Williams R Calculator
Calculate Williams Percent Range oscillator for momentum and overbought/oversold conditions. Enter values for instant results with step-by-step formulas.
Calculator
Adjust values & calculateMulti-Period Williams %R
Formula
Where Highest High is the maximum high price over the lookback period (typically 14), Lowest Low is the minimum low price over the same period, and Close is the current closing price. Values range from 0 to -100, with -20 to 0 being overbought and -80 to -100 being oversold.
Last reviewed: December 2025
Worked Examples
Example 1: Williams %R Calculation
Example 2: Overbought/Oversold Signal
Background & Theory
The Williams %r Calculator applies the following established principles and formulas. Foreign exchange markets facilitate the conversion of one currency into another and serve as the largest and most liquid financial markets in the world, with daily turnover exceeding seven trillion US dollars. Exchange rates are quoted as currency pairs, expressing the price of one unit of a base currency in terms of a quote currency. For example, a EUR/USD rate of 1.0850 means one euro buys 1.0850 US dollars. The smallest standardized price movement in most pairs is the pip, typically the fourth decimal place, with a value of 0.0001 per unit for USD-denominated pairs. The bid price is the rate at which a dealer will buy the base currency, while the ask price is the rate at which it will sell. The spread between bid and ask represents the dealer's compensation and varies with liquidity and volatility. Leverage amplifies both gains and losses by allowing traders to control positions larger than their deposited margin. A 100:1 leverage ratio means a one-percent adverse move eliminates the entire margin, making position sizing and risk management critical. Two parity conditions from international economics anchor exchange rate theory. Purchasing Power Parity (PPP) holds that exchange rates should adjust over time so that identical goods trade at equivalent prices across countries: S = P_d / P_f, where S is the spot rate and P_d and P_f are domestic and foreign price levels. PPP performs well over long horizons but poorly in the short run due to trade barriers, non-tradable goods, and capital flows. Covered Interest Rate Parity (CIRP) is a near-arbitrage condition stating that forward exchange rate premiums or discounts exactly offset interest rate differentials between two currencies: F/S = (1 + r_d) / (1 + r_f). Deviations from CIRP create riskless arbitrage opportunities that traders rapidly eliminate. Uncovered Interest Rate Parity posits that high-yielding currencies should depreciate to offset their interest advantage, though empirical evidence is mixed and the carry trade — borrowing in low-rate currencies to invest in high-rate ones — has generated persistent returns.
History
The history behind the Williams %r Calculator traces back through the following developments. For much of the nineteenth century and early twentieth century, the international monetary system operated under the classical gold standard, under which each participating currency was fixed to a defined weight of gold, making bilateral exchange rates effectively constant. The system provided price stability and facilitated global trade but constrained governments' ability to respond to economic downturns. World War One shattered the gold standard as nations suspended convertibility to finance wartime expenditures. The interwar period saw attempts to restore gold convertibility, most notably the British return to the gold standard in 1925 at the pre-war parity, a decision criticized by John Maynard Keynes as deflationary. The Great Depression forced widespread currency devaluations and the effective collapse of the international gold standard by the early 1930s. The Bretton Woods Conference of July 1944 established a new order in which member currencies were pegged to the US dollar, while the dollar alone was convertible into gold at 35 dollars per troy ounce. The International Monetary Fund and World Bank were created at the same conference to oversee the system. Bretton Woods delivered exchange rate stability during the postwar growth era but came under strain as US deficits and European dollar accumulation outpaced American gold reserves. On August 15, 1971, President Nixon announced the suspension of dollar-gold convertibility — the so-called Nixon Shock — effectively ending the Bretton Woods system. By 1973, major currencies had transitioned to floating exchange rates determined by market supply and demand, a regime that has persisted. On September 16, 1992, hedge fund manager George Soros shorted the British pound against the European Exchange Rate Mechanism constraints, forcing the UK's withdrawal in what became known as Black Wednesday. Electronic trading platforms emerged in the 1990s and 2000s, replacing voice-brokered interbank markets and dramatically reducing transaction costs for institutional and retail participants alike.
Frequently Asked Questions
Formula
%R = (Highest High - Close) / (Highest High - Lowest Low) x -100
Where Highest High is the maximum high price over the lookback period (typically 14), Lowest Low is the minimum low price over the same period, and Close is the current closing price. Values range from 0 to -100, with -20 to 0 being overbought and -80 to -100 being oversold.
Worked Examples
Example 1: Williams %R Calculation
Problem: Over the last 14 periods, the highest high is 161 and the lowest low is 148. The current close is 156. Calculate Williams %R.
Solution: Williams %R = (Highest High - Close) / (Highest High - Lowest Low) x -100\n%R = (161 - 156) / (161 - 148) x -100\n%R = 5 / 13 x -100\n%R = 0.3846 x -100\n%R = -38.46\nInterpretation: Close is 38.46% below the period high\nZone: Middle range (between -20 and -80)\nNo extreme signal present
Result: Williams %R = -38.46 | Neutral Zone | Close is 61.5% above the period low
Example 2: Overbought/Oversold Signal
Problem: Williams %R has moved from -85 (oversold) to -75, crossing above the -80 threshold. Current close is 150, 14-period high is 155, low is 143. Evaluate the signal.
Solution: Previous %R: -85 (oversold, below -80)\nCurrent %R: (155 - 150) / (155 - 143) x -100 = -41.67\nActual calculation: %R = 5/12 x -100 = -41.67\nSignal: %R has exited oversold territory (crossed above -80)\nThis is a bullish signal indicating selling pressure is diminishing\nConfirm with volume expansion and bullish candle pattern
Result: Bullish Exit Signal | %R moved from -85 to -41.67 | Exited oversold zone | Potential long entry
Frequently Asked Questions
How is Williams %R calculated step by step?
Williams %R is calculated using a simple formula that compares the current closing price to the range of prices over the lookback period. First, you determine the Highest High over the last N periods (typically 14). Then find the Lowest Low over the same N periods. The formula is Williams %R = (Highest High - Current Close) / (Highest High - Lowest Low) multiplied by -100. For example, if the 14-period highest high is 161, the lowest low is 148, and the current close is 156, then %R = (161 - 156) / (161 - 148) x -100 = (5 / 13) x -100 = -38.46. This reading indicates the close is about 38 percent below the period high, placing it in the neutral to slightly bullish zone.
What do overbought and oversold readings mean in Williams %R?
In Williams %R, overbought conditions occur when the indicator reads between 0 and -20, meaning the current close is within 20 percent of the period high. This does not automatically mean the price will fall, but rather that buying pressure has pushed the price to the upper end of its recent range. Oversold conditions occur when %R reads between -80 and -100, meaning the close is within 20 percent of the period low. Many traders make the mistake of immediately selling at overbought readings or buying at oversold readings. In strong trends, the indicator can remain in overbought or oversold territory for extended periods. The best signals come when %R exits these extreme zones, such as falling below -20 from overbought or rising above -80 from oversold.
How does Williams %R compare to the Stochastic Oscillator?
Williams %R and the Fast Stochastic %K are mathematically identical but displayed differently. The Stochastic %K formula is (Close - Lowest Low) / (Highest High - Lowest Low) x 100, which gives a value between 0 and 100. Williams %R is (Highest High - Close) / (Highest High - Lowest Low) x -100, giving values between 0 and -100. If you add 100 to Williams %R and flip the sign, you get the Stochastic %K value. The key difference is that the Stochastic Oscillator includes a smoothed signal line (%D) which provides crossover signals, while Williams %R is typically used as a standalone oscillator. The Stochastic also uses the slow version with additional smoothing, making it less responsive but smoother than raw Williams %R.
What are the best Williams %R trading strategies?
The most reliable Williams %R strategy involves trading divergences between price and the indicator. When price makes a new high but %R makes a lower high, it suggests weakening momentum and a potential bearish reversal. Conversely, when price makes a new low but %R makes a higher low, bullish momentum divergence is present. Another effective strategy is the overbought or oversold exit signal, where you wait for %R to move into extreme territory and then exit, entering a trade in the direction of the exit. Failure swings provide high-probability signals when %R fails to re-enter an extreme zone on a retest. Combining %R with trend-following indicators like moving averages helps filter signals to trade only in the direction of the dominant trend.
What lookback period should I use for Williams %R?
The standard and most commonly used lookback period for Williams %R is 14, which works well on daily charts for swing trading. Shorter periods like 7 or 10 make the indicator more sensitive and responsive, generating more frequent signals but with a higher percentage of false signals. These shorter periods are useful for active day traders who need quick signals. Longer periods like 21 or 28 smooth out the indicator and reduce noise, making signals more reliable but slower to develop. For intraday trading on 5-minute or 15-minute charts, a 14-period setting captures a meaningful amount of recent price action. Some traders use multiple Williams %R periods simultaneously, such as 7 and 21 periods, looking for agreement between the short-term and long-term readings before entering trades.
How do you identify divergence signals with Williams %R?
Divergence between Williams %R and price action is one of the most powerful signals the indicator can produce. Bullish divergence occurs when price makes a lower low while Williams %R simultaneously makes a higher low, indicating that selling momentum is weakening despite the lower price. This often precedes a reversal to the upside. Bearish divergence happens when price makes a higher high but Williams %R makes a lower high, suggesting buying momentum is fading even as price reaches new highs. For divergence signals to be reliable, both the price extreme and the %R extreme should be clear and distinct. The best divergence signals occur when %R is in or near an extreme zone. Divergences can take multiple bars to complete and should be confirmed by a price action trigger like a reversal candle pattern.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy