Greater Than Or Less Than Calculator

Understanding Greater Than, Less Than, and Equality

Comparing two numbers is one of the fundamental concepts in mathematics, science, and computer programming. The greater than ($>$) and less than ($<$) symbols indicate the relative ordering of quantities on a standard mathematical number line.

This calculator compares any two values (including whole numbers, decimals, fractions like $3/4$, percentages, and negative integers), calculates absolute and relative differences, shows simplified ratios, and renders a dynamic number line visualization. If you are solving algebraic inequalities, check our Inequality Solver or Fractions Solve for Unknown X Calculator.

Inequality Symbols and Meaning

• Greater Than ($>$): Means the value on the left is strictly larger than the value on the right. The open side of the angle bracket always points toward the larger quantity (e.g. $15 > -8$).
• Less Than ($<$): Means the value on the left is strictly smaller than the value on the right (e.g. $-9 < -6$).
• Equal To ($=$): Means both quantities have identical numerical value (e.g. $0.5 = 1/2$).
• Greater Than or Equal To ($\ge$): Allows the left side to be larger or equal.
• Less Than or Equal To ($\le$): Allows the left side to be smaller or equal.

How to Compare Positive and Negative Numbers

1. Opposite Signs: Any positive number is always greater than any negative number (e.g. $2 > -100$).
2. Both Positive: The number located farther to the right from zero (with the greater absolute value) is larger (e.g. $12 > 5$).
3. Both Negative: The number closer to zero (with the smaller absolute magnitude) is larger (e.g. $-3 > -8$, because $-3$ is to the right of $-8$ on the number line).
4. Fractions: Convert fractions to a common denominator or convert them to decimal approximations to compare numerators directly.

Number Comparison Metrics

Beyond binary inequality, several numerical measures quantify how much two values differ:

• Difference: $A - B$
• Absolute Difference: $|A - B|$
• Percentage Difference: $\frac{|A - B|}{(A + B)/2} \times 100\%$
• Simplified Ratio: $A : B$ reduced to the lowest integer terms.