Seasonal indices show how much each month or quarter typically runs above or below average. Calculate them from history with the classical ratio-to-moving-average method and remove seasonality to see the underlying trend.
How it works
Calculate seasonal indices with the classical ratio-to-moving-average method and remove seasonality from a monthly or quarterly series to reveal the underlying trend.
Centered moving average (2×m): CMA(t) = [½Y(t−m/2) + Y(t−m/2+1) + … + Y(t+m/2−1) + ½Y(t+m/2)] ÷ m
Ratio(t) = Y(t) ÷ CMA(t)
Raw index(season) = average of ratios for that season
Index = Raw index ÷ average of raw indices; Deseasonalized = Y ÷ IndexCommon uses
- Building seasonality into budgets and forecasts
- Comparing months fairly in performance reports
- Staffing and capacity planning for peak periods
Worked example
The calculator above opens with this example. Change any input to see the results update instantly, or select Reset to return to these figures.
| Time series (oldest first) | 412 398 436 445 468 452 441 459 487 503 498 541 455 437 481 492 515 501 487 506 535 556 549 597 489 468 515 528 553 538 522 544 571 594 588 638 |
| Frequency | Monthly (12 seasons) |
| First period (month) | 2024-01 |
| Peak season | Dec |
| Low season | Feb |
| Seasonal range | 24.3% |
| Complete cycles | 3 |
Indices average exactly 1.00. Multiply a deseasonalized forecast by the index to restore seasonality.
Interpreting the results
- An index of 1.08 means the season typically runs 8% above the average period.
- Use three or more years when possible; with only two, each index rests on one or two ratios.
- Recalculate indices annually; shifts in holidays, promotions or service mix change seasonal patterns.
Frequently asked questions
What does a seasonal index of 1.10 mean?
An index of 1.10 means that period typically runs 10% above the average period. An index of 0.90 means it typically runs 10% below. The indices average exactly 1.00 across the year.
How do I use seasonal indices in a forecast?
Forecast the deseasonalized trend, then multiply each period’s forecast by its seasonal index to restore the seasonal pattern. The Driver-Based Revenue Model on this site accepts the indices directly.
How much history do I need?
At least two full years are required, and three or more give more reliable indices because each month’s index averages several observations. Exclude unusual years, such as those affected by one-time events, if possible.
Related calculators
- Moving Average & Exponential Smoothing Forecast: SMA, WMA, simple, Holt and Holt-Winters forecasts with fit statistics.
- Driver-Based Revenue Model: Monthly revenue forecast from volume, conversion, price and seasonality drivers.
- Rolling Forecast Builder: 12- to 24-month rolling forecast from monthly actuals using four methods.
- Average Daily Census & Occupancy Calculator: Average daily census, occupancy rate, ALOS and bed turnover.
- Fiscal Calendar & Business Days Calculator: Business days between dates, fiscal year and quarter, and working days by fiscal period.