Calculators
Mean Squared Error Calculator
Calculate MSE, RMSE, and mean absolute error from paired actual and predicted values privately in your browser.
Measure prediction errors from paired observations.
Mean squared error (MSE) = Σ(predicted − actual)² / n. Root mean squared error (RMSE) = √MSE. Mean absolute error (MAE) = Σ|predicted − actual| / n. For actual values 3, 5, 7 and predictions 2, 5, 9, MSE is 5/3, RMSE is approximately 1.29099444874, and MAE is 1. MSE uses squared units; RMSE and MAE retain the original measurement units. All three are zero for perfect predictions, and larger errors contribute more strongly to MSE. This tool evaluates paired predictions and divides by n, without a fitted-model degrees-of-freedom correction. Use the same observations and units when comparing models; a lower error on training data alone does not establish better generalization. Enter one actual and predicted pair per line, up to 10000 pairs, using commas, semicolons, or spaces within each pair. Signed numbers, zero, and scientific notation are supported. Nonzero magnitudes must be between 1e-100 and 1e100. Scaled differences and compensated sums reduce rounding error, but floating-point arithmetic can still lose very small relative contributions. Results show up to 12 significant digits. Everything runs in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How are MSE and RMSE calculated?
Average the squared differences between predictions and actual values to get MSE. Take its square root to get RMSE. For actual 3, 5, 7 and predicted 2, 5, 9, MSE is 5/3 and RMSE is about 1.29099444874.
How does MAE differ from MSE?
MAE averages absolute errors in the original units. MSE averages squared errors in squared units and gives greater influence to large errors. RMSE returns the MSE measure to the original units.
Does this apply a degrees-of-freedom correction?
No. These prediction metrics divide by the number of pairs n, including when predictions were produced by a fitted model. This is not an estimate of residual variance with an n minus parameters denominator.
Are my observations uploaded?
No. Calculations run entirely in your browser. Enter up to 10000 actual and predicted pairs, one per line, with consistent units.