Absolute Value Calculator
|-5|5.0000
Distance from Zero5.0000
The absolute value of a number is its distance from zero on the number line, always reported as a non-negative quantity regardless of the original sign. This calculator strips the sign from any real number you enter, so −7.5 and 7.5 both return 7.5. Because absolute value measures magnitude rather than direction, it shows up everywhere from error bounds to coordinate geometry.
Formula
|x| = x if x ≥ 0, and |x| = −x if x < 0
- x
- The input number, which may be positive, negative, or zero
- |x|
- The absolute value: the non-negative magnitude of x
How it works
- Type any real number into the input field — positive, negative, a decimal, or zero. The sign is the only thing that matters for the operation.
- The calculator applies the absolute-value operation, which keeps positive numbers and zero unchanged and flips negative numbers to their positive counterpart.
- Read the result as both the absolute value and the equivalent distance from zero, since the two are numerically identical.
Worked example
Find the absolute value of −7.5.
- The input −7.5 is negative, so the rule |x| = −x applies.
- Negate the value: −(−7.5) = 7.5.
The absolute value of −7.5 is 7.5, meaning it sits 7.5 units from zero.
Frequently asked questions
- What is the absolute value of zero?
- The absolute value of zero is zero. Zero is exactly on the origin of the number line, so its distance from zero is nothing.
- Can an absolute value ever be negative?
- No. Absolute value reports a magnitude or distance, which is never negative. Even if the number inside the bars is negative, the result is its positive counterpart.
- How is absolute value different from rounding or truncation?
- Rounding and truncation change the size of a number, while absolute value only removes the sign and keeps the magnitude exactly the same. |−7.5| stays 7.5, not 7 or 8.
- Why does absolute value appear in distance and error calculations?
- Distances and measurement errors are inherently non-directional, so the sign of a difference is irrelevant. Taking the absolute value of a difference guarantees a meaningful, non-negative magnitude.