Root Mean Square Error Calculator

RMSE Formula:

\[ RMSE = \sqrt{ \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 } \]

Root Mean Square Error (RMSE):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Root Mean Square Error?

Root Mean Square Error (RMSE) is a standard way to measure the error of a model in predicting quantitative data. It represents the square root of the average of squared differences between predicted and observed values.

2. How Does the Calculator Work?

The calculator uses the RMSE formula:

\[ RMSE = \sqrt{ \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 } \]

Where:

\( y_i \) — Actual observed values
\( \hat{y}_i \) — Predicted values
\( n \) — Number of observations

Explanation: The RMSE first calculates the squared differences between actual and predicted values, averages them, and then takes the square root to return to the original units.

3. Importance of RMSE

Details: RMSE is widely used in statistics and machine learning to assess model accuracy. Lower RMSE values indicate better fit, with 0 representing perfect prediction.

4. Using the Calculator

Tips: Enter comma-separated lists of actual and predicted values. Both lists must have the same number of values. Example: "1,2,3" and "1.1,1.9,3.05".

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between RMSE and MSE?
A: MSE (Mean Squared Error) is the average of squared errors, while RMSE is the square root of MSE, making it in the same units as the original data.

Q2: What is a good RMSE value?
A: There's no universal threshold - it depends on your data scale. Compare RMSE to the range of your actual values.

Q3: Can RMSE be negative?
A: No, since it's based on squared errors, RMSE is always ≥0.

Q4: How does RMSE compare to MAE?
A: RMSE gives more weight to larger errors due to squaring, while MAE (Mean Absolute Error) treats all errors equally.

Q5: When shouldn't I use RMSE?
A: When your data has many outliers (consider MAE instead) or when errors aren't normally distributed.