# Percent change calculator

Life is a numbers game. We live in a world where numbers, data and statistics matter a lot. And one constant thing about all aspects of life is that change is inevitable. This percentage change calculator comes in handy when you need it the most!Hundreds of people find this tool very useful in several, daily applications like finance, sales, tax and inflation rate, chemistry, physics and diverse areas of mathematics. In computing the growth or decline of a variable, you can quickly use this percentage change calculator to find the percentage increase or decrease in the value of two numbers.

### How to use our Percent Change Calculator

It is very simple, easy and quick to use!
Step 1: Simply fill in the initial and new values in the provided boxes.
Step 2: Hit the “calculate” button
Step 3: You’ll get your percentage change in a twinkle of an eye!

### Percentage Change Formula

(New Value – Initial Value)/(Initial Value) * 100 = percentage increase or decrease

Examples1. Calculate the percentage increase of the rentIf the monthly cost of renting an apartment is \$789 in June and the landlord has decided to charge a new price of \$807.46 in the month of July. Calculate the percentage increase in the rent between June and July.

(807.46 – 789) / 789 × 100 = 18.46 / 789 × 100 = 2.339

Your rent has increased by 2.34%. We can verify that: 789 × 1.0234 = 807.46

2. Calculate the production decline in percentage

The production of a company diminishes from 2345 pieces per day to 1870 pieces per day. What is the percentage decrease in production of this company?

(1870 – 2345) / 2345 × 100 = −20.256

The decrease in production is equal to -20.26%. We can verify that: 2345 × (1 – 20.26 / 100) = 2345 × 0.7974 = 1870 rounded to the nearest unit.

3. How to determine the percentage of a reduction

A seller gives you a discount of 30 USD on a household electrical appliance to 210 USD. What is the percentage reduction? You will pay 180 USD instead of the 210 USD requested. The tool gives us:

(180 – 210) / 210 × 100 = −14.29. The change from 210 to 180, in percentage, represents a decrease of -14.29% of 210.
We can verify that: 210 x (1 – 14.29 /100) = 210 x 0.8571 = 180.

4. Calculate the evolution in percentage of negative values

In order to calculate the change in percentage on negative values, one must take the absolute value of the initial value:
(new-old) / |old|.

A temperature drops from -20 degrees Fahrenheit to -45 degrees Fahrenheit. What is the percent change?
(-45 – (-20)) / 20 * 100 = 125
The temperature has dropped by 125%.
We can verify: 125% of 20 degrees Fahrenheit represents 25 degrees Fahrenheit. This gives -20 – 25 = -45 degrees.

Calculating percentage change in the value of a number has never been made easier. The fact that our FREE website has a minimal load time makes the online percentage calculator fun and super-fast. We guarantee there’s no downtime.Thanks to its compatibility, you can even use this online tool on your smartphone or personal computer. It is an excellent tool for online users.

TheoryOn this website we discuss what a percent change is (= a variation in percent)Example 1
Dad weighed 75 kg before the holidays. When he returned, his weight had increased by 5%. How much does Dad weigh now?
75 + 5% * 75= 75 + 3.75 = 78.75 kg

Example 2
Mom weighed 62 kg before the holidays. She then lost 8% of her initial weight. How much does Mom weigh now?
62 – 8% * 62 = 62 – 4.96 = 57.04 kg

A percent change is the variation, expressed in percent, of a quantity over time.
Initial value ± percentage of change = final value

Example 1 (continued)
We can simplify the operation 75 + 5% * 75 by factorising. Therefore:
75 + 5% * 75 = 75 * (100% + 5%).
In doing so, we find the following percent change (100% + 5%)

Example 2 (continued)
We can simplify the operation 62 – 8% * 62 by factorising. Therefore:
62 – 8% * 62 = 62 * (100% – 8%).
In doing so, we find the following percent change (100% – 8%)

Initial Value Vi * percentage (multiplication) factor q = Final Value Vf
The multiplication factor in a percentage notation: q=(100%±p%)
The multiplication factor in a decimal notation: q=(1±p/100)

In the case of an increase, the multiplication factor is higher than 1.

Example 1 (continued)
q=(100%+5%)=105%=1.05

In the case of a decrease, the multiplication factor is lower than 1

Example 2 (continued)
q=(100%-8%)=92%=0.92

1. Percent change: increaseIn this chapter we examine what a percent increase is.Example
Dad weighted 75 kg before the holidays. When he returned, his weight had increased by 5%. How much does Dad weigh now?
75 + 5% * 75 = 75 + 3.75 = 78.75 kg
The percent increase is the increase, expressed in percentage, of a quantity over time.
Initial Value ± percentage of change = final value

Example (continued)
We can simplify the operation 75 + 5% * 75 by factoring. Therefore:
75 + 5% * 75 = 75 * (100% + 5%).

In doing so, we find the following percent change (100% + 5%)

The Percent change in a percentage notation: q=(100%+p%)
The Percent change in a decimal notation: q=(1+p/100)

Terms such as “increase”, “growth”, “rise” can help you identify that it is a matter of calculating a rate of increase. If you know two of the three values (initial value, multiplication (percentage) factor, final value), then you can easily find the third one. To do this, simply apply the above equation (with the value to be found on the left side).

1.1. Calculating the final value

Vf = Vi * q

Example
A smartphone of the “Pear” brand costs \$300.
Given the increase in demand, the manufacturer increases the price by 25%.
How much does the smartphone cost after the price increase?
Vf = 300 * (1 + 25/100) = 300 * (1 + 0.25) = 300 * 1.25 = 375
After the price increase, the smartphone costs \$375

1.2. Calculating the initial value

Vi = Vf / q

Example
After a 25% increase from its initial price, a smartphone now costs \$375. How much did it cost before the price increase?
Vi = 375/(1+25/100)=375/(1+0.25)=375/1.25=300

Before the price increase, the smartphone was costing \$300.

1.3. Calculating the Percent change

q = Vi / Vf

Example
The smartphone manufacturer increases the price of the smartphone from 300\$ to 375\$. By what percentage has the price increased?
q=375/300=1.25

The price increased to 125% of the initial price.

2. Percent change: decreaseIn this chapter we examine what a percent decrease is.Example
Mom weighed 62 kg before the holidays. She then lost 8% of her initial weight. How much does Mom weigh now?
62 – 8% * 62 = 62 – 4.96 = 57.04 kg

A percent decrease is the decrease, expressed in percentage, of a quantity over time.
Initial value – rate of decrease = final value

Example (continued)
We can simplify the operation 62 – 8% * 62 by factorising. Therefore:
62 – 8% * 62 = 62 * (100% – 8%).
In doing so, we find the rate of decrease (100% – 8%)

The initial value Vi * decrease percentage (multiplication) factor q = Final Value Vf

Rate of decrease in the percentage notation: q=(100% – p%)
Rate of decrease in the decimal notation: q=(1 – p/100)

Terms such as “decrease”, “reduction”, “lowering”, “fall” can help you identify that it is a matter of calculating a rate of decrease. If you know two of the three values (initial value, multiplication factor, final value), then you can easily find the third one. To do this, simply apply the above equation (with the value to be found on the left side).

2.1. Calculating the final value

Vf = Vi * q

Example
A smartphone of the “Pear” brand costs \$300.
Given the decrease in demand, the manufacturer lowers the price by 25%. How much does the smartphone cost after the price decrease?
Vf = 300 * (1 – 25/100) = 300 * (1 – 0.25) = 300 * 0.75 = 225
After the price decrease, the smartphone costs \$225.

2.2. Calculating the initial value

Vi = Vf * q

Example
After a 25% decrease from its initial price, the smartphone now costs \$225. How much did the phone cost before the price decrease?
Vi = 225(1+25/100)=225(1+0,25)=225*1,25=300
Before the price decrease, the smartphone cost \$300.

2.3. Calculating the percent change

q = 1 – Vi / Vf

Example
The smartphone manufacturer lowers the price from \$300 to \$225. By what percentage has the price decreased?
q=1-225/300=1-0.75=0.25
The price decreased by 25% from the initial price.

3. Particular characteristics of the percent of change3.1. Percentage increase and decrease of the same percentageContrary to popular belief, if a starting value increases by p % and then decreases by the same percentage, this does not lead to the starting value. This also applies to a decrease of p% and then an increase of the same percentage.

Example
The price of a product costing \$50 increases by 10%
Vf=50⋅(1+10/100)=50⋅(1+0,1)=50*⋅1,1 =55
After the price increase, the product now costs \$55. We now lower its price by 10%.
Vf−=55⋅(1-10/100)=55⋅(1-0,1)=55*⋅0,9 =49,5
The product now costs \$49.5 rather than \$50 as one might have expected.

3.2. The percent change of a percentage

The change of a percentage can be written in percentage or in percentage points.

Example
The XYZ party scored 20% in previous elections, and got 30% of the vote in today’s elections.
Saying that “the XYZ party got 10% more votes compared to previous elections” is erroneous! An increase of 10% would only result in 22% of the vote in today’s elections.
20⋅(1+10/100)=20*⋅1.1=22
The absolute variation between two percentages is given in percentage points.

Example (continued)
30-20=10
The XYZ party scored 20% in previous elections, and got 30% of the vote in today’s elections.
Saying that “the XYZ party got 10% more votes than in the previous elections” is erroneous! An increase of 10% would only result in 22% of the vote in today’s elections.
20⋅(1+10/100)=2*0⋅1.1=22
The absolute variation between two percentages is given in percentage points.

Example (continued)
30-20=10
In today’s elections, the XYZ party got 10 percentage points more votes than during the previous elections.
The relative change between two percentages is given in percent.

Example (continued)
Initial value V : 20 (initial percentage)
Percentage value P : 10 (absolute variation)
p = P/V= 10/20 = 0.5
In today’s elections, the XYZ party received 50% more votes than in the previous elections.

4. Multiplication (percentage) factorIn this chapter we examine what a multiplication factor (also known as percentage factor) is.Example 1
Dad weighed 75 kg before the holidays. When he returned, his weight had increased by 5%. How much does Dad weigh now?
75 + 5% * 75 = 75 + 3.75 = 78.75 kg

Example 2
Mom weighed 62 kg before the holidays. She then lost 8% of her initial weight. How much does Mom weigh now?
62 – 8% * 62 = 62 – 4.96 = 57.04 kg

A percent change is the variation, expressed in percent, of a quantity over time.
Initial value ± percentage of change = final value

Example 1 (continued)
We can simplify the operation 75 + 5% * 75 by factorising. Therefore:
75 + 5% * 75 = 75 * (100% + 5%).
In doing so, we find the following percent change: (100% + 5%)

Example 2 (continued)
We can simplify the operation 62 – 8% * 62 by factorising. Therefore:
62 – 8% * 62 = 62 * (100% – 8%).
In doing so, we find the following percent change: (100% – 8%)

Initial Value Vi * multiplication (percentage) factor q = Final Value Vf
The multiplication factor in a percentage notation: q=(100%±p%)
The multiplication factor in a decimal notation: q=(1±p/100)
In the case of an increase, the multiplication factor is higher than 1 (“increase rate”).

Example 1 (continued)
q=(100%+5%)=105%=1.05

In the case of a decrease, the multiplication factor is lower than 1 (“decrease rate”).

Example 2 (continued)
q=(100%-8%)=92%=0.92

5. Multiplication factor and percentageThe percentage indicates by how many percent the initial value was modified.Example
A price increasing from \$50 to \$60 corresponds to an increase of 20%.
⇒Percentage = 20 % = 0.2

The multiplication (percentage) factor indicates the percentage to which the initial value has been modified.

Example
A price increase from \$50 to \$60 corresponds to an increase to 120%.
⇒ Multiplication factor = 120 % = 1.2

5.1. Calculating a multiplication factor (from a percentage)

If the percentage p% is given, the multiplication factor is calculated as follows:
Increase: q=(1+p/100)
Decrease: q=(1-p/100)

Example 1
Increase of 30 %: p%=30%⇒q=(1+30/100)=1+0.3=1.3

Example 2
Decrease of 20 % : p%=20%⇒q=(1-20/100)=1-0.2=0.8

5.2. Calculating the percentage (from a multiplication factor)

If the multiplication factor p% is given, the percentage is calculated as follows:
multiplication factor > 1: p%=q-1
multiplication factor < 1: p%=1-q

Example 1
Increase to 160 %: q=1.6⇒p%=1.6−1=0.6=60%

Example 2
Decrease to 30 %: q=0.3⇒p%=1−0.3=0.7=70%

6. Percentage pointsIn this chapter we discuss what percentage points are.Exercise data
When comparing percentages between them (> percent change), you need to differentiate between the absolute change and the relative change.

Example
The XYZ party scored 20% in past elections, and got 30% of the vote in today’s elections.
Saying that “the XYZ party got 10% more votes than in the previous elections” is erroneous! An increase of 10% would only result in 22% of the vote in today’s elections.
20 * (1+10/100)=20 * 1.1=22
The absolute variation between two percentages is given in percentage points.

Example (continued)
30-20=10
In today’s elections, the XYZ party got 10 percentage points more votes than during the previous elections.
The relative change between two percentages is given in percent.

Example (continued)
Initial value V : 20 (initial percentage)
Percentage value P : 10 (absolute variation)
p = P/V= 10/20 = 0.5
In recent elections, the XYZ party won 50% more votes than in the previous elections.

Source : Percent change calculator