CV(RMSE) and NMBE calculator

Paste measured and predicted energy to get CV(RMSE), NMBE and RMSE, and compare them with commonly cited calibration limits for monthly or hourly data.

Paste your data: measured (Y) and predicted (Ŷ)One row per period. Two columns separated by a tab, comma, semicolon or space: the metered value first, then the model or simulation value.

Number of model parameters (p)

Data interval

Data points (n): —
Mean measured (Ȳ): —
RMSE: —
CV(RMSE): —
NMBE: —

Formula

\mathrm{NMBE} = 100 \times \frac{\sum (Y_i - \hat{Y}_i)}{(n - p)\,\bar{Y}}

\mathrm{CV(RMSE)} = \frac{100}{\bar{Y}} \sqrt{\frac{\sum (Y_i - \hat{Y}_i)^{2}}{n - p}}

Y is the measured value, Ŷ the predicted value, Ȳ the mean of the measured values, n the number of data points and p the number of model parameters.

How it works

NMBE shows overall bias: a positive value means the model predicts less than was measured. CV(RMSE) shows how far individual periods miss. A model can have a small NMBE because errors cancel and still have a large CV(RMSE), so check both.

For calibrated simulation models, ASHRAE Guideline 14 is commonly cited with limits of NMBE within ±5% and CV(RMSE) up to 15% for monthly data, and ±10% and 30% for hourly data. The check above uses these values. Confirm the edition and the limits that your project or program requires.

Signs differ between sources: some define the error as predicted minus measured. Only the sign of NMBE changes; CV(RMSE) is the same.

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Results are estimates for study and screening. Check the inputs, units and assumptions before you use them for design, billing or contract decisions.