Moving Average Calculator
Smooth a bumpy series of numbers by averaging each value with the ones before it, and see where the trend is heading.
Results
What this tool does
Daily figures jump about for reasons that have nothing to do with the trend — a bank holiday, one big order, a wet Tuesday. A moving average replaces each reading with the average of the last few, which keeps the shape of the series and throws away most of the noise. Paste your numbers, choose how many go into each average, and the smoothed series comes back alongside the plain average of everything, so you can see whether the recent run is above or below the long-run level.
Formula
each point is the average of the N values ending at it ; the weighted version gives weights 1, 2, 3… to the most recent
Variables
| Symbol | Meaning | Unit |
|---|---|---|
numbers | Your numbers, one per line or separated by commas | — |
window | How many to average at a time | — |
OUT | The smoothed series | — |
LA | Most recent average | — |
FA | First average | — |
WT | Weighted towards the recent | — |
PM | Plain average of everything | — |
AB | Latest against the plain average | — |
TR | Movement from first to last | — |
PO | Points in the result | — |
PD | Points the window swallows | — |
Worked example
- Your numbers, one per line or separated by commas1240, 1180, 1390, 1310, 1450, 1520, 1470, 1610, 1580, 1690
- How many to average at a time3
- The smoothed series1270 1293.333333 1383.333333 1426.666667 1480 1533.333333 1553.333333 1626.666667
- Most recent average1626.67
- First average1270.00
- Weighted towards the recent1640.00
- Plain average of everything1444.00
- Latest against the plain average182.67
- Movement from first to last356.67
- Points in the result8
- Points the window swallows2
Frequently asked questions
Why are the first few values missing?
Because a three-point average cannot exist until there are three points. With a window of three the first two readings have nothing behind them, so the smoothed series starts at the third. That is why a long window steadies the line but also makes it start later and react more slowly — the choice of window is the whole art of it.
What is the weighted figure for?
A plain moving average treats a reading from a week ago exactly like this morning's, which is often wrong. The weighted figure gives the most recent value the largest share and the oldest in the window the smallest, in the order 1, 2, 3 and so on. When it sits well above the plain average, the recent readings are pulling upward and the series is turning.