Last updated: July 26, 2026
Absolute Value Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
|x| = x (if x ≥ 0), -x (if x < 0)
Where:
- x=Input value
- |x|=Absolute value of x
Worked Examples
Negative number: x = -12
Absolute value removes the sign.
- 1|x| = |-12|
- 2Distance from 0 to -12 is 12
- 3So |-12| = 12
Positive number: x = 8.5
Positive values stay the same.
- 1|x| = |8.5|
- 2x is already non-negative
- 3So |8.5| = 8.5
Zero case: x = 0
Zero is its own absolute value.
- 1|0| = 0
- 2Distance from 0 to 0 is 0
Introduction
The Absolute Value Calculator computes |x|, the non-negative distance of a number from zero on the number line. Absolute value ignores direction (sign) and keeps only magnitude, which is why opposite numbers have equal absolute values.
What Absolute Value Means
Absolute value represents distance from zero, so it is never negative.
|-9| = 9 and |9| = 9
|0| = 0
Distance is always non-negative
Absolute value ignores left/right direction on the number line
Piecewise Rule
The mathematical definition of absolute value is piecewise.
If x ≥ 0, then |x| = x
If x < 0, then |x| = -x
Example: x = -4 → |x| = -(-4) = 4
Example: x = 7 → |x| = 7
How to Use This Calculator
Enter a value and the calculator returns absolute value, distance from zero, and input sign.
Enter any real number (negative, positive, or zero)
Read Absolute Value |x| for final result
Read Distance from Zero for interpretation
Read Input Sign to confirm input classification
Key Properties of Absolute Value
Absolute value follows useful algebraic properties.
|ab| = |a||b|
|a/b| = |a|/|b| (b ≠ 0)
|a| ≥ 0 for all real a
|a| = 0 only when a = 0
Real-World Uses
Absolute value appears wherever only size matters, not direction.
- Finance:
price movement magnitude
- Physics:
displacement magnitude
- Statistics:
absolute error
- Engineering:
tolerance and deviation limits
- Data analysis:
distance-based metrics
Common Mistakes
Most absolute-value errors are sign mistakes.
- Wrong:
|-5| = -5
- Correct:
|-5| = 5
- Wrong:
absolute value can be negative
- Correct:
absolute value is never negative
FAQs
Can absolute value ever be negative?
No. Absolute value is distance from zero, and distance cannot be negative.
Why do -5 and 5 have the same absolute value?
They are both 5 units away from zero, just on opposite sides of the number line.
What is |0|?
It is 0, because zero is zero units away from itself.
Is absolute value the same as removing parentheses?
No. Absolute value bars have a specific meaning and must be evaluated using the piecewise rule.
Does this calculator support decimals?
Yes. It supports integers and decimal values.
Where is absolute value used in algebra?
It is used in inequalities, equations, distance formulas, and error bounds.