Absolute Difference Calculator
Calculate the absolute difference between two numbers. Find the distance between values, check tolerances, compare multiple pairs, or calculate Mean Absolute Deviation.
|a - b| = |b - a| (distance between a and b)Absolute Difference
|a - b|
8
Calculate Absolute Difference
First number
Second number
Number Line Visualization
Step-by-Step Solution
Step 1: Identify the values
a = 15, b = 23
Step 2: Calculate the difference (a - b)
15 - 23 = -8
Step 3: Take the absolute value
|-8| = 8 (remove negative sign)
Verify: Order does not matter
|b - a| = |23 - 15| = |8| = 8
|15 - 23| = |23 - 15| = 8
Expected or ideal value
Measured or observed value
Acceptable deviation
Absolute Difference: |98 - 100| = 2.00
Tolerance Range: 100 +/- 5 = [95.00, 105.00]
Within Tolerance
Margin remaining: 3.00
Absolute Deviation
2.00
Percent Deviation
2.00%
Examples of Absolute Difference
| a | b | a - b | |a - b| | Note |
|---|---|---|---|---|
| 10 | 7 | 3 | 3 | Positive difference |
| 7 | 10 | -3 | 3 | Negative becomes positive |
| -5 | 3 | -8 | 8 | Negative to positive |
| -8 | -3 | -5 | 5 | Both negative |
| 5 | 5 | 0 | 0 | Equal values = 0 |
| 0 | -7 | 7 | 7 | Zero involved |
Absolute Difference
|a - b|
8
?What is Absolute Difference?
The absolute difference between two numbers a and b is |a - b|, which represents the distance between them on a number line. It is always non-negative and symmetric (order does not matter). For example, |5 - 8| = |8 - 5| = 3. The absolute difference tells you how far apart two values are without considering direction.
Understanding Absolute Difference
Absolute difference (|a - b|) measures the unsigned distance between two numbers. Unlike regular subtraction, the result is always non-negative because the absolute value removes any negative sign. This property makes it ideal for measuring how different two values are, regardless of which is larger. It is fundamental in statistics (mean absolute deviation), quality control (tolerance checking), and any application requiring unsigned comparisons.
Key Facts About Absolute Difference
- Formula: |a - b| = |b - a| (symmetric)
- Always non-negative (zero or positive)
- Represents distance between two values
- Order of values does not matter
- |a - b| = 0 means a = b (identical values)
- Used in error calculation, tolerance checking, and statistics
- Mean Absolute Deviation uses absolute differences
- Common in quality control and measurement comparison
Quick Answer
The absolute difference between two numbers a and b is |a - b|, which represents the distance between them on a number line. It is always non-negative and symmetric (order does not matter). For example, |5 - 8| = |8 - 5| = 3. The absolute difference tells you how far apart two values are without considering direction.
Frequently Asked Questions
Absolute difference |a - b| is the unsigned distance between two numbers. It is always non-negative (zero or positive) and symmetric, meaning |a - b| = |b - a|. For example, |5 - 8| = |8 - 5| = 3.
Regular subtraction (a - b) preserves direction and can be negative. Absolute difference |a - b| removes the sign, so the result is always non-negative. For example: 5 - 8 = -3, but |5 - 8| = 3.
No, the order does not matter. Absolute difference is symmetric: |a - b| = |b - a|. Whether you calculate |5 - 8| or |8 - 5|, the result is 3. This makes it ideal for measuring "how different" two values are.
Mean Absolute Deviation is the average of absolute differences between each data point and the mean. It measures how spread out values are from the average. MAD = (1/n) x sum of |xi - mean| for all data points.
Absolute difference is used in: tolerance checking (is the error within limits?), quality control, calculating Mean Absolute Deviation (MAD), measuring prediction accuracy, comparing measurements, and any situation where you need to know "how far apart" two values are.
Last updated: 2025-01-15
Absolute Difference
|a - b|
8