Calculate RMSE and MSE: Root Mean Squared Error forecast accuracy formula

Penalize large forecast misses in original unit scale

Averaging raw errors (Actual - Forecast) lets +10 and -10 cancel out to zero. Mean Squared Error (MSE) squares every error before averaging so over-forecasts and under-forecasts both add positive penalty—and large misses carry quadratic weight.

Taking SQRT(MSE) produces Root Mean Squared Error (RMSE), restoring the metric back into original units (dollars, units, or degrees) for intuitive model comparison.

Single-cell RMSE and MSE formulas

Squared errors sum to 16 + 36 + 9 + 25 = 86; MSE = 86 / 4 = 21.5; RMSE = SQRT(21.5) = 4.64.

=ROUND(SQRT(SUMPRODUCT((A2:A5 - B2:B5)^2) / ROWS(A2:A5)), 2)

Mean Squared Error (MSE) without square root

Omit SQRT when comparing loss functions directly against statistical regression outputs.

=SUMPRODUCT((A2:A5 - B2:B5)^2) / ROWS(A2:A5)

Inputs and interpretation

Both ranges must contain complete numeric pairs in the same row order, with no missing values or errors. The denominator is the number of prediction pairs, not a regression residual degrees-of-freedom correction. Compare forecasts on the same evaluation sample, horizon and units; use held-out observations when assessing predictive performance and keep unrounded values for downstream calculations.

Further reading

• Microsoft Support — SUMPRODUCT function