Indicator library · Momentum
Rate of Change (ROC)
The simplest momentum measure there is: how much price has changed over a fixed lookback, as a percentage. Most of the momentum indicators on this site are this number with smoothing applied.
The calculation
ROC = ((close ÷ close n periods ago) − 1) × 100. A reading of 4 means price is four per cent higher than it was n bars back. Zero means unchanged over the window, regardless of the route taken to get there, a point worth holding on to, because a quiet drift and a violent round trip can produce identical readings.
Two properties follow immediately, and both matter more than any setting. The output is a percentage, so values from different instruments are comparable, which is why it is the input of choice for anything that ranks a universe. And it is unbounded, so it has no natural extremes: unlike RSI, there is no scale on which 70 means the same thing everywhere.
Reading it
The zero line is the only reading with a fixed meaning: above it, price is higher than n bars ago. Everything else is comparative. The extremes tell you when the move was fastest, which is typically the middle of a trend rather than its end, so a falling ROC in positive territory describes a trend that is still rising but decelerating, which is the most useful thing this indicator says and the easiest to over-read.
Divergence works as it does everywhere: price makes a higher high while the rate of change does not, meaning the second push covered less ground in the same time. Because ROC is unsmoothed, it produces far more apparent divergences than a smoothed oscillator does, and most of them are noise. This is precisely the problem PMO was built to solve, by smoothing the same input twice before plotting it.
What it is actually used for
Rarely on its own, and that is not a criticism. The rate of change is a component: it is the input the Price Momentum Oscillator smooths twice, the quantity Momentum expresses in points instead of per cent, and the basis of most relative-strength rankings, where a list of instruments is sorted by their percentage change over a common window. Being scale-free is what makes that sorting legitimate, the same exercise on MACD values would rank price levels rather than momentum.
Its second use is as a check on a moving-average system. An average can rise while the rate of change falls, which describes a trend that is still intact but slowing; the average alone cannot say that, because it is a summary of level rather than of speed. Reading the two together costs nothing and distinguishes a trend that is maturing from one that has simply paused.
Two forms, one measurement
The single most common confusion around this indicator is not about interpretation but about units. Three quantities travel under overlapping names, and a platform may plot any of them under the label ROC.
| Form | Formula | Reads as |
|---|---|---|
| Percentage ROC | ((close ÷ close[−n]) − 1) × 100 | Zero when unchanged. Comparable between instruments. |
| Ratio form | (close ÷ close[−n]) × 100 | One hundred when unchanged. Same shape, different centre line. |
| Difference (Momentum) | close − close[−n] | Zero when unchanged, in the instrument’s own currency. Not comparable. |
Take a stock that moves from 50.00 to 52.50 over the lookback. The percentage form reads 5.00, the ratio form reads 105.00, and the difference form reads 2.50. All three are correct and only one of them can be compared with the same calculation on another instrument. Before quoting any level from a chart you did not build, establish which of the three it is plotting; a "ROC of 105" and a "ROC of 5" can be the identical market condition.
Where the extremes fall
Read against the price panel, the rate of change peaks in the middle of a move rather than at its end, because that is where the n-bar change was largest. This is not a lag to be corrected. It is what a speed measurement does, and it carries one genuinely useful reading and one persistent trap.
The useful reading is deceleration. A positive but falling ROC describes an advance that is still an advance and is covering less ground per bar than it was. When that persists over several bars it is worth noting, particularly alongside a breadth or volume measure that is also thinning.
The trap is treating the peak as a top. In a strong trend the fastest stretch often arrives early and the trend then continues for months at a slower pace, producing a long, steady decline in the rate of change while price rises the whole way. Anyone who sold the first lower ROC peak in such a trend sold near the start of it. The measure describes the speed of the move and has nothing at all to say about how much further it runs.
Where it misleads
| Situation | What goes wrong |
|---|---|
| General thresholds | Unbounded and volatility-dependent. A level drawn from one instrument means nothing on another. |
| Short lookback | A one- or two-period rate of change is close to pure noise; every indicator built on it smooths it first. |
| Percentage confused with points | Two platforms plotting different forms of "ROC" disagree by orders of magnitude. |
| Route ignored | Only the two endpoints enter the calculation. A steady drift and a violent round trip can read identically. |
| Unadjusted prices | A split produces a single enormous reading that persists for the length of the lookback. |
Frequently asked questions
Percentage or points: which is right?
Both are in use and they are not interchangeable, which is a frequent source of confusion between platforms. The percentage form divides by the earlier close and is scale-free, so a value from one instrument can be compared with another. The difference form subtracts and leaves the result in the instrument’s own units, which makes it useless for comparison and is usually labelled Momentum rather than ROC. If two charts of "ROC" disagree by orders of magnitude, this is why.
What lookback should I use?
Whatever period the decision spans, and no shorter. A one-period rate of change is almost pure noise, which is exactly why the indicators built on it, such as the Price Momentum Oscillator, smooth it twice before anyone looks. Longer lookbacks produce a steadier line that describes a longer move; the number is a choice of horizon, not a quality setting.
Is there an overbought level?
No. ROC is unbounded in both directions and its typical range depends entirely on the instrument’s volatility: a value of 8 is unremarkable for a small-cap and extreme for a broad index. Any threshold has to be drawn from that instrument’s own history, and thresholds quoted in general are describing whatever happened to be on the author’s screen.
Why does the line cross zero after the turn in price rather than at it?
Because zero means "unchanged over the last n bars", not "unchanged today". After a price high, the current close has to fall below the close n bars ago before the reading turns negative, and how long that takes depends on how much ground was covered in the window. The crossing is therefore always late, by an amount that varies with the shape of the move, which is why the zero line is read as confirmation and never as a turning point.
Can it be annualised or made comparable across lookbacks?
It can be scaled, and the result should be treated carefully. Dividing a 20-day change by 20 gives an average daily rate, which is comparable across windows in the same way a speed is; compounding it out to a year is arithmetically fine and financially misleading, because it projects a fortnight of one instrument’s behaviour across twelve months. Comparing raw ROC values computed over different lookbacks, however, is simply an error, a 5 per cent move over six days and over sixty are not the same observation.
How does it differ from a moving average of returns?
ROC uses two endpoints and ignores everything between them; an average of daily returns uses every observation in the window. In a smooth trend they behave similarly. They separate when the path is rough: a window containing one enormous gap up and a steady drift down can show a positive ROC and a negative average return, and the average is the better description of what the period was like. The endpoint measure is more common because it is what a chart of price already shows.
Is ROC the same as momentum?
They are the same measurement expressed in different units. Momentum, as the term is usually implemented, subtracts the close n bars ago and leaves the answer in the instrument’s currency; ROC divides by it and leaves a percentage. The shapes of the two lines over a short window are nearly identical. The difference matters when comparing instruments, or when the price level changes substantially over the history being plotted.
What lookbacks are commonly used?
Ten, twelve and fourteen periods on daily charts, and 21 or 63 where the intent is a month or a quarter. In relative-strength ranking, windows of one, three, six and twelve months are the convention, often blended. None of these carry any special property; they are round numbers in the calendar and, as with most defaults, their real advantage is that other people use them too.