RMSE (Root Mean Square Error) is the square root of the average of squared differences between observed and predicted values. It expresses prediction error in the same units as the original data, making it easy to interpret alongside your measurements.

What is the formula for RMSE?

RMSE = sqrt( (1/n) * sum( (observed_i - predicted_i)^2 ) ). First compute the squared error for each pair, average those squared errors (MSE), then take the square root.

How is RMSE different from MAE?

MAE (Mean Absolute Error) treats all errors equally. RMSE squares each error before averaging, so large errors are penalized more heavily. If large prediction mistakes are particularly costly, RMSE is more informative; if all errors should be weighted equally, use MAE.

What is a good RMSE value?

There is no universal threshold. RMSE must be interpreted relative to the scale of your data and domain. A common rule of thumb is to compare RMSE to the standard deviation of the observed values — an RMSE much smaller than the standard deviation indicates a model that adds predictive value.

Can RMSE be negative?

No. RMSE is always zero or positive because it is the square root of a sum of squared (non-negative) values. RMSE equals zero only when every prediction is exactly correct.

MSE (Mean Squared Error) is the average of squared errors — it is RMSE squared. MSE penalizes large errors even more heavily than RMSE, but its value is in squared units of the original data, which can make physical interpretation harder.

RMSE Calculator

Name: RMSE Calculator
Availability: InStock
Author: Nham Vu

Enter observed and predicted value pairs to instantly compute RMSE, MSE, and MAE with a per-row squared error breakdown.

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Paste two columns of numbers separated by commas, one pair per line. Example: 3.5, 3.2

Data Pairs

# Observed Predicted

Results

RMSE —

MSE —

MAE —

Enter at least 1 valid pair to compute metrics.

Per-Row Squared Error Breakdown

#	Observed	Predicted	Error	Sq. Error	% of MSE
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Summary