Home > Attention, Cognitive Bias, Metacognition, Pattern Recognition > Isn’t The Weber-Fechner Law The Same As Any Other Equation? Never mind, I Just Noticed The Difference

Isn’t The Weber-Fechner Law The Same As Any Other Equation? Never mind, I Just Noticed The Difference


Imagine that you and your best friend are sitting in the back of the classroom during a lecture on a Friday afternoon. All you can think about is the concert  you’re going to tonight that you’ve been excited about for months, so you give up on trying to listen to your professor explain nuclear chemistry. You quietly whisper back and forth with your friend, talking about what you plan on wearing and what time you need to leave. Finally, the lecture ends and before you know it you’re at the concert. The music is blasting and you’re having a great time, but after singing along to several songs you decide you need to go buy something to drink. You start to tell your friend that you’ll be right back, but she doesn’t hear you. You say her name louder a few times, but she still doesn’t notice. Finally, you lean in close and yell in her ear. She nods and says something back but you can’t hear it over the music. You could hear each other just fine a few hours ago in class, but now it’s nearly impossible. What you’re experiencing is a difference in background intensity, and Ernest Weber and Gustav Fechner have a law that will tell you all about it.

The Weber-Fechner Law is a mathematical equation that was developed to calculate whether or not a person will be able to detect a difference between an original stimulus and a new stimulus in the environment (Krantz, 1971). A stimulus can be anything that you see, hear, taste, smell, or feel. In order for a person to detect a change in the environment, a stimulus must reach something known as the absolute threshold. This refers to the minimal intensity a stimulus must be in order to be noticed. For example, if you turn on your television and the volume is at 0, you will need to turn it up in order to hear it. However, you still might not be able to hear anything at 1 or 2, or even 3. If the first time you can detect sound is at a volume setting of 4, this is your absolute threshold. As you continue to increase the volume, what you are doing is increasing the intensity of the stimulus.

The Weber-Fechner Law began as a simple equation developed by Weber that Fechner expanded on. Weber’s law states that there is a proportional relationship between the intensity of a stimulus and something that he referred to as the Just Noticeable Difference (Nutter, 2010). The Just Noticeable Difference, or JND, refers to the smallest amount by which a stimulus can be changed and be detected by an individual. Consider this example: a person is given a 2 pound weight to lift. After they lift that weight, they are given another weight that is 2.05 pounds and asked whether or not this one is the same weight or different from the first. Because the change is so small, the person will not be able to detect a difference. Next, the person is given a 2.2 pound weight, and this time they are able to detect a change. This would be the JND. Now consider this person being asked to start by lifting a 5 pound weight. Following this, they are given a 5.2 pound weight. Although this weight difference was detected in the first trial with the 0.2 pound difference, the person is unable to detect it here. In fact, the smallest change that they are able to notice from the 5 pound weight is 0.5 pounds. Weber suggested that this data had a proportional relationship that could be represented mathematically. If a 2 pound weight required a 0.2 pound difference to be noticed and the 5 pound weight required a 0.5 pound difference to be noticed, the JND was directly proportional to the “intensity,” or original weight, of the stimulus. In this case, the ratio is 0.1. He came up with the equation K=JND/S, where K is a constant known as the Weber fraction, JND is the just noticeable difference, and S is the intensity of the original stimulus. Put simply, if the intensity of the original stimulus increases, the change required for a person to detect it also increases. In the case of our classroom and concert situations earlier, when the noise intensity in the classroom was low, a whisper was detectable. Likewise, when the noise intensity at the concert was very high, yelling was required to get the attention of your friend.


The sensory organs–which include the eyes, ears, nose, mouth, and skin–allow information from one’s environment to be converted into signals that the brain can understand. All stimulus from the environment produces a sensory effect, but the effects are not always brought into conscious awareness (Carr, 1927). With the incredible amount of information coming at us from the environment at every moment, it would be impossible to attend to every single thing. Even when we are attending to our environment, changes easily go unnoticed, and the nature of our attention can be used against us. Change blindness is when a new visual stimulus is introduced and a person does not notice it (Chabris & Simmons, 2010). In the Money Business Illusion, participants are presented with a video with people passing basketballs around. They are instructed to count how many passes one team makes. Several people fail to notice a person in a gorilla costume walking through the scene, and even more miss the color of the curtains changing behind everyone. If something this dramatic is missed by most people, it is not at all surprising that changes in the environment go unnoticed unless they reach a particular threshold.


Let’s consider the image of the squares with dots in them. Do you see a difference between 10 dots and 20 dots? For most people, it should be pretty obvious. What about between 110 and 120 dots? Not so easy anymore. According to the Weber-Fechner Law, the 120 dots have a very small change relative to the intensity of the original 110 dot stimulus. However, the relative change from 10 dots to 20 dots is much greater, so the change exceeds the Just Noticeable Difference. What does this tell us about how perception and attention influence our experiences with our environment? Basically, we miss a lot.

But why is the Weber-Fechner Law relevant to our daily lives? The biggest implication we can take away from this information is how to effectively manipulate prices of items in the business world so they will still sell. For example, consider that you’re a small business owner wanting to raise the price on a shirt you’re selling. You’ve been selling it for $10, but you’d really like to sell it for $15 now. If you raised your price directly from $10 to $15, the ratio would be relatively large, people would notice the difference, and they would stop buying the shirt because they feel it is overpriced now. However, if you raise the price from $10 to $12, the ratio is much smaller and people are less likely to notice the change. After a while, the price can then be changed from $12 to $15, and people will still buy the shirt because the ratio is relatively small. This strategy can be applied to anything from gas prices and grocery store items to cars, and it is extremely effective. But of course you’d notice the difference right? According to Weber and Fechner, probably not.


Carr, Harvey. “An Interpretation of the Weber-Fechner Law.” Psychological Review, vol. 34, no. 4, Psychological Review Company, July 1927, pp. 313–19, doi:10.1037/h0074044.

Chabris, Christopher & Simmons, Daniel. (2010). The Invisible Gorilla. http://www.theinvisiblegorilla.com

Krantz, David H. “Integration of Just-Noticeable Differences.” Journal of Mathematical Psychology, vol. 8, no. 4, Elsevier Science, Nov. 1971, pp. 591–99, doi:10.1016/0022-2496(71)90008-3.

Nutter, Forrest W. “Weber-Fechner Law.” Encyclopedia of Research Design (2010): 1612, doi:10.4135/9781412961288.n494.



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