Absolute Deviation Calculator
Last updated: June 2026 · Free · No sign-up required
Enter values above and click Calculate to see your result instantly.
Quick reference
| Term | Definition |
|---|---|
| Deviation | x − center (mean or median) |
| Absolute deviation | |x − center| (always ≥ 0) |
| MAD (mean) | Average of |x − mean| |
| MAD (median) | Average of |x − median| |
| Use | Robust, intuitive measure of spread |
functions Shows the working, not just the answer
For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.
calculate Accurate to the spec
Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.
school Free for classroom use
Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.
tips_and_updates Pair with the spoke articles
Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.
Interpretation guide
| MAD size | What it means |
|---|---|
| MAD near 0 | Values cluster tightly at the center |
| Larger MAD | Values are more spread out |
| MAD vs SD | MAD is smaller and resists outliers |
| Median-based MAD | Most robust to extreme values |
Formula & methodology
Formula: MAD = (1/n) × Σ |xᵢ − x̄|
How the result is calculated
Mean absolute deviation averages how far each value sits from the center, using absolute values so positive and negative gaps do not cancel. Unlike standard deviation it does not square the gaps, making it more intuitive and less sensitive to outliers.
- Find the center — the mean (or median) of your data set.
- Subtract the center from each value and take the absolute value of each difference.
- Add all absolute deviations and divide by the count n.
Example
For 2, 4, 6, 8 the mean is 5. Absolute deviations: 3, 1, 1, 3 → sum 8. MAD = 8 / 4 = 2.0.
Frequently asked questions
Explore the full statistics toolkit
Every CalcaTools statistics calculator — descriptive measures, probability distributions, hypothesis tests, confidence intervals, and Six Sigma process metrics — with step-by-step workings on each result.