Absolute Value Calculator - Distance & Magnitude Functions
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How Absolute Value Works
Input Number
Enter any real number (x)
Check Sign
Positive, negative, or zero
Apply Rule
Remove negative sign if present
Mathematical Rules:
- ā¢ If x ā„ 0, then |x| = x
- ā¢ If x < 0, then |x| = -x
- ā¢ |x| ā„ 0 for all real numbers x
- ā¢ |x| represents distance from zero on number line
Common Examples
Distance Formula
d = |xā - xā|
Between two points
Error Analysis
|measured - actual|
Measurement accuracy
Physics Magnitude
|velocity|
Speed calculation
Finance
|profit - loss|
Net change
What is Absolute Value?
Definition
The absolute value of a number is its distance from zero on the number line, always resulting in a non-negative value.
Purpose
Used in physics for magnitude calculations, in statistics for error analysis, and in mathematics for distance measurements.
Applications
Speed calculations, measurement errors, financial analysis, and geometric distance problems.
Calculation Table - Real World Applications
| Input Value | Calculation | Result | Real World Example |
|---|---|---|---|
| -15Ā°C | |-15| | 15Ā°C | Temperature magnitude |
| -$500 | |-500| | $500 | Debt amount |
| 25 m/s | |25| | 25 m/s | Speed (velocity magnitude) |
| -0.05 | |-0.05| | 0.05 | Measurement error |
| 0 | |0| | 0 | Perfect accuracy |
| -9.8 m/sĀ² | |-9.8| | 9.8 m/sĀ² | Gravity magnitude |
| -3.14159 | |-Ļ| | 3.14159 | Mathematical constant |
| 100.5 | |100.5| | 100.5 | Positive measurement |
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 resulting in a non-negative value. It's denoted as |x| and represents magnitude without direction.
How do you calculate absolute value?
For positive numbers and zero, the absolute value is the number itself. For negative numbers, remove the negative sign. For example: |5| = 5, |-3| = 3, |0| = 0.
Can absolute value be negative?
No, absolute value is always non-negative (ā„ 0). By definition, it represents distance, which cannot be negative. The smallest possible absolute value is 0.
What are real-world applications of absolute value?
Common uses include: calculating speed from velocity, measuring temperature differences, determining measurement errors, financial loss/gain analysis, and distance calculations in physics and engineering.
What's the difference between absolute value and regular value?
Regular value includes sign (positive/negative), while absolute value only shows magnitude. For example: -5 has a regular value of -5 but an absolute value of 5.
How is absolute value used in statistics?
In statistics, absolute value is used for calculating mean absolute deviation, measuring data spread, determining outliers, and computing error margins without considering direction.
Does this calculator work with decimals and fractions?
Yes, our calculator handles integers, decimals, and negative numbers with high precision. Enter decimal numbers directly (e.g., -3.14, 0.5, -0.001).
What's the mathematical notation for absolute value?
Absolute value is written as |x| where x is any real number. The vertical bars (| |) are the standard mathematical notation for absolute value or magnitude.