Math
Absolute Value Calculator
Absolute value measures distance from zero, so it is never negative.
Enter a number to get |x| with a plain explanation, enter two numbers to get their distance on the number line, or solve an equation of the form |ax + b| = c: the calculator splits it into the two cases, solves each, checks the solutions, and explains why there are two, one, or no answers.
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Result
Result
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- Meaning
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- Details
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Study path
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What the absolute value calculator solves
How far a number sits from zero, so the answer is never negative. measures distance from zero, so it is never negative. Enter a number to get |x| with a plain explanation, enter two numbers to get their distance on the number line, or solve an equation of the form |ax + b| = c: the calculator splits it into the two cases, solves each, checks the solutions, and explains why there are two, one, or no answers.
Formula
How to use it
- Pick a mode: a single absolute value, the distance between two numbers, or an absolute value equation.
- Enter the number(s) or the The number multiplying a variable, like the 3 in 3x. a, b, and c for |ax + b| = c.
- Read the result and the number-line meaning, then follow the case-by-case steps for equations.
How to read the answer
Absolute value strips the sign: |-7.5| = 7.5 and |7.5| = 7.5, because both are 7.5 units from 0. The distance between two numbers is the absolute value of their difference, in either order. An equation |ax + b| = c has two solutions when c > 0, one solution when c = 0, and none when c < 0, because an absolute value can never be negative.
Common mistakes and edge cases
- Thinking |x| = -x is always wrong; it is exactly right when x is negative.
- Solving |2x - 3| = 7 with only the positive case and missing x = -2.
- Trying to solve |x + 1| = -4; there is no solution.
- Computing distance as a - b without the absolute value and getting a negative distance.
- Confusing |a - b| with |a| - |b|: |3 - (-4)| = 7, but |3| - |-4| = -1.
Worked examples
|-7.5|
7.5 units left of 0.
Result
7.5
|0|
The only number with absolute value 0.
Result
0
Distance from -4 to 9
|-4 - 9| = 13.
Result
13
Solve |2x - 3| = 7
Two cases: 2x - 3 = 7 or 2x - 3 = -7.
Result
x = -2 or x = 5
One solution |3x + 6| = 0
Only the inside = 0 case.
Result
x = -2
No solution |x + 1| = -4
Absolute values are never negative.
Result
no solution
Decimal coefficients
|0.5x + 1.25| = 2.
Result
x = -6.5 or x = 1.5
Frequently asked questions
What is the absolute value of a negative number?+
Its positive counterpart: |-7.5| = 7.5. Absolute value measures distance from 0, and distances are never negative.
What is |0|?+
0. It is the only number whose absolute value is 0, because it is the only number at distance 0 from itself.
How do I find the distance between two numbers on a number line?+
Subtract them in either order and take the absolute value: the distance between -4 and 9 is |-4 - 9| = |-13| = 13.
Why do absolute value equations have two solutions?+
|ax + b| = c says the inside is c units from 0, which can happen at +c or -c. Each gives its own linear equation. When c = 0 the two cases coincide, and when c < 0 neither is possible.
Can an absolute value be negative?+
No. |x| is always 0 or positive, which is why |x + 1| = -4 has no solution.
Is |a - b| the same as |a| - |b|?+
No. |3 - (-4)| = 7 while |3| - |-4| = -1. The distance formula needs the absolute value of the difference.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026