**Percentage increase** and **percentage decrease** calculations are important in everyday life. They tell the impact of a pay raise or cut, show how big a tip should be, help monitor stock performance, and describe whether a business is thriving or faltering. But, how do you calculate them correctly? Here is the formula for percentage change, a closer look at percentage increase and decrease, and some practical examples.

### How to Calculate Percentage Change

**Percentage change** compares the change in a final condition to the initial condition as a percentage. It is the difference between new and original values, divided by the original value, and multiplied by 100%.

**percentage change = (final value – initial value)/initial value x 100%**

Assuming the initial value is a positive number, a positive answer is a percentage increase, while a negative answer is a percentage decrease. The only “tricky” part of the calculation is remembering that the difference between the initial and final condition is compared to the initial condition (not the final condition).

### How to Calculate Percentage Increase

You see a percentage increase when the new number is larger than the original number. There are two common types of calculations involving percentage increase. The first calculates the percentage increase. The second is when you’re given the percentage increase and see what effect it has. Here are examples.

#### Calculating Percentage Increase

For example, a worker goes from working 35 hours a week to 40 hours a week. What percentage increase is this?

percentage increase = (final value – initial value)/initial value x 100%

percentage increase = (40 – 35)/35 x 100%

percentage increase = 5/35 x 100%

percentage increase = 14.3%

#### Calculating a Pay Raise

For example, a worker making $10.50 per hour gets a 3.5% pay raise. How much is the new pay rate?

The new pay rate is the original pay plus the raise. To solve this, remember how percentage are written as decimal numbers. So, 3.5% is the same as 0.035.

new pay rate = original pay rate + (original pay rate)(percent increase)

new pay rate = 10.50 + (10.50)(0.035)

new pay rate = 10.50 + 0.3675

new pay rate = $10.87

### How to Calculate Percentage Decrease

Percentage decrease occurs when the final number is smaller than the starting number. It’s fine to either include the negative sign or to omit the sign and simply say a value decreased by a certain percent.

#### Calculating Percentage Decrease

For example, a shirt changes price from $15 to $13. What is the percentage decrease in the price?

percentage decrease = (final value – initial value)/initial value x 100%

percentage decrease = (13 – 15)/15 x 100%

percentage decrease = (-2)/15 x 100%

percentage decrease = -13.3%

### What Is a 50% Increase?

A 50% increase is the same as saying a number increases again by half its original value. So, a 50% from 100 is 150 (100 + 50). A 50% increase from 200 is 300 (200 + 100). A 50% decrease from 100 is 50 (100 – 50).

### What Is a 100% Increase

A 100% increase is the same as saying a number doubles or is 200% of its initial value. So, a 100% increase from 100 is 200 (2 x 100). A 100% increase from 200 is 400 (2 x 200). A 100% decrease is 0.

### Where It Gets Confusing

The cases of a 50% change and 100% change make sense, but sometimes percentage change calculations aren’t intuitively obvious.

- Multiplying a number times a certain percent is not the same as a percentage increase. For example, an increase of 800% is actually 9 times larger than the original amount (100% + 800% = 900%).
- Sequential percentage changes are not additive. For example, if you have a 10% increase in value, followed by a 10% decrease in value, you aren’t back to the original number. Let’s say a $200 item has a 10% price increase, raising its price to $220, followed by a 10% price decrease (a $22 price cut). This brings its value to $198, not $200.

### Practical Percentages in Science

Now that you understand how percentage change works, see it in action in science.

### References

- Bennett, Jeffrey; Briggs, William (2005).
*Using and Understanding Mathematics / A Quantitative Reasoning Approach*(3rd ed.). Pearson Addison Wesley. ISBN 0-321-22773-5. - Törnqvist, Leo; Vartia, Pentti; Vartia, Yrjö (1985). “How Should Relative Changes Be Measured?”.
*The American Statistician*.**39**(1): 43–46. doi:10.2307/2683905