AbsBench
Absolute Value Calculator
Removes the sign. |x|.
Absolute value of positive and negative numbers
Absolute value is the distance from zero, so it is never negative. Positive numbers and zero are unchanged.
| Input | Absolute value |
|---|---|
| -15 | 15 |
| -7.5 | 7.5 |
| -1 | 1 |
| 0 | 0 |
| 1 | 1 |
| 7.5 | 7.5 |
| 15 | 15 |
The table is symmetric about zero, which is the whole idea: -15 and 15 are both 15 units from the origin. Absolute value turns up wherever direction is irrelevant but size is not - the magnitude of an error, the distance between two points on a line, or the size of a temperature change regardless of whether it rose or fell. In an equation, |x| = 5 has two solutions, 5 and -5, which is why absolute-value equations routinely produce twice as many answers as expected.
Magnitude without direction
Absolute value strips away the sign and keeps only the size — |−5| and |5| are both 5, because both are 5 units from zero on the number line.
Why it matters
It's essential whenever you care about how far apart two things are but not which direction — error margins, temperature differences, or distance calculations all rely on absolute value.
Frequently asked questions
What is absolute value?
|x| is the distance of x from zero on the number line, always non-negative. |5| = 5, |−5| = 5, |0| = 0. It strips the sign and keeps only the magnitude. Formally: |x| = x if x ≥ 0, and |x| = −x if x < 0.
How do I solve absolute value equations?
|x| = 5 means x = 5 or x = −5. |x − 3| = 7 means x − 3 = 7 or x − 3 = −7, so x = 10 or x = −4. Always split into two cases — the positive and negative. If the right side is negative (like |x| = −3), there's no solution.
What is absolute value used for?
Error measurement (how far off a prediction was), distance between numbers, signal magnitude in electronics, and any calculation where direction doesn't matter but size does. In statistics, mean absolute deviation uses it.
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Last updated: September 6, 2026