Relative Strength Index (RSI): Formula, the 70 and 30 Levels, and What They Did on Real Prices

The Relative Strength Index (RSI) compares the size of recent up closes with the size of recent down closes and scales the result from 0 to 100. J. Welles Wilder described it in his 1978 book New Concepts in Technical Trading Systems, with a 14-period default and with 70 and 30 as the overbought and oversold levels. It is one of the best-known momentum oscillators, and a high reading is easy to misread: a high RSI describes a strong advance, not a market that has to fall. Below, the formula as Wilder wrote it, the ways to read it, and what the 70 and 30 levels did on a year of daily S&P 500 ETF prices and on Bitcoin.

How RSI is calculated

Each bar, take the change from the previous close. An up change counts as a gain and a down change as a loss, written as a positive number. Wilder averages the gains and the losses with his own smoothing: the first average is the simple mean of the first 14 values, and each later average keeps 13/14 of the previous one and adds 1/14 of the new value. The ratio of the two averages is the relative strength, RS, and RSI rescales it.

Because of the smoothing, RSI keeps a memory of every past bar, with a weight that shrinks over time. Two platforms can show slightly different values on the same chart if they started the calculation on different bars. On our daily S&P 500 ETF series, an RSI(14) started 300 bars later than another differed from it by 1.76 points on its first value, 0.22 point 43 bars after its start and 0.004 point 100 bars after its start.

How to read RSI

StockCharts lists three more signals, two of them from Wilder himself: divergences and failure swings, which he read as signs of a coming reversal. A divergence is a new price high without a new RSI high, or the reverse at a low. A failure swing is a pattern inside the indicator itself: in the bullish version RSI falls below 30, bounces, pulls back without going under 30 again, then breaks above its bounce high. A centerline cross, above or below 50, is read as a shift in momentum. Constance Brown added the idea of ranges: in an uptrend RSI tends to hold between 40 and 90, and in a downtrend between 10 and 60, so a dip to 40 in a bull market can be a buying zone rather than a warning.

The 70 and 30 levels on real prices

The 250-day chart above shows RSI(14) on the daily S&P 500 ETF from October 30, 2025 to October 28, 2026, 250 trading days. We counted every cross of the two levels in that window and looked at the close 20 trading days later.

The single oversold episode, two sessions in late March, came near the low of the spring decline, and the ETF was 12.79% higher a month later. The six overbought crosses all came in the rally that followed. Twenty days after the first five, the ETF was higher; only the sixth, on May 26, was followed by a lower close. A trader who sold short at each cross above 70 would have stood against the strongest leg of the year. RSI also stayed between 40 and 90 on 234 of the 250 days, which fits Brown’s bull market range; it fell under 40 on only 16 days, 12 of them between March 6 and March 30, 2026, around the spring low. Bitcoin, over its own window, spent 37 days under 40, 31 of them between May 27 and July 1, 2026.

Bitcoin over its own last 250 days, from February 21 to October 28, 2026, shows the other side. RSI went under 30 on June 2 with a close of 66,760.83, kept falling to its window low of 15.47 on June 6, and crossed back above 30 on June 11 at 63,625.99, 4.70% below the first oversold close. Twenty days after that June 11 recovery the close was 5.66% lower again. In the other direction, RSI crossed above 70 on August 19 at 69,334.79, rose to its window high of 85.95 on August 21, and Bitcoin was 13.16% higher twenty days after the cross. That was the first of the window’s four crosses above 70; the next ones, on August 31, September 3 and September 21, were followed twenty days later by +3.30%, +3.85% and −3.29%, so three of the four were followed by a higher close. On both markets, in this window, the extreme readings came with the trend and not against it.

The True Strength Index, a smoother cousin

William Blau’s True Strength Index (TSI) starts from the same raw material, the change from one close to the next, but it smooths that change twice with exponential averages, 25 and then 13 periods, and divides it by the same double smoothing of its absolute value. Blau presented the trading method in the May 1992 issue of Stocks and Commodities, after introducing the indicator in November 1991. TSI runs from −100 to +100 in theory but has no fixed overbought level; TradingView notes that a signal line is usually an EMA of 7 to 12 periods of TSI.

The double smoothing removes most of the small turns. Over the same 250 days on the S&P 500 ETF, TSI crossed zero 10 times and its 7-day signal line 23 times, when RSI(14) crossed its own midpoint of 50 38 times. TSI ranged from −31.63 on March 30, 2026 to 48.13 on May 14, 2026. The cost is lateness: TSI reacts to a new trend more slowly than RSI.

Does RSI work?

We have no long-run measurement of RSI: our bench tests chart patterns detected by rule against random entries, not indicators (see our methodology). The crosses above are two markets over one year, worked through to show how the levels behave, not a test. In that year, reading 70 as a sell signal would have been wrong on the ETF, and 30 as a buy signal wrong on Bitcoin in June. A fair test would run a fixed RSI rule on many markets and decades, with costs, against a random entry.

For more momentum tools, see the stochastic oscillator, which compares the close with the recent range, the Stochastic RSI, which applies that formula to RSI itself, the MACD, or the full list of momentum indicators.