Calculator Input
Use commas, spaces, new lines, or semicolons between numbers.
Example Data Table
This sample can be loaded directly into the calculator with the example button.
| Obs | Actual | Predicted | Weight | Residual | Absolute Error |
|---|---|---|---|---|---|
| 1 | 120.00 | 118.00 | 1.00 | 2.00 | 2.00 |
| 2 | 135.00 | 140.00 | 1.20 | -5.00 | 5.00 |
| 3 | 150.00 | 148.00 | 0.90 | 2.00 | 2.00 |
| 4 | 160.00 | 158.00 | 1.10 | 2.00 | 2.00 |
| 5 | 175.00 | 180.00 | 1.40 | -5.00 | 5.00 |
| 6 | 190.00 | 192.00 | 1.00 | -2.00 | 2.00 |
| 7 | 205.00 | 201.00 | 1.30 | 4.00 | 4.00 |
| 8 | 220.00 | 225.00 | 1.20 | -5.00 | 5.00 |
| 9 | 235.00 | 230.00 | 0.80 | 5.00 | 5.00 |
| 10 | 250.00 | 247.00 | 1.10 | 3.00 | 3.00 |
Formula Used
Residual: eᵢ = yᵢ - ŷᵢ
Absolute Error: |eᵢ|
Squared Error: eᵢ²
MAE: (1/n) Σ |eᵢ|
MSE: (1/n) Σ eᵢ²
RMSE: √MSE
Bias: (1/n) Σ eᵢ
MAPE: (100/n) Σ |eᵢ / yᵢ| for nonzero actual values.
sMAPE: (100/n) Σ |yᵢ - ŷᵢ| / ((|yᵢ| + |ŷᵢ|)/2)
WAPE: 100 × Σ |eᵢ| / Σ |yᵢ|
R²: 1 - SSE / TSS, where SSE = Σ eᵢ² and TSS = Σ (yᵢ - ȳ)².
Weighted metrics: replace the simple mean with Σ(wᵢ × metricᵢ) / Σwᵢ.
Lower MAE, RMSE, and WAPE usually indicate tighter predictions. Bias reveals directional drift, while R² summarizes fit relative to the actual series variance.
How to Use This Calculator
Paste the actual values into the first field and the predicted values into the second. Keep both series in the same order so each observation matches correctly.
Add optional weights when some observations deserve more influence, such as higher revenue accounts, larger contracts, or measurements with stronger confidence.
Choose the number of decimal places, click Calculate Metrics, and review the result section displayed above the form. The calculator shows metric cards, detailed tables, and Plotly graphs immediately.
Use the CSV button to export the observation table and summary metrics. Use the PDF button to save the visible results block as a shareable report.
Frequently Asked Questions
1) What is the difference between MAE and RMSE?
MAE averages absolute misses evenly. RMSE squares errors first, so large misses matter much more. Use RMSE when big outliers should carry stronger penalties.
2) Why can MAPE show “Not available”?
MAPE divides by actual values. When an actual value equals zero, that row cannot contribute safely. The calculator excludes those rows and reports how many remained valid.
3) When should I use sMAPE instead of MAPE?
sMAPE is often better when values vary greatly or predictions can sit near zero. It uses both actual and predicted magnitudes to reduce asymmetry.
4) What does a positive bias mean?
Bias uses actual minus predicted. A positive result means predictions tend to be lower than actual values overall. A negative result suggests overprediction.
5) Should I trust R² alone?
No. R² describes variance explained, not the whole error story. Pair it with MAE, RMSE, and bias to understand scale, stability, and directional drift.
6) What are weighted metrics for?
Weighted metrics give selected observations more influence. This helps when some rows represent higher business value, larger exposure, or more reliable measurements.
7) Why does RMSLE require special values?
RMSLE uses logarithms of one plus each value. Values must stay above minus one. It is useful when proportional misses matter more than absolute misses.
8) What does the residual graph show?
It shows signed errors by observation. Random scatter around zero usually looks healthier. Repeating patterns can suggest drift, seasonality, nonlinearity, or missing features.