Absolute Value Calculator
Find the absolute value |x| of any positive, negative, or decimal number instantly. The absolute value is always the non-negative magnitude of a number.
Use this calculator to find the absolute value of any number. Enter a positive or negative whole number or decimal. The absolute value of a number is its distance from zero on a number line:
What is Absolute Value?
The absolute value of a number tells you how far that number is from zero — regardless of direction. Whether the number is positive or negative, the result is always non-negative.
Imagine a number line. The number 5 is 5 units from zero. The number −5 is also 5 units from zero. So |5| = 5 and |−5| = 5 — the same distance, just different directions.
Example Absolute Value Calculations
Example 1: Absolute value of 9
9 is already positive, so the absolute value is 9.
Example 2: Absolute value of −9
−9 is 9 units from zero, so |−9| = 9.
Example 3: Absolute value of 0
Zero is neither positive nor negative. |0| = 0.
Example 4: Absolute value of −7.5
Works for decimals too. |−7.5| = 7.5.
Absolute Value Rules & Properties
| Property | Formula | Example |
|---|---|---|
| Non-negativity | |x| ≥ 0 | |−5| = 5 ≥ 0 |
| Identity | |x| = 0 only if x = 0 | |0| = 0 |
| Symmetry | |−x| = |x| | |−8| = |8| = 8 |
| Multiplication | |xy| = |x| · |y| | |−3 × 4| = 3 × 4 = 12 |
| Triangle Inequality | |x + y| ≤ |x| + |y| | |−3 + 5| = 2 ≤ 3 + 5 = 8 |
| Square root | |x| = √(x²) | |−6| = √36 = 6 |
Absolute Value in Real Life
- Temperature change: If temperature drops from 15°C to −5°C, the absolute change is |15 − (−5)| = 20°C
- Bank balance: Being $200 overdrawn means |−200| = $200 owed
- Elevation: Dead Sea is at −430m; absolute elevation = 430m below sea level
- Sports scores: A team lost by |−14| = 14 points
- Error measurement: Absolute error = |measured − actual|
- Stock price: |−$3.50| = $3.50 drop in price
Absolute Value in Programming
In code, absolute value is a built-in function in every language:
| Language | Function | Example |
|---|---|---|
| Python | abs(x) | abs(-9) → 9 |
| JavaScript | Math.abs(x) | Math.abs(-9) → 9 |
| Java / C# | Math.abs(x) | Math.abs(-9) → 9 |
| C / C++ | abs(x) or fabs(x) | abs(-9) → 9 |
| Excel | =ABS(x) | =ABS(-9) → 9 |
| PHP | abs(x) | abs(-9) → 9 |