How do MAE and RMSE differ?

MAE (Mean Absolute Error) and RMSE (Root Mean Squared Error) both measure prediction errors in regression, but they treat large mistakes differently.

How they calculate error

• MAE: averages the absolute differences between actual and predicted values.
• RMSE: squares the errors, averages them, then takes the square root.

MAE  = (1 / n) × Σ|yi - ŷi|
RMSE = √[(1 / n) × Σ(yi - ŷi)²]

Both are expressed in the same units as the target, and lower is better.

Example: one large prediction error

Suppose three predictions have absolute errors of 1, 1, and 7.

MAE  = (1 + 1 + 7) / 3 = 3
RMSE = √[(1² + 1² + 7²) / 3] ≈ 4.12

RMSE is higher because squaring gives the error of 7 more influence.

Which metric should you use?

• Choose MAE when you want an easily understood average absolute error and prefer each unit of error to contribute proportionally.
• Choose RMSE when large prediction mistakes are particularly costly and should weigh more heavily in model evaluation.

What do their values tell you?

For the same set of predictions, RMSE is always at least as large as MAE. A wide gap between the two can indicate that some errors are much larger than others.

Neither metric alone tells you whether the errors are acceptable in your application; compare them against a baseline and the real-world cost of mistakes.

In short, MAE measures average absolute error, while RMSE gives large errors more influence. Use MAE for straightforward error interpretation and RMSE when large mistakes matter more.