by default, because trailing zeros in whole numbers are ambiguous. Writing 100. (with a trailing decimal) gives 3 sig figs, and using scientific notation like 1.00 × 10² also clearly indicates 3 sig figs.

Are trailing zeros significant?

Trailing zeros after a decimal point are always significant (2.50 has 3 sig figs). Trailing zeros in a whole number without a decimal point are ambiguous and typically not counted (1200 has 2 sig figs by default). A trailing decimal point makes all digits significant (1200. has 4 sig figs).

What is the difference between sig fig rules for addition and multiplication?

For addition and subtraction, the result should have the same number of decimal places as the input with the fewest decimal places. For multiplication and division, the result should have the same number of significant figures as the input with the fewest significant figures. For example, 12.5 + 1.27 = 13.8 (1 decimal place), while 12.5 × 1.27 = 15.9 (3 sig figs).

How do you round a number to significant figures?

Count from the first non-zero digit to find the Nth significant digit. Look at the digit immediately after it. If that digit is 5 or greater, round up; if less than 5, keep the digit as is. For example, 0.004560 rounded to 3 sig figs: the 3rd sig fig is 6, the next digit is 0 (less than 5), so the answer is 0.00456.