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Calculate the absolute value |x| of any number. Get the distance from zero with step-by-step explanations and number line visualization.
Examples: -15, 10-25, |-7|, |5-12|
Enter a value to calculate absolute value
Type any number (positive or negative) or expression in the input field. You can enter simple numbers like -15, or expressions like 10-25.
Click the "Calculate" button or press Enter to see the absolute value. The calculator will show the result along with a number line visualization.
View the step-by-step solution to understand how the absolute value was calculated and see the distance interpretation.
|x| = x if x ≥ 0
|x| = -x if x < 0
The absolute value of a number is its distance from zero on the number line.
|a - b| = distance between a and b
Example: |5 - 12| = |-7| = 7 units
• |x| ≥ 0 (always non-negative)
• |-x| = |x|
• |xy| = |x| × |y|
• |x/y| = |x| / |y| (y ≠ 0)
• |-7| = 7
• |15| = 15
• |0| = 0
• |-3.5| = 3.5
Absolute value is the distance of a number from zero on the number line, regardless of direction. It's always non-negative. For example, both -5 and 5 have an absolute value of 5 because they're both 5 units away from zero.
If the number is positive or zero, the absolute value is the number itself. If the number is negative, the absolute value is the number without the negative sign. Mathematically: |x| = x if x ≥ 0, and |x| = -x if x < 0.
No, absolute value is always non-negative (≥ 0). The smallest possible absolute value is 0, which occurs when the input is 0. All other numbers have positive absolute values.
|a-b| represents the distance between two numbers a and b. For example, |5-12| = |-7| = 7, which means 5 and 12 are 7 units apart on the number line.
When |x| = 5, there are two solutions: x = 5 or x = -5, because both 5 and -5 are 5 units away from zero. In general, if |x| = a (where a > 0), then x = a or x = -a.
Absolute value is used in many applications: calculating distances regardless of direction, measuring error or deviation in statistics, determining temperature differences, computing magnitude in physics, and analyzing profit/loss in finance.
Absolute value is a fundamental concept in mathematics that represents the magnitude or size of a number without considering its sign. Denoted by vertical bars |x|, it measures the distance of a number from zero on the number line.
This concept is essential in many areas of mathematics and real-world applications. In geometry, it helps calculate distances. In physics, it measures magnitude. In statistics, it's used to measure deviations and errors.