QuickCalculators returns the absolute value of a number as its distance from zero on the number line, always nonnegative for real inputs, and can compute the absolute difference |a − b| as a mode on the same page. Enter one value for |x|, or two values for the gap between them.
Absolute value strips direction while keeping magnitude. That reading supports distance, error size, and absolute-value equations with two candidate solutions.
Calculate the absolute value of a number
The absolute value of a number is its distance from zero, written |x|. For a nonnegative x, |x| equals x. For a negative x, |x| equals −x, which is positive. QuickCalculators evaluates that piecewise definition and reports a nonnegative result for ordinary real inputs.
Example: |−8| = 8 and |8| = 8. Zero has absolute value zero. The notation never leaves a lone minus outside the bars when the bars already denote the nonnegative distance.
Understand absolute value as distance
Distance on a number line is never negative. Absolute value measures how far a point sits from zero regardless of left or right. QuickCalculators frames |x| as that distance so students do not confuse sign with size. If a point is 8 units left of zero, its coordinate is −8 and its distance is 8.
The same distance appears for +8 on the right. Magnitude language matches absolute value in this real-number setting.
Calculate the absolute difference
The absolute difference of a and b is |a − b|, the distance between the two numbers. Order does not matter because |a − b| equals |b − a|. QuickCalculators offers this mode so the older absolute-difference tool folds into one page.
Example: |10 − 3| = 7 and |3 − 10| = 7. Absolute difference answers "how far apart" without asking which value is larger first.
Solve absolute value equations
An equation |x| = k with k > 0 has solutions x = k and x = −k. If k = 0, the only solution is x = 0. If k is negative, no real solution exists because absolute value cannot be negative. QuickCalculators states the case so both roots are considered when they exist.
Example: |x| = 5 yields x = 5 or x = −5. Checking means substituting each candidate back into the absolute-value expression.
Find the absolute value of −8
The fixture evaluates |−8| on QuickCalculators.
- Identify that −8 is negative.
- Apply |x| = −x for negative x, so −(−8) = 8.
- Confirm that 8 is the distance from −8 to 0 on the number line.
The absolute difference between −8 and 0 is also 8, matching the same distance reading.
Avoid this common misconception
A frequent confusion is thinking absolute value "always drops the minus" in every expression, including cases like −|−8|. Absolute value makes the inside nonnegative, but a minus outside the bars still negates the result. Here |−8| = 8, while −|−8| = −8. QuickCalculators evaluates the bars first so outer signs stay visible.
Frequently asked questions
What is absolute value?
Absolute value is the distance of a number from zero on the number line. It is written |x| and is nonnegative for real x.
What is the absolute value of −8?
The absolute value of −8 is 8. Entering −8 on this page returns that fixture.
What is absolute difference?
Absolute difference is |a − b|, the distance between two numbers. It does not depend on which number is listed first.
How many solutions does |x| = 5 have?
The equation |x| = 5 has two real solutions, x = 5 and x = −5, because both lie 5 units from zero.
Can absolute value be negative?
The absolute value of a real number is never negative. An equation |x| = −3 has no real solution.
Does order matter for |a − b|?
Order does not matter for |a − b| because |a − b| equals |b − a|. Both express the same distance.
Summary
QuickCalculators reports |x| as distance from zero and |a − b| as absolute difference. Negative inputs map to positive magnitudes under the bars. Equations |x| = k yield two real roots when k is positive. The fixture |−8| equals 8. A minus outside the bars is not removed by absolute value itself.