How to use this calculator
- Enter or choose actual (observed) values.
- Enter or choose predicted (forecast) values, same order.
- The mAE updates as you type. Use Copy result or Share to keep it.
Method
eᵢ = actualᵢ − predictedᵢ; MAE = Σ|eᵢ| ÷ n; bias = Σeᵢ ÷ n
- eᵢ
- error for pair i
- n
- number of pairs
Worked example
- Errors: 0.5, −0.5, 0, 1; absolute errors 0.5, 0.5, 0, 1.
- MAE = 2 ÷ 4 = 0.5.
- Bias = (0.5 − 0.5 + 0 + 1) ÷ 4 = 0.25: on average the predictions are a little low.
The predictions miss by 0.5 units on average and run 0.25 units low overall.
What the result means
MAE answers “how far off are we, typically?”. Pair it with the bias: a small bias with a large MAE means errors in both directions; a bias close to MAE means the model is consistently high or low and could be recalibrated.
Assumptions and limits
- Each predicted value is paired with the actual value in the same position.
- Errors are actual minus predicted, so a positive bias means under-prediction.
- MAE is scale-dependent, so it cannot compare series measured in different units; use MAPE or a scaled error for that.
Questions
Why is MAE never larger than RMSE?
Squaring before averaging gives large errors more weight, so RMSE ≥ MAE, with equality only when all errors are the same size.
Which forecast minimises MAE?
The median of the outcome distribution; the mean minimises RMSE.