# How to Calculate Relative Increases

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If the price of a loaf of bread goes from $3 to$8, that seems like a big deal. If the price of a car goes from $10,000 to$10,005, not so much. What seems to matter is the relative size of the increase. The absolute increase from an old value O to a new value N is N–O. To find the increase relative to the old value, divide the absolute increase by the old value O to get the relative increase, (N–O)/O. This value is the fraction of the old value that was added to get the new value. If you want to express the relative increase as a percentage, you can multiply it by 100.

## Calculating Relative Increase

Write down the old value of the object of interest. In the first example, the old value is $3, and in the second example, it is$10,000. This is your starting point.

Write down the new value of the object. In the first example, the new value is $8, and in the second example, it is$10,005. This is where you end up.

Calculate the absolute increase. In the bread example the absolute increase is 8–3 = 5. In the car example, the absolute increase is 10,005–10,000 = 5 as well.

Calculate the relative increases. For the first example, use the method of directly dividing the absolute increase by the old value, 5/3 = 1.67, or 167 percent. Note that the new price is not 167 percent of that of the old loaf, it is 167 percent higher than the old price. The price of the new loaf is actually 267 percent of the old price. For the second example, you can instead use the equation (N–O)/O to get (10,005–10,000)/10,000 = 0.0005 or 0.05 percent. The new value is only 0.05 percent higher than the original value. In these two examples, the absolute increases are the same, but the relative increases are very different.

#### Tips

• The idea that people respond to changes relative to a background level means that they actually respond to relative increases. This idea is used in a field called psychophysics and is known as the Weber-Fechner law.