The Linear Relationship Between Fast Stochastic and Williams %R

Summary

Fast stochastic %K and Williams %R both measure a closing price’s position within the high-low range over a chosen lookback window. The document defines %K as the close’s distance above the low, scaled to a 0–100 range, and %R as the distance below the high, scaled to a −100–0 range. Because both use the same close, high, and low, their readings are related by a simple linear transformation: %R equals %K minus 100.

The answer derives the relationship by solving the %K formula for the close and substituting that expression into the %R formula. Thus, when calculated with the same period and price data, the indicators contain the same positional information but use different scales. The explanation does not discuss how traders interpret thresholds, whether implementations vary, or whether either indicator produces useful trading signals; those questions remain outside its scope.

Key ideas

• Both indicators locate the close within a lookback period’s high-low range.
• Fast stochastic %K scales that position from zero to one hundred.
• Williams %R expresses the same position on a scale from minus one hundred to zero.
• With matching inputs and periods, Williams %R equals %K minus one hundred.
• The explanation establishes mathematical equivalence but does not evaluate trading performance.

Tags

# stochastic fast vs. williams r


# stochastic fast vs. williams r












I'm sort of new to technical indicators, and I was looking at stochastic fast and williams r. As I understand the definitions, they are:

```
C = the most recent closing price
L14 = the low of the 14 previous trading sessions
H14 = the highest price traded during the same 14-day period
(the period can be changed from 14 for more sensitive or smoother results)

Stochastic Oscillator
%K = 100[(C - L14)/(H14 - L14)]

Williams %R
%R = -100[(H14 - C)/(H14 - L14)]
```

Doesn't this mean that `%R = %K - 100`? In which case, why have both?

Thanks.

-Erik

## Answer by Alex C (score 2, accepted)

https://quant.stackexchange.com/a/41013

Both measures express where C is within the interval from L14 to H14.

%K ranges from 0 when C is at the 14 day low, to 100 when C is at the 14 day high.

%R ranges from -100 when C is at the 14 day low, to 0 when C is at the 14 day high.

So they are actually linked by a simple linear relationship. We can derive it as follows:

$\%K = 100[(C - L14)/(H14 - L14)]$

This can be reversed to express C as a function of %K:

$C=L14+\%K/100(H14-L14)$

We can plug this into the definition of %R

$\%R=-100[(H14 - C)/(H14 - L14)]=-100[(H14-L14+\%K/100(H14-L14)/(H14-L14)]=-100+\%K$

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.