Williams %R: The Inverse Stochastic with a Negative Scale

Williams %R measures where the current close sits within the recent high-low range — then inverts the scale. Values run from 0 to -100. Near 0 means price closed near the top of its range (overbought). Near -100 means price closed near the bottom (oversold). Developed by Larry Williams, it is mathematically the inverse of fast Stochastic %K.

Section 1: Core Mechanics

Williams %R answers the same question as Stochastic: where did price close within its recent range? The difference is the scale direction. Stochastic scores 0 at the bottom of the range and 100 at the top. Williams %R scores 0 at the top of the range and -100 at the bottom. The numerator uses Highest High instead of Lowest Low, then negates the result.

Formula

Where N is the lookback period (default 14).

Relationship to Stochastic:

Stochastic %K of 80 = Williams %R of -20. Both describe the same condition: price closed in the upper 20% of its 14-bar range. The math is identical; only the scale differs.

Inputs

• High, Low, Close for each bar
• Period (N): Lookback for Highest High and Lowest Low (default 14)

Parameters

Output

Williams %R outputs a single value between 0 and -100. Zone interpretation:

• 0 to -20: Overbought — close near the top of the N-period range
• -20 to -80: Middle range — no extreme signal
• -80 to -100: Oversold — close near the bottom of the N-period range

Understanding the Negative Scale

The reversed scale trips up beginners. Here is the key mapping:

A %R value of -5 is extreme overbought (near the top). A value of -98 is extreme oversold (near the bottom). This is opposite to what traders expect from a 0–100 scale. Read this twice before using the indicator live.

Section 2: Interpretation & Signals

Signal Zones

Entry and Exit Rules

Oversold entry (buy setup):

• Wait for %R to drop below -80 (oversold zone entered)
• Entry: %R crosses back above -80 (exits oversold zone)
• Stop: Below the oversold price low
• Target: %R reaches -20 or prior resistance

Overbought entry (sell/short setup):

• Wait for %R to rise above -20 (overbought zone entered)
• Entry: %R crosses back below -20 (exits overbought zone)
• Stop: Above the overbought price high
• Target: %R reaches -80 or prior support

The entry is NOT when %R enters the extreme zone — it is when %R exits the zone. This avoids entering during a continuing trend move.

Divergence

Williams %R divergence works identically to RSI and Stochastic divergence:

Bullish: Price makes a lower low. %R makes a higher low (less negative). Momentum is improving before price.

Bearish: Price makes a higher high. %R makes a lower high (more negative, closer to -100). Momentum is weakening before price peaks.

Because %R is mathematically equivalent to Stochastic, their divergence signals are nearly identical. The scale is different; the underlying calculation is the same.

Best Market Conditions

Williams %R works best in ranging and mean-reverting markets. In strong trends, like Stochastic, %R can remain in an extreme zone for extended periods. The exit-from-zone entry rule (enter when %R crosses back above -80, not when it enters) reduces the risk of entering too early in a trending market.

Section 3: Pass vs. Live — Real-Time Reliability

Williams %R uses the live bar's high and low in the Highest High and Lowest Low calculations (identical to Stochastic's repaint mechanism). As the current bar's intraday high extends, the Highest High window may expand, shifting %R. At bar close, the final high and low are fixed. The value is permanent. No historical bars change.

Section 4: Practical Use Cases

Real example — Gold (XAUUSD), Q3 2022: Gold weekly Williams %R dropped to -97.4 in late September 2022 as gold hit $1,622 — the lowest weekly %R reading in over 5 years. The following week, %R recovered to -84.6, then crossed above -80 two weeks later as gold reclaimed $1,660. The weekly oversold exit on %R marked the beginning of a sustained recovery rally that carried gold to $2,050 by May 2023.

Section 5: Pseudo Code

INPUT: high[], low[], close[], period=14, ob=-20, os_=-80

PROCESS:
  Step 1: For each bar i >= period - 1:
            highest_high = max(high[i - period + 1 : i + 1])
            lowest_low = min(low[i - period + 1 : i + 1])
            range_hl = highest_high - lowest_low
  Step 2: Calculate %R:
            if range_hl == 0:
              wr[i] = -50  # No range — set to neutral
            else:
              wr[i] = ((highest_high - close[i]) / range_hl) * -100

OUTPUT: wr[] — values between -100 and 0
EDGE CASES:
  - range_hl == 0 (all bars identical close/high/low): set to -50 (neutral)
  - Fewer than `period` bars: return NaN
  - close[i] exactly equals highest_high: wr[i] = 0 (at top of range)
  - close[i] exactly equals lowest_low: wr[i] = -100 (at bottom of range)
  - NaN in high, low, or close: propagate NaN

Section 6: Parameters & Optimization

Standard Conventions

Parameter Impact

Section 7: Synergies & Conflicts

Section 8: Common Mistakes

Section 9: Cheat Sheet