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RMSE Calculator

The RMSE calculator determines the root mean square error (RMSE) of a prediction based on the observed and predicted values.

How to Use the RMSE Calculator?

  1. First, enter the observed and predicted values with a comma or space separator. Example: 12,15,32 or 12 15 32.
  2. Make sure both lists have the same entries.
  3. Press the 'Calculate' button.
  4. Finally, the tool returns the root mean square error (RMSE) for a prediction.

How to Calculate RMSE?

The root mean square error (RMSE) is calculated using the following formula:

RMSE =   √

Σ(Pi - Oi)2

n

Where,
Σ = Symbol define 'sum',
Pi = Predicted value for the ith data point,
Oi = Observed value for the ith data point,
n = Number of data points or sample size.

Here is an example:

Example:

Calculate the root mean square error (RMSE) for the actual values of [5, 12, 23] and the predicted values of [15, 32, -0.24].

Solution:

Here,
Pi = [15, 32, -0.24]
Oi = [5, 12, 23]

Apply the formula.

RMSE = √ Σ(Pi - Oi)2 / n

= √(15-5)2 + (32-12)2 + (-0.24-23)2 / 3

= √ (10)2 + (20)2 + (-23.24)2 / 3

= √ (100 + 400 + 540.0976) / 3

= √ 346.6992

RMSE = 18.62

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