What is the percent of increase from 6 to 9?

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Percentage increase/decrease calculation

The percentage increase/decrease from initial value (Vinitial) to final value (Vfinal) is equal to the initial and final values difference divided by the initial value times 100%:

percentage increase = (Vfinal - Vinitial) / Vinitial × 100%

Example #1

Price percentage increase from initial value of $1000 to final value of $1200 is caluclated by:

percentage increase = ($1200 - $1000) / $1000 × 100%

 = 0.2 × 100% = 20%

Example #2

Price percentage increase from initial value of $1000 to final value of $800 is caluclated by:

percentage increase = ($800 - $1000) / $1000 × 100%

= -0.2 × 100% = -20%

So

percentage decrease = 20%

Difference and final value calculation

The difference d is equal to the initial value V0 times the percentage increase/decrease p divided by 100:

d = V0 × p / 100

The final value V1 is equal to the initial value V0 plus the difference d:

V1 = V0 + d

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See also

Use this percent increase calculator to easily calculate the result from a percentage increase by any amount.

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Percent increase is a useful thing to calculate when comparing time periods, estimating growth percent (yearly, monthly, daily etc.), or comparing a new state to an old state of things, e.g. a new salary or hourly rate, versus your previous one. The formula for calculating percent increase used in our percentage increase calculator is:

    Percent increase formula

Percent increase = new / old * 100 - 100

where new is the newer quantity or measure, and old is the older (or original) quantity or measure.

In other cases, you know the starting, or original quantity, measure, or price, and you want to estimate what it would be if it were increased by a given percentage. In this case the formula used is:

Increased value = base + base * % increase / 100

where base is the starting amount and % increase is the percentage to increase it by. Let us see some examples to see how it works.

    Percent increase calculation examples

Several practical examples on how to work out a percentage increase should illustrate the use of relative growth calculations in various applied scenarios.

New versus old salary / hourly rate

Let us say your salary is $50,000 and you were offered a 20% increase, then to calculate your new salary do: $50,000 + $50,000 * 20 / 100 = $50,000 + $50,000 * 0.2 = $50,000 + $10,000 = $60,000. Let us say you have been approached with an opportunity for a new job and they offer you $60,000 instead of your current $50,000 salary. What is the percentage increase from the difference of $10,000? We plug the numbers into the first formula above to get $60,000 / $50,000 * 100 - 100 = 1.2 * 100 - 100 = 120 - 100 = 20% increase. You can verify this using this online percent increase calculator.

If, for example, your current rate is $20/h and you are offered a 10% increase, your new hourly rate can be calculated like so: $20 + $20 * 10 / 100 = $20 + $20 * 0.1 = $20 + $2 = $22. On the other hand, if your current hourly rate is $20/h, and you are offered $22/h, what is that in percentage change? Using the formula, we get 22 / 20 * 100 - 100 = 1.1 * 100 - 100 = 110 - 100 = 10% increase.

Business growth examples

Say you are running a small business and you have an average revenue of $20,000 per month by serving 20 customers a month, and you want to increase your revenue by 20%. How many new customers would you need? You need to multiply 20 by 20% and add 20, so that is 5 + 20 = 25. So you would need to serve 5 more customers to a total of 25 customers per month, in order to increase your revenue by 20%, assuming that revenue per customer stays the same.

In another example, say you have, on average, 20 new clients per month. However, in December you got 30 new clients, and you want to tell what that is in terms of percentage increase. Of course, it is easiest to use our free online percentage increase calculator, but if you choose to do the math by hand, it is 30 / 20 * 100 - 100 = 1.5 * 100 - 100 = 150 - 100 = 50%. A growth of 10 clients represents a fifty percent increase in the number of new clients.

Calculate price with tax

In another situation you might see a price on an item, but it doesn't have tax (e.g. VAT) included. The price is $10 and you know that there is a 20% tax, and you want to know the final price you need to pay. Using a percent increase calculator you will quickly find that the final price is $12. The price increase was two dollars. Or you can use our specialized VAT calculator instead.

Increase in property value example

In this example use case of our percent increase calculator, you have bought a property worth $500,000 and now its valuation has increased to $550,000 and you want to know what the percentage increase is. You divide the new price by the old price: $550,000 / $500,000 = 1.1, then multiply by 100 to get 110, then subtract 100. The final result is that your property value has increased by 10% over that time period via its gain in value to the amount of 50,000 USD.

The percentage increase calculator is a useful tool if you need to calculate the increase from one value to another in terms of a percentage of the original amount. Before using this calculator, it may be beneficial for you to understand how to calculate percent increase by using the percent increase formula. The upcoming sections will explain these concepts in further detail.

The concept of percent increase is basically the amount of increase from the original number to the final number in terms of 100 parts of the original. An increase of 5 percent would indicate that, if you split the original value into 100 parts, that value has increased by an additional 5 parts. So if the original value increased by 14 percent, the value would increase by 14 for every 100 units, 28 by every 200 units and so on. To make this even more clear, we will get into an example using the percent increase formula in the next section.

🙋 While the percentage increase calculator is important in mathematics, it is also useful in science, such as calculating the percent increase in mass of a chemical element in a compound.

The percent increase formula is as follows:

Percent increase = [(new value - original value)/original value] * 100

An example using the formula is as follows. Suppose a $1,250 investment increased in value to $1,445 dollars in one year. What is the percent increase of the investment? To answer this, us the following steps:

1. Identify the original value and the new value.
2. Input the values into the formula.
3. Subtract the original value from the new value, then divide the result by the original value.
4. Multiply the result by 100. The answer is the percent increase.
5. Check your answer using the percentage increase calculator.

Working out the problem by hand we get:

1. [(1,445 - 1,250)/1,250] * 100
2. (195/1,250) * 100
3. 0.156 * 100
4. 15.6 percent increase.

The percentage growth calculator is a great tool to check simple problems. It can even be used to solve more complex problems that involve percent increase. You may also find the percentage calculator is also useful in this type of problem.

If you want to know how to calculate percent decrease, we follow a very similar process as percent increase. Notice the slight modification of the formula:

Percent decrease = [(original value - new value)/original value] * 100

Suppose we have the same investment value after one year of $1,445. A year later the value decreased to $1,300. The percent decrease would be calculated as follows:

1. [(1,445 - 1,300)/1,445] * 100
2. (145/1,445) * 100
3. 0.10 * 100 = 10 percent decrease

Although we have just covered how to calculate percent increase and percent decrease, sometimes we just are interested in the change in percent, regardless if it is an increase or a decrease. If that is the case, you can use the percent change calculator or the percentage difference calculator. A situation in which this may be useful would be an opinion poll to see if the percentage of people who favor a particular political candidate differs from 50 percent.

If you want to learn how to express the relative error between the observed and true values in any measurement, check our percent error calculator.

Percentage increase is useful when you want to analyse how a value has changed with time. Although percentage increase is very similar to absolute increase, the former is more useful when comparing multiple data sets. For example, a change from 1 to 51 and from 50 to 100 both have an absolute change of 50, but the percentage increase for the first is 5000%, while for the second it is 100%, so the first change grew a lot more. This is why percentage increase is the most common way of measuring growth.

1. Divide the larger number by the original number. If you have already calculated the percentage change, go to step 4.
2. Subtract one from the result of the division.
3. Multiply this new number by 100. You now have the percentage change.
4. Divide the percentage change by the period of time between the two numbers.
5. You now have the percentage increase over time. Remember that the units will be % / [time], where time is the units you divided by, e.g. s for seconds, min for minutes etc. Please note that this does not take into account compounding.
6. For linear plots, multiply this number by any time difference to get the percentage change between the two times.
7. For non-linear plots, just replace the larger number with your equation and solve algebraically. This will only find the percentage change between a number you input and the original number.

If you want to increase a number by a certain percentage, follow these steps:

1. Divide the number you wish to increase by 100 to find 1% of it.
2. Multiply 1% by your chosen percentage.
3. Add this number to your original number.
4. There you go, you have just added a percentage increase to a number!

1. Divide the number you wish to add 5% to by 100.
2. Multiply this new number by 5.
3. Add the product of the multiplication to your original number.
4. Enjoy working at 105%!

To add two percentages together follow these steps:

1. Calculate the first percentage by dividing the number you wish to find the percentage of by 100.
2. Multiply the result by the percentage in its percentage form (e.g. 50 for 50%) to get the percentage of the original number.
3. Repeat steps 1 & 2 for the other number.
4. Add these two numbers together to get the addition of two percentages.
5. If the number you wish to find the percentage of is the same for both percentages, you can just add the two percentages together and use this new percentage to get the result of the addition.

1. Divide the number you are adding the increase to by 10.
2. Alternatively multiply the value by 0.1.
3. Add the product of the previous step to your original number.
4. Be proud of your mathematical ability!

1. Decide two things - the number which you want to find the percentage of and your chosen percentage.
2. Divide the chosen number by 100.
3. Multiply this new number by your chosen percentage.
4. There you go, you’ve just made a percentage!

A 50% increase is where you increase your current value by an additional half. You can find this value by finding half of your current value and adding this onto the value. For example, if you wanted to find what a 50% increase to 80 was, you’d divide by 2 to get 40, and add the two values together to get 120. A 50% increase is different to a 100% increase, which is double the original value.

While it's easier to use the Omni Percentage Increase Calculator, here are the steps to calculate discount rate in Excel:

1. Input the original number (for example into cell A1).
2. Input the increased number (for example into cell B1).
3. Subtract the original number from the increased number (In C1, input =B1-A1) and label it 'difference'.
4. Divide the difference by the original price and multiply it by 100 (In D1, input =(C1/A1)*100) and label it 'percentage increase'.
5. Right click on the final cell and select Format Cells.
6. In the Format Cells box, under Number, select Percentage and specify your desired number of decimal places.

1. Divide the original number by 100 to get 1% of it.
2. Multiply 1% by your desired percentage, in this case 20.
3. Add the product of the previous step to your original number.
4. Congratulate yourself on adding 20% to your number!