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Williams %R: Formula, −20/−80 Levels and Stochastic Comparison

Williams %R(14) places the close within its 14-session range from −100 to 0. The formula, the −20/−80 conventions and its link to stochastics.

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Williams %R shows where the latest close sits within the high–low range of the last 14 sessions, on a scale from −100 to 0. A reading of 0 means the close equalled the 14-session high; −100 means it equalled the 14-session low. It was developed by Larry Williams and is the fast stochastic oscillator turned upside down.

Williams %R Formula

%R = −100 × (highest high of 14 sessions − close) ÷ (highest high of 14 sessions − lowest low of 14 sessions)

The 14-session window includes today. The result is always between −100 and 0, because the close always lies within that session range.

Illustrative example: if the 14-session high is 50, the low is 40 and the close is 47, %R = −100 × (50 − 47) ÷ 10 = −30. The close is 30% of the range below the high.

How To Read Williams %R: −20 And −80

By convention, readings from −20 to 0 are called overbought and readings from −100 to −80 oversold. They mean only that the close is near the top or the bottom of its recent range. During a steady rise the close keeps landing near the top, so %R can stay above −20 for weeks; during a decline it can stay below −80. The levels are conventions, not rules.

Williams %R Vs The Stochastic Oscillator

The two measure the same thing. The fast (raw) stochastic %K is 100 × (close − lowest low) ÷ (range); Williams %R equals that value minus 100. A raw %K of 70 is a %R of −30.

On Vyreon pages the two numbers will not line up exactly, because Vyreon's stochastic oscillator is the slow version, smoothed twice over three sessions. Williams %R is not smoothed, so it reacts to today's close alone and moves more sharply from day to day.

How Vyreon Calculates It

  • Williams %R(14) on daily bars adjusted for splits and dividends, so a split does not appear as a fall to the bottom of the range.
  • Highest high and lowest low of the 14 sessions up to and including the reported day; no later session is used.
  • No smoothing is applied, and no overbought or oversold label is attached.
  • If every price in the window is identical (no range), the value is withheld rather than guessed.

What Williams %R Does Not Tell You

  • It describes where today's close sits in a recent range. It does not forecast the next move.
  • It ignores volume and anything before the 14-session window.
  • The range changes as old sessions drop out, so %R can jump when an unusually high or low day leaves the window.
  • −20 and −80 are trading conventions, not signals that something must happen.

Related: stochastic oscillator · RSI · CCI · price channels · candlestick patterns

Sources

  • Larry R. Williams, How I Made One Million Dollars Last Year Trading Commodities (1973): introduced %R.
  • George C. Lane, credited with developing the stochastic oscillator and its %K and %D lines; Williams %R is the fast stochastic on an inverted scale.
  • John J. Murphy, Technical Analysis of the Financial Markets (New York Institute of Finance, 1999): %R and stochastics.

The −20 and −80 levels are trading conventions; we know of no peer-reviewed source establishing them.