Absolute Value Kalkulator

Cara menggunakan kalkulator ini

1. Masukkan Number (x)
2. Klik butang Kira
3. Baca keputusan yang dipaparkan di bawah kalkulator

What Is Absolute Value?

The absolute value of a number is its distance from zero on the number line, regardless of direction. Written as |x|, the absolute value is always non-negative. For any real number x: if x ≥ 0, then |x| = x. If x < 0, then |x| = -x (the negative of x, which makes it positive).

Examples: |7| = 7, |-7| = 7, |0| = 0, |-3.14| = 3.14. The absolute value represents magnitude without regard to sign. Think of it as the physical distance between the number and the origin on a number line — distance is always positive.

In notation: |x - y| represents the distance between two points x and y on the number line. This interpretation extends to complex numbers as the modulus: |a + bi| = √(a² + b²), representing the distance from the origin in the complex plane.

Properties and Rules of Absolute Value

Absolute value follows several important algebraic properties. Non-negativity: |x| ≥ 0 for all real x. Identity: |x| = 0 if and only if x = 0. Multiplicativity: |x × y| = |x| × |y|. Triangle inequality: |x + y| ≤ |x| + |y| — one of the most important inequalities in mathematics.

Solving absolute value equations requires considering both cases. |x| = 5 means x = 5 or x = -5. |2x - 3| = 7 means 2x - 3 = 7 (so x = 5) or 2x - 3 = -7 (so x = -2). Always check both solutions in the original equation.

Absolute value inequalities: |x| < a means -a < x < a. |x| > a means x < -a or x > a. These arise frequently in error analysis, tolerance specifications in engineering, and defining neighborhoods in calculus.

Absolute Value in Real-World Applications

Absolute value appears throughout science, engineering, and daily life wherever you care about magnitude rather than direction. In physics, speed is the absolute value of velocity — a car moving at -60 mph (backwards at 60 mph) has a speed of 60 mph. In finance, when analyzing percentage changes, you may want the absolute deviation from a benchmark.

In statistics, mean absolute deviation (MAD) uses absolute value to measure data spread: MAD = (1/n) × Σ|xi - mean|. Unlike variance, MAD is in the same units as the data and less sensitive to outliers. It's used in robust statistics and quality control.

In programming, abs() or fabs() functions implement absolute value. It's used in comparison functions, distance calculations, and signal processing. The L1 norm (sum of absolute values of vector components) is used in machine learning regularization (lasso regression) to produce sparse models.

Frequently Asked Questions