Absolute Value Calculator
Enter any number below to instantly get its absolute value.
What Is Absolute Value?
Absolute value strips away a number's sign and leaves only its distance from zero. It's written with vertical bars: |x|.
Absolute value also matters when solving equations. |x| = 5 has two solutions, x = 5 and x = −5, because both numbers are 5 units from zero. But an absolute value can never equal a negative number — |x| = −5 has no real solution, since a distance can't be negative.
Worked example
Find |−7|.
−7 is 7 units from zero on the number line.
|−7| = 7
A second example, with a decimal: find |−3.5|.
−3.5 is 3.5 units from zero on the number line.
|−3.5| = 3.5
Common mistake
It's tempting to assume |a + b| = |a| + |b|, but that's not generally true. |−3 + 1| = |−2| = 2, while |−3| + |1| = 3 + 1 = 4. The correct relationship is |a + b| ≤ |a| + |b|, known as the triangle inequality.
Keep going
- Absolute value and square root are related by definition -- √(x²) always equals |x|; the square root calculator picks up right where this one leaves off. Square Root Calculator
Frequently Asked Questions
What does absolute value mean?
Absolute value is a number's distance from zero on the number line, always expressed as a non-negative number. |5| = 5 and |−5| = 5, since both are 5 units from zero.
Can absolute value be negative?
No. Absolute value measures a distance, and distances are never negative. The smallest possible absolute value is 0, for the number 0 itself.
How do you calculate absolute value?
If the number is positive or zero, its absolute value is itself. If it's negative, its absolute value is the number with the negative sign removed.
What are the solutions to |x| = 5?
Two: x = 5 and x = −5, since both numbers sit 5 units from zero. In general, |x| = a for a positive number a has two solutions, a and −a.
Can an absolute value equal a negative number?
No. An equation like |x| = −5 has no real solution, because absolute value output is never negative — there's no number whose distance from zero is negative.
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