Absolute Value Calculator
The absolute value is a number's distance from zero, so it is never negative. Type a number, or two numbers to find the distance between them.
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Absolute value
7.5
Negative number- Number
- −7.5
- Opposite (−x)
- 7.5
Show working
- −7.5 < 0 ⇒ |−7.5| = −(−7.5) = 7.5
How to use
- Choose |x| or |a − b|.
- Type the number (or the two numbers).
- Read the absolute value and the steps.
Good to know
|x| = x when x is 0 or positive, and −x when x is negative. So |−7.5| = 7.5 and |7.5| = 7.5. On the number line it is how far the number is from 0, whichever side it is on.
|a − b| is the distance between a and b on the number line, and it doesn't matter which you subtract from which: |3 − 10| = |10 − 3| = 7. The midpoint (a + b) ÷ 2 is shown too. Distances, errors and tolerances (for example a reading within ±0.5) are all absolute values.
Useful rules: |a × b| = |a| × |b|, but |a + b| ≤ |a| + |b| (the triangle inequality). An equation like |x| = 5 has two answers, x = 5 and x = −5.
Questions
What is the absolute value of −12?
12.
Can an absolute value be negative?
No. It is a distance, so it is 0 or positive.
What is |−3| + |5|?
3 + 5 = 8.
How do I solve |x| = 4?
x = 4 or x = −4, because both are 4 units from zero.
How do I find the distance between −2 and 6?
|−2 − 6| = |−8| = 8. Choose |a − b| and type the two numbers.