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Williams %R: the close's position within the range

Williams %R places the close between the highest high and lowest low of a recent window: zero is the upper edge and -100 the lower; extremes need context.

Cite this entry

This reference cites the Cyclepedia entry. The documents it draws on are listed in the entry’s sources.

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Williams %R shows where the latest close sits within the range of a recent window. A close at the highest high gives 0; a close at the lowest low gives −100. It does not measure whether price is expensive or cheap, and it does not predict the next bar by itself.

In plain terms — Picture a lift with floor 0 at the top and floor −100 at the bottom. %R tells you where price stopped: near 0 means near the recent high; near −100 means near the recent low.

Williams %R — from the close to the 0/−100 scale Interactive diagram connecting Williams %R price window, formula, scale, and market context. INDICATOR · POSITION WITHIN THE RANGE Williams %R — from the close to the 0/−100 scale CYCLEPEDIA DIAGRAM · EMICICLO A number describes where price closed, not where it will go. 01 · WINDOW High, low, and close high 65 close 58 low 55 02 · FORMULA Distance from high / range −100 × (H − C) H − L −100 × (65 − 58) / (65 − 55) RESULT −70 03 · SCALE 0 at the top, −100 below 0−20−50−80−100 upper bandlower band −70 04 · CONTEXT The same zone, two regimes RANGE an extreme may revert TREND an extreme may persist 1 2 3 4
The same close becomes a number on the 0/−100 scale. An extreme zone describes a position; context determines whether it reflects exhaustion or persistence.
Select the highlighted points to explore the detail

From price to number

For an n-period window, let Hn be the highest high, Ln the lowest low, and Ct the current close:

%R = −100 × (Hn − Ct) / (Hn − Ln)

Example: high 65, low 55, close 58. The distance from the high is 7 and the range is 10, so %R is −70. The minus sign sets the direction of the scale: as the close falls towards the low, the value approaches −100.

The historical excerpt reproduced by the author's site calculates the original measure over ten days and expresses the distance from the high on a positive 0-to-100 scale. TradingView plots the same distance with a negative sign and uses 14 periods by default; other platforms may adopt different conventions. Ten and fourteen are therefore not mathematical laws: the window belongs to the indicator's specification.

Reading it without reversing it

The 0/−20 and −80/−100 bands are widely used references for closes packed respectively near the upper and lower parts of the range. They do not mean “sell” and “buy.” In a strong trend, %R can remain extreme because closes keep gathering near the same edge.

The −50 midpoint is more literal: above −50, the close lies in the upper half of the window; below −50, it lies in the lower half. This too describes position, not future direction.

A testable procedure

  1. State the window and data. Record bar count, timeframe, market, and price source before viewing the result.
  2. Read price first. Separate ranges from trends; the same extreme may mean different things in those regimes.
  3. Define the event. “%R below −80” is a state; a rule must specify crossing, re-entry, confirmation, and invalidation.
  4. Test out of sample. A backtest must include costs, repeated signals, and periods when an extreme persists without a reversal.

Its relationship with the Stochastic

With the same window and no smoothing, Williams %R and the fast %K line of the Stochastic contain the same information on shifted scales:

Williams %R = fast %K − 100

A close at the high gives %K = 100 and %R = 0; a close at the low gives %K = 0 and %R = −100. Combining them does not create independent confirmation. Differences on a chart usually come from the lookback, smoothing, price source, or platform rules.

Limits and implementation cases

  • If Hn = Ln, the denominator is zero and the value is mathematically undefined. A platform should disclose whether it returns missing data, carries the prior value, or applies another convention.
  • The current bar's %R can change until the bar closes; comparing an intrabar reading with a close-based test changes the rule.
  • Sessions, gaps, historical adjustments, and different feeds can change the window's high and low.
  • Optimising period and thresholds on the same sample used to judge performance creates overfitting risk.

Provenance and attribution

Larry Williams dates the development of Percent R to 1966 and acknowledges influence from Allan C. Davis. The book excerpt, which Williams says he wrote in 1973, documents the ten-day calculation and stresses that the indicator should be read within a market regime. This is an authorial primary source: it documents what Williams published and claimed, not an independent validation of the examples' profitability.

Sources

  • Larry Williams, Original Williams %R — stated excerpt from the book written in 1973, ten-day definition, worked example, and limits described by the author.
  • Larry Williams, Trading Indicators — claimed 1966 chronology and Allan C. Davis influence.
  • TradingView, Williams %R — negative-scale formula, configurable levels, and that platform's default.
  • Fidelity, Williams %R — mathematical relation to the fast Stochastic and persistence of extremes.

Larry Williams · Stochastic · Price range · Trend · Backtest · Indicators

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