Mean Absolute Deviation (MAD) Calculator
Measure the average magnitude of your forecast error, in the same units as demand.
Mean Absolute Deviation (MAD) Template — free, works offline, formulas included.
What Is MAD? (And Why Should You Care?)
Mean Absolute Deviation (MAD) answers a simple question: on average, how far off is your forecast? It's the most direct, least mathematically dressed-up way to measure forecast accuracy — take every forecast error, ignore whether it was too high or too low, and average the size of the misses.
Forecasts are never perfect, and that's fine — the useful question isn't "was this forecast wrong," it's "how wrong, typically, and is that getting better or worse over time." MAD gives you a single number to track that, in the same units as the demand itself, which makes it intuitive: "our forecast is usually off by about 3.5 units" is immediately meaningful in a way a raw error percentage sometimes isn't.
How Does It Work?
For each period, subtract the forecast from the actual demand and take the absolute value — so an over-forecast and an under-forecast of the same size count equally, rather than canceling each other out. Average those absolute errors across all periods and that's MAD. A lower MAD means tighter, more accurate forecasts; there's no upper bound, since it scales with however large your errors happen to be.
Real-World Example
Actual demand: 100, 120, 110, 130
Forecast: 105, 115, 108, 128
MAD = (5+5+2+2) / 4 = 3.5
This forecast method is off by about 3.5 units per period, on average.
Compare a much rougher forecast on the same actual demand: 80, 140, 90, 150.
MAD = (20+20+20+20) / 4 = 20
A MAD of 20 versus 3.5 makes the comparison obvious — the second forecasting method is missing by roughly six times as much, on average, even though both methods happened to average out to zero net bias across the period.
Key Assumptions & Limitations: When Does This Work?
MAD treats every unit of error the same regardless of how big the underlying demand was, which makes it a poor tool for comparing accuracy across products with very different volumes — a MAD of 5 is excellent for a product that sells 1,000 units a week and alarming for one that sells 10. For that kind of cross-product comparison, MAPE (which expresses error as a percentage) usually makes more sense.
5 Ways People Get MAD Wrong
Comparing MAD across products of very different sizes.A MAD of 5 doesn't mean the same thing for a high-volume SKU and a low-volume one. Use MAPE instead when comparing across products.
Treating a single MAD reading as the full picture.MAD alone doesn't tell you whether errors are trending up, down, or holding steady — track it over time, not as a one-off snapshot.
Ignoring what MAD doesn't show — bias. Two forecasts can have the same MAD while one is consistently over-forecasting and the other under-forecasting. MAD hides that distinction since it only measures magnitude, not direction.
Never using it to actually compare methods. MAD is most useful side by side — moving average against exponential smoothing against whatever else you're considering. Calculating it for one method in isolation tells you less than comparing it across a few.
Chasing a lower MAD at any cost. An overly complex forecasting method that shaves a small amount off MAD may not be worth the added effort to maintain — weigh the improvement against the complexity.
Industry Benchmarks & Context
There's no universal "good" MAD — it depends entirely on the scale of demand for the product being forecast. The meaningful benchmark is relative: track MAD as a percentage of average demand over time (which is effectively what MAPE does), or compare MAD across competing forecasting methods on the same product to see which one actually performs better.
Next Steps & Related Tools
Once you know how accurate your forecast is:
- Check MAPE too — especially if comparing accuracy across products with different demand volumes.
- Try adjusting your forecasting method — different alpha values or window sizes, then recheck MAD to see if it actually improved.
Learn More
Books:
- Forecasting: Principles and Practice by Rob J Hyndman and George Athanasopoulos (free online)
Standards & curricula:
- APICS (ASCM) CSCP certification curriculum (demand planning module)
General references for further study, not endorsements — verify course availability and content directly with the provider.
Interview Preparation
Questions like these come up in supply chain and operations interviews — here's how to answer them.
What does MAD measure, and what kind of tool is it — a forecasting method or something else?
MAD is a forecast-accuracy metric, not a forecasting method — it doesn't produce a forecast, it measures how far off an existing forecast (from moving average, exponential smoothing, or any other method) has been running, in the same units as demand.
How would you explain MAD to a beginner?
For every period, find how far the forecast missed the actual number, ignore whether it was too high or too low, and average those misses. If MAD is 3.5, your forecast is typically off by about 3.5 units, whichever direction.
Why take the absolute value of each error instead of just averaging the errors directly?
Without the absolute value, an over-forecast and an under-forecast of the same size would cancel out, making a genuinely inaccurate forecast look perfect on average. Taking the absolute value measures the magnitude of the miss regardless of direction.
When would MAD not be the right metric to reach for?
When comparing forecast accuracy across products with very different demand volumes — a MAD of 5 is excellent for a product selling 1,000 units a week and alarming for one selling 10. MAPE, which expresses error as a percentage, is the better choice there.
What does MAD fail to tell you that you might still need to know?
It hides bias — two forecasts can have identical MAD while one consistently over-forecasts and the other consistently under-forecasts, since MAD only measures the size of errors, not their direction.
Frequently Asked Questions
- What's a 'good' MAD value?
- There's no universal number — it depends entirely on the scale of demand for that product. Judge it relative to average demand, or compare MAD across different forecasting methods on the same product to see which performs better.
- Is MAD the same as MAPE?
- No. MAD reports error in raw units (e.g., '3.5 units off'), while MAPE reports the same idea as a percentage. MAPE is generally better for comparing accuracy across products with different volumes.
- Can I use MAD to compare two different forecasting methods?
- Yes — that's one of its most useful applications. Run the same actual demand through moving average, weighted moving average, and exponential smoothing, and the method with the lowest MAD is performing best for that product.
- Why do my forecast and actual arrays need to be the same length?
- MAD pairs each actual value with its corresponding forecast for that same period — a mismatched length means the calculation would compare demand from one period against a forecast meant for a different one.