Calculators · Momentum
Rate of Change, Computed Bar by Bar
The simplest momentum measure there is: today against a bar a fixed distance back. Because both ends of that comparison move, half the surprises in the series come from the bar leaving the window rather than the one arriving.
Rate of change calculator
Both forms are printed for every bar: the percentage change and the same move in points. Watch the two columns diverge as the price level changes, that gap is the whole argument for using the percentage form when comparing anything with anything.
The formula, and both of its forms
Take the current close, subtract the close n bars earlier, and divide by that earlier close:
ROC = ((close − close[n bars ago]) ÷ close[n bars ago]) × 100
Drop the division and you have what is usually labelled momentum: close − close[n bars ago], in points. The two series have the same shape and cross zero at the same moments, and they differ in one respect that decides which one to use: the percentage form is scale-free and the point form is not.
That distinction is not academic. A one-point move on a twelve-dollar instrument is an eight per cent event; the same point on a four-hundred-dollar one is a rounding error. Any comparison across instruments, or across enough years that the price level has changed materially, has to be in percentage terms or it is measuring the price level rather than the momentum.
The lookback bar is half the calculation
Every reading has two ends, and only one of them is today. When the bar dropping out of the lookback window is unlike the bar arriving, the reading moves for a reason that has nothing to do with the current session.
The figure above shows it plainly at the right-hand edge, and it is the same structural property as a simple moving average turning down on an up day. It matters more here because rate of change is frequently read as a live statement about today: an unbounded momentum series falling while price rises looks exactly like the classic bearish divergence, and a good share of the time it is instead an arithmetic consequence of what happened n bars ago.
The check takes seconds. Look at the close entering the window and the close leaving it. If the leaver is the extreme one, the reading is telling you about history rather than about a change in behaviour.
Where the two forms disagree
| Situation | Percentage form | Point form |
|---|---|---|
| Comparing two instruments at different price levels | Comparable, this is the reason the form exists | Meaningless: the larger number is the more expensive instrument |
| A long history through a big change in price level | Consistent, though the asymmetry of percentages still applies | Later years dominate entirely |
| Sizing a move against the instrument’s own recent range | Workable | Legitimate here, and average true range answers it better |
| A fall and the recovery that undoes it | Asymmetric: −50 per cent then +100 per cent | Symmetric: the same number, opposite signs |
The last row is the one that catches people, and it is why an average of rate-of-change readings should be handled carefully: the upside readings are arithmetically larger than the downside ones that undid them, so a mean of the series drifts positive on a series that went nowhere.
Why this measure is worth understanding before the others
Most of the momentum indicators in the library are this calculation with something added. RSI separates the up moves from the down moves, smooths each and puts the result on a bounded scale. Stochastics replaces the fixed lookback close with the range of the lookback window. Rate of change does none of that, which makes it a poor signal generator and an excellent teaching case: everything that goes wrong with the sophisticated versions is already visible here in its simplest form.
Two of those failures generalise. The unbounded scale means there is no level at which a reading is high, a value that was extreme in one market is ordinary in another, so any fixed threshold is borrowed from a sample you did not see. And the sign flips are frequent in a range and late in a trend, which is a property of the measure rather than a shortcoming of a particular setting: no lookback fixes both at once.
Applying it to volume
Volume is a better subject for this measure than price is, for a reason worth stating: volume does not trend. It oscillates around a level, so a comparison against a bar a fixed distance back is a fair one rather than a comparison against a different era.
The caution is the calendar. A twelve-bar volume comparison on daily data spans two and a half weeks and so compares a Tuesday with a Friday, and volume’s day-of-week pattern is strong enough to show up in the result. Either use a lookback that is a whole number of weeks, or use a ratio against a volume average long enough to smooth the pattern out, which is the form nearly every volume measure on this site actually uses.
Checking your figures against a platform
Rate of change is the one measure on this site where a disagreement is almost never about method, because there is no smoothing constant and no seed to argue over. Three things account for essentially every mismatch.
The off-by-one. Some implementations compare against the close n bars back and others against the close n − 1 bars back, which on a twelve-bar setting is an eight per cent difference in the lookback distance. Compare the first non-empty bar of each series: whichever starts earlier is using the shorter distance.
The scaling. A platform may report the result as a percentage, as a ratio around 1, or as an index around 100. All three are the same series; only the axis differs.
The input series. Adjusted against unadjusted prices, as everywhere else. A split inside the lookback window turns a percentage change into nonsense, and it is the one error here that produces a plausible-looking number rather than an obvious one.
Frequently asked questions
What does rate of change measure?
The difference between the current close and the close a fixed number of bars earlier, expressed as a percentage of that earlier close. That is all. There is no smoothing, no bounded scale and no threshold. It is the rawest of the momentum measures, which makes it the best one to understand first: almost every other momentum indicator is this quantity with something done to it afterwards.
Why does the lookback bar matter so much?
Because it is half of the calculation and nobody watches it. A rate-of-change reading can fall sharply on a day the price rose, simply because the bar dropping out of the lookback was a low one, exactly the two-ended-window problem a simple moving average has. When a momentum reading moves for no visible reason, look at what happened n bars ago before looking at today.
Percentage or points?
Percentage, in almost every case, because it is scale-free: a two-point move means something different on a twelve-dollar stock than on a four-hundred-dollar one, and only the percentage form is comparable across instruments or across a long history of the same instrument. The point form has one legitimate use, which is comparing a move against the instrument’s own recent range in its own units, and for that purpose average true range is the better tool.
Is momentum the same thing?
Nearly. What is usually labelled momentum is the same subtraction without the division, close minus close n bars ago, in points. Rate of change is that quantity divided by the earlier close and multiplied by a hundred. They rise and fall together and give identical crossings of zero; they differ in scale, and only the percentage form can be compared between two instruments.
What lookback should I use?
One that matches the horizon you care about, chosen before you look at the results. Twelve and twenty-five bars are the conventional daily settings and there is nothing special about either. What is worth knowing is the trade-off: a short lookback produces a reading that reacts immediately and crosses zero constantly, while a long one is steadier and can stay positive through a decline that has not yet erased the earlier gain.
Does a zero crossing mean anything?
It means the price is now at the same level it was n bars ago, which is a factual statement about the past and a weak basis for a decision. In a trending market the reading spends long periods on one side of zero and the crossings are late; in a sideways market it crosses repeatedly and each crossing is noise. This is the standard difficulty with every unbounded momentum measure, and it is why practitioners tend to watch the shape of the series rather than its sign.
Can rate of change be applied to volume?
Yes, and it is more useful there than most people expect, because volume has no trend to speak of. It oscillates around a level rather than drifting upward for years. A rate of change of volume against a fixed lookback is therefore a reasonable way to say how much heavier today was than the comparable session, though for that purpose a ratio against a volume average is easier to read and less sensitive to the single bar in the denominator.
Why is the denominator a problem?
Because a percentage change is asymmetric and the base is the earlier price. A fall from 100 to 50 is −50 per cent; the recovery from 50 to 100 is +100 per cent, and the two describe the same two prices. Over a long history that asymmetry accumulates in any average of rate-of-change readings, which is why comparisons across very different price levels — or averages of the readings themselves — should be treated with suspicion.