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Algebra

Absolute Difference Calculator

Find the absolute difference between numbers. Free online Absolute Difference Calculator. Calculate absolute difference online — fast, accurate, mobile-friendly

|a − b|
7

Derivation

  1. ├── 01Givena = 8, b = 15
  2. ├── 02Formula|t-a|
  3. ├── 03Substitute|t-8|
  4. └── 04Compute |a − b|7
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§01What is

Understanding the Absolute Difference Calculator

The Absolute Difference Calculator computes |a − b| from 2 inputs: number a, number b. Find the absolute difference between numbers.

Algebra is the art of solving for the unknown. Rearranging a formula to isolate the variable you actually need is the single most common real-world math skill — and doing it with real numbers under time pressure is where errors happen. The Absolute Difference Calculator sits in that toolkit — it find the absolute difference between numbers. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

|t-a|

Where

a
Number a
b
Number b
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Number a = 8, Number b = 15.

  1. 01Start by noting the input — Number a: 8.
  2. 02Start by noting the input — Number b: 15.
  3. 03Substitute these values into the formula: |t-a|
  4. 04Compute |a − b|: the calculator returns 7.
  5. 05Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Absolute Difference Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Number a halved

a = 4 (from 8)

Keep every other input at its default and halve the number a. See how |a − b| responds.

  1. 01New Number a: 4
  2. 02Baseline |a − b|: 7
  3. 03New |a − b|: 11
  4. 04|a − b| increases by 57.1% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Number a doubled

a = 16 (from 8)

Keep every other input at its default and double the number a. See how |a − b| responds.

  1. 01New Number a: 16
  2. 02Baseline |a − b|: 7
  3. 03New |a − b|: 1
  4. 04|a − b| decreases by 85.7% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Number b halved

b = 7.5 (from 15)

Keep every other input at its default and halve the number b. See how |a − b| responds.

  1. 01New Number b: 7.5
  2. 02Baseline |a − b|: 7
  3. 03New |a − b|: 0.5
  4. 04|a − b| decreases by 92.9% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Number b doubled

b = 30 (from 15)

Keep every other input at its default and double the number b. See how |a − b| responds.

  1. 01New Number b: 30
  2. 02Baseline |a − b|: 7
  3. 03New |a − b|: 22
  4. 04|a − b| increases by 214.3% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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