Absolute Value Calculator
Calculate the absolute value of any number or mathematical expression
Calculate Absolute Value
Enter any positive, negative number, or zero
Example Calculations
Positive Numbers
|5| = 5
|3.14| = 3.14
|100| = 100
Negative Numbers
|-5| = 5
|-3.14| = 3.14
|-100| = 100
Zero
|0| = 0
|0.0| = 0
Expressions
|-3 + 1| = |-2| = 2
|2 * -4| = |-8| = 8
|-10 / 2| = |-5| = 5
Absolute Value Properties
Always Non-negative
|x| ≥ 0 for all real numbers
Identity for Positive Numbers
|x| = x when x ≥ 0
Negation for Negative Numbers
|x| = -x when x < 0
Distance from Zero
Represents distance on number line
Mathematical Rules
|a · b| = |a| · |b|
Product rule
|a / b| = |a| / |b|
Quotient rule (b ≠ 0)
|a + b| ≤ |a| + |b|
Triangle inequality
|a^n| = |a|^n
Power rule
Understanding Absolute Value
What is Absolute Value?
The absolute value of a number is its distance from zero on the number line, regardless of direction. It's always a non-negative number. The absolute value is represented by vertical bars around the number, like |x|.
Mathematical Definition
For any real number x:
- • |x| = x if x ≥ 0
- • |x| = -x if x < 0
- • |0| = 0
Real-World Applications
- •Distance Measurement:
Calculate distance between two points regardless of direction
- •Error Analysis:
Measure deviation from expected values in experiments
- •Computer Graphics:
Calculate pixel distances and color differences
- •Economics:
Measure magnitude of changes in prices or quantities
Example: Temperature Difference
If the temperature drops from 5°C to -3°C, the change is 5 - (-3) = 8°C. The absolute difference |5 - (-3)| = |8| = 8°C shows the magnitude of change.