Stochastic Oscillator: Fast, Slow and Full Formulas, and the 80 and 20 Levels on Real Prices
Lane’s stochastic from its documented formulas: how the close is placed in a 14-bar range, why the fast, slow and full versions differ only in smoothing, and what the crosses and the 80 and 20 zones did on daily Bitcoin and the S&P 500 ETF.
On this page
The stochastic oscillator says where the latest close sits inside the range of the last 14 bars: 100 at the top of the range, 0 at the bottom. George C. Lane developed it in the late 1950s, and StockCharts reports his view that “as a rule, the momentum changes direction before price.” It comes in three versions, fast, slow and full, which differ only in how much the first line is smoothed, and it is read with an 80 and a 20 level. Below, the formulas for each version, the usual signals, and what they gave on daily Bitcoin and on the S&P 500 ETF.
Full stochastic (14, 3, 3) on daily Bitcoin
- Price, daily candles (hollow up, filled down)
- %K, 14 bars, SMA(3) smoothed (solid line)
- %D, SMA(3) of %K (solid line, second color)
How the stochastic oscillator is calculated
The raw line, %K, takes the distance from the lowest low of the last 14 bars to the close, and divides it by the full height of the range, from that lowest low to the highest high. A second line, %D, is a 3-bar simple moving average of %K and serves as the signal line.
| Version | %K shown | %D | Usual settings |
|---|---|---|---|
| Fast | The raw %K | 3-bar SMA of the raw %K | 14, 3 |
| Slow | 3-bar SMA of the raw %K (the fast %D) | 3-bar SMA of the slow %K | 14, 3 |
| Full | SMA of the raw %K over a chosen period | SMA of the full %K over a chosen period | 14, 3, 3 |
The full stochastic with 14, 3 and 3 is the same as the slow stochastic; its only advantage is that both smoothing periods can be changed. That is the version on the chart above. The smoothing is what decides how many %K and %D crosses you get to read, as the counts below show over the same 250 daily bars.
%K and %D crosses in 250 daily bars, by setting
- Bitcoin
- S&P 500 ETF
How to read it
- Above 80 and below 20: StockCharts calls these the overbought and oversold zones. A close near the top of the range puts %K above 80, and in an uptrend that can last.
- %K and %D crosses: %K crossing above %D is read as bullish, crossing below as bearish. Some traders keep only the crosses that happen in the 80 or 20 zones, as the count below does.
- Divergences: a new price low without a new stochastic low, or the reverse at a high, is read as a sign that the move is losing momentum. See divergence.
The signals on real prices
The first chart in the text, under the introduction, shows the full stochastic (14, 3, 3) on daily Bitcoin from February 21 to October 28, 2026, 250 days; the small chart in the page header shows only its last 60 days. The rules of the count: the indicator is computed on the whole price history, a cross is a day when %K moves from at or below %D to above it (bullish) or from at or above it to below it (bearish), and a cross is "under 20" or "above 80" when %D is under 20 or above 80 on the day of the cross. The result ten days later compares the close ten days after the cross with the close of the cross day.
Bitcoin ten days after each bullish cross under 20
On the full version, %K crossed above %D 8 times while %D was below 20, and crossed below %D 12 times while %D was above 80. Ten days after the 8 bullish crosses Bitcoin was higher 4 times and lower 4 times. Three of the four losing ones came together: crosses on May 20, May 23 and May 30, 2026, at closes of 77,552.23, 76,752.01 and 73,884.38, were followed ten days later by falls of 4.73%, 13.02% and 16.45%, as Bitcoin went down to a close of 60,884.62 on June 6. The next cross, on June 5 at 61,056.47, was followed by a gain of 8.64%; the fourth losing one, on June 11 at 63,625.99, lost 0.49%. Ten days after the 12 bearish crosses Bitcoin was lower 4 times and higher 8 times.
| Longest run | Dates | Close at the start and end |
|---|---|---|
| %K above 80, Bitcoin | 12 days, August 20 to 31, 2026 | 73,025.15 to 78,581.29, +7.61% |
| %K below 20, Bitcoin | 15 days, May 28 to June 11, 2026 | 73,617.51 to 63,625.99, −13.57% |
| %K above 80, S&P 500 ETF | 29 days, April 8 to May 18, 2026 | 672.60 to 734.93, +9.27% |
Full stochastic (14, 3, 3) on the S&P 500 ETF: 29 days above 80 in April and May 2026
- Price, daily candles (hollow up, filled down)
- %K, 14 bars, SMA(3) smoothed (solid line)
- %D, SMA(3) of %K (solid line, second color)
In each of those runs, selling at 80 or buying at 20 meant acting against a move that kept going. On the S&P 500 ETF over its own last 250 days, from October 30, 2025, the full stochastic gave only 4 bullish crosses under 20 but 17 bearish crosses above 80, a count that reflects the rising market rather than 17 tops: ten days after those 17 bearish crosses the ETF was lower 8 times and higher 9 times.
Does it work?
We have no long-run measurement of the stochastic oscillator: our bench tests chart patterns detected by rule against random entries, not indicators (see our methodology). The signals above are two markets over one year, worked through to show how the indicator behaves, not a test. They show the same thing as the RSI in that year: in a trend, the 80 and 20 levels describe the trend more than they predict its end.
For related tools, see the Stochastic RSI, the Williams %R, another range-position oscillator, or the full list of momentum indicators.
Frequently asked questions
What is the stochastic oscillator?
A momentum indicator by George C. Lane that places the close inside the high-low range of the last 14 bars, on a 0 to 100 scale. A %D signal line, a 3-bar average, is drawn with it, and 80 and 20 mark the overbought and oversold zones.
Is the Stochastic RSI better than the stochastic oscillator?
They measure different things. The stochastic places the price in its range; the Stochastic RSI places RSI in its own range, so it moves faster and reaches its extremes more often. Neither has been shown to be better in general.
What are the 5-3-3 stochastic settings?
A full stochastic with a 5-bar range, %K smoothed over 3 bars and %D over 3 bars. The shorter range makes the indicator react to the last week rather than the last three weeks. It does not always mean more signals: over 250 daily bars it gave 62 crosses on Bitcoin against 66 for 14, 3, 3, but 67 on the S&P 500 ETF against 62.
What is the difference between fast and slow stochastic?
The slow %K is the fast %D, a 3-bar average of the raw %K, and the slow %D is a 3-bar average of that. The slow version gives fewer crosses: on daily Bitcoin over 250 days, 66 instead of 103.
What do 80 and 20 mean on the stochastic?
That the close is in the top or bottom fifth of the recent range. It is a description of where the price stands, not a forecast; on the S&P 500 ETF in spring 2026 %K stayed above 80 for 29 days in a row while the ETF rose 9.27%.
Sources
Passionate about finance, quantitative trading and data analysis. Amaury built the PatternsWizard test bench, which detects each pattern on full price history and measures what happened next against random entries.
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