Reverse Percentages Calculator
Welcome to the our Reverse Percentages Calculator.
Here you will our reverse percentage calculator which will help you to find the original value before a percentage increase or decrease.
Our calculators will not only find the original values, but also show you all the working out along the way!
Which Reverse Percentage Calculator do I need?
Reverse Percentage Calculator 1
Example: 32% of a number is 150. What's the number?
Reverse Percentage Calculator 2
Example: After a 12% decrease, the price of a car is $15,000. How much did the car originally cost?
Reverse Percentages Calculator 1
This calculator will help you to find the original value, when you have been given the final value and the percentage of the original value that made it.
Example: if 70% of a number is 210 then it will find the original value using the steps below.
- Type 70 for the percentage.
- Type 210 as the Final Value.
- Click 'Find Original Value'.
- Answer: 300. So 70% of 300 = 210.
Reverse Percentages Calculator 2
This calculator will help you to find the original number, when you have been given the percentage increase or decrease and the final number.
Example: if a toy in a sale marked 20% off costs $210, what is the original price?
- Type 20 for the percentage.
- Select 'Percentage Decrease' because the items is 20% less in the sale.
- Type 210 into the Final Number box.
- Click 'Find Original Number'.
- Answer: 262.5. So the original price is $262.50
Example: Tyger jumps 320 cm which is 15% further than Sally. How far did Sally jump to the nearest cm?
- Type 15 for the percentage.
- Select 'Percentage Increase' as the jump was 15% more.
- Type 320 into the Final Number box.
- Click 'Find Original Number'.
- Answer: 278.26. So Sally jumped 278 cm to the nearest cm
What is a Reverse Percentage?
Reverse percentages are also called inverse percentages.
When you have a reverse percentage it means that you are given a final amount and a percentage (which could be a straightforward percentage or a percentage increase or decrease).
With reverse percentages you need to find the original value by working backwards from the final value and the given percentage.
Reverse Percentage Calculators Video
We have created a short video to show you all about reverse percentages.
In the video, you will see:
- what a reverse percentage is
- how to spot a reverse percentage problem
- which calculator you should use to solve the problem
- a worked example showing how to solve the problem without a calculator
How to find Reverse Percentages
Read on below if you want to find out how to solve reverse percentage questions without the calculators.
Reverse percentages are used when the percentage and the final number are given, and the original number needs to be found.
Finding the Reverse Percentage of a number in 3 easy steps.
Step 1) Get the percentage of the original number.
If the percentage is an increase then add it to 100, if it is a decrease then subtract it from 100.
- Example: if the percentage is an 18% increase, then the percentage is 100 + 18 = 118%
- Example: if the percentage is a 37% decrease, then the percentage is 100 - 37 = 63%
Step 2) Find 1% of the missing number by dividing the final number by the percentage from Step 1)
Step 3) Find 100% of the missing number by multiplying the result from Step 2) by 100.
Examples of Reverse Percentages
Example 1) 35% of a number is 320. What is the number?
Step 1) The percentage of the original value is 35%
Our percentage equation is 35% of ? = 320
Step 2) So 1% of ? = 320 ÷ 35 = 9.1429 (to 4dp).
Steo 3) 100% of ? = 9.1429 x 100 = 914.29 (to 2dp)
Answer: the original value was 914.29 to 2dp.
You can use calculator 1 to solve this problem.
Example 2) A car is reduced by 20% in price to $40,000. What was the original price?
Step 1) The percentage of the original number is 100% - 20% = 80%
Our percentage equation is 80% of ? = $40,000
Step 2) So 1% of ? = $40,000 ÷ 80 = $500
Step 3) 100% of ? = $500 x 100 = $50,000
Answer: the original car cost $50,000
You can use calculator 2 to solve this problem.
Example 3) Sally invests money in some shares. Five years later, she sells them for $7200 at a profit of 25% of their original value. How much did she spend on the shares?
Step 1) The percentage of the original number is 100% + 25% = 125%
Our percentage equation is 125% of ? = $7200
Step 2) So 1% of ? = $7200 ÷ 125 = $57.60
Step 3) 100% of ? = $57.60 x 100 = $5760
Answer: the amount she spent on shares was $5760.
You can use calculator 2 to solve this problem.
Example 4) Tyger buys a mountain bike. Three years later, he sells it for $675 which is 45% of its original value. How much did he pay for the bike originally?
Step 1) The percentage of the original number is 45%
Our percentage equation is 45% of ? = $675
Step 2) So 1% of ? = $675 ÷ 45 = $15
Step 3) 100% of ? = $15 x 100 = $1500
Answer: the amount he paid for the bike was $1500.
You can use calculator 1 to solve this problem.
More Recommended Math Resources
Take a look at some more of our resources similar to these.
Online Percentage Practice Zone
Our online percentage practice zone gives you a chance to practice finding percentages of a range of numbers.
You can choose your level of difficulty and test yourself with immediate feedback!
Percentage Of Calculator
This is the calculator to use if you want to find a percentage of a number.
Simple choose your number and the percentage and the calculator will do the rest.
Find the Percentage Increase Calculator
If you need to find the percentage increase/decrease between 2 numbers, then this calculator is the one you need.
Simple input the original number, then the new number and the calculator will tell you the percentage increase or decrease.
Converting Percentage Calculator
If you need to convert a percentage to a fraction - either a decimal fraction or a fraction in its simplest form, then use this calculator.
You can also use the fraction to percentage calculator for converting any fraction into a percentage.
This calculator takes a percentage and converts it at the click of a button.
Looking for more math calculators?
We have a wide range of free math calculators to help you.
Most of our calculators show you their working out so that you can see exactly what they have done to get the answer.
Our calculator hub page contains links to all of our calculators!
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