Absolute Value Calculator
Find the absolute value and distance on a number line.
Distance is measured from this point
Results update as you type.
How it works
Absolute value answers a simple question: how far is a number from zero, ignoring whether it lies to the left or the right? Written with vertical bars as the modulus of x, it strips the sign from a number so that both plus five and minus five have an absolute value of five. This absolute value calculator returns that result for any number you enter, and it also computes the distance from an optional reference point, which is the absolute value of the difference between the two numbers. Distance is where the concept becomes genuinely useful: the gap between minus three and four is seven, found by subtracting and dropping the sign. The idea underpins error and tolerance calculations, where you care about the size of a deviation rather than its direction; it appears in the definitions of distance and magnitude throughout geometry and physics; and it is essential for solving absolute-value equations and inequalities in algebra. Because the calculator accepts decimals and negatives freely, you can use it for measured data, temperatures below zero, financial gains and losses, or any situation where the magnitude of a quantity matters more than its sign.
|x| = x if x ≥ 0, else −x; distance = |x − reference|
The absolute value of a number is its distance from zero on the number line, so it is the number itself when it is already positive or zero, and the negated number when it is negative, which always yields a non-negative result. Extending the idea, the distance between any two numbers is the absolute value of their difference, because subtraction measures the gap and the absolute value discards the direction, leaving only how far apart they are.
Source:Standard definition of absolute value
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Worked example
How to use this calculator
- 1
Enter your values
Enter number.
- 2
Adjust the options
Adjust reference (optional) if they apply — sensible defaults are already set.
- 3
Read your result
Absolute value updates instantly as you type — no button to press.
Frequently asked questions
What is the absolute value of a number?
The absolute value of a number is its distance from zero on the number line, always reported as a non-negative value. It is the number unchanged when the number is positive or zero, and the number with its sign flipped when it is negative. So the absolute value of minus nine is nine, and the absolute value of six is six. It measures size while ignoring direction.
Can absolute value ever be negative?
No. Absolute value is defined as a distance, and a distance can never be negative. The smallest possible absolute value is zero, which happens only when the number itself is zero. Even if you enter a large negative number, the calculator returns the corresponding positive magnitude, because the sign is exactly what absolute value is designed to discard.
How do I find the distance between two numbers?
Subtract one number from the other and take the absolute value of the result, which removes any negative sign so the answer reflects only how far apart they are. Enter your number and a reference value, and the calculator reports this distance automatically. For example, the distance between minus three and four is the absolute value of minus seven, which is seven.
Where is absolute value used in real life?
Absolute value appears whenever the size of a difference matters more than its direction. Quality control uses it to measure how far a part deviates from its target size; navigation and physics use it for distances and magnitudes; finance uses it to size gains or losses; and statistics uses it in measures like mean absolute deviation. Anytime you say how far off something is, you are using absolute value.
Is absolute value the same as the modulus?
For real numbers, yes: modulus is another name for absolute value, and both are written with the same vertical-bar notation. The term modulus is more common in some countries and in higher mathematics, where it extends to complex numbers, in which case it means the distance from the origin in the complex plane. For ordinary numbers the two words mean exactly the same thing.