Percentage increase
t = (VA − VD) ÷ VD × 100
Difference divided by the starting value.
Percentage increase calculator
Calculate the percentage increase from a starting value to a final value, add X% to a price or a salary, or find the original value before an increase. Formulas, growth factor and the trap of successive increases explained.
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How does this tool work?
This page answers the three questions an increase raises: by what percentage did a value go up, what is it worth after an X% increase, and what was it worth before the increase. Use it for a raise, a rent, price or fee increase, growth in revenue, subscribers or population, and for percentage change exercises.
Percentage increase between two values: t = (final value − starting value) ÷ starting value × 100. The difference is always divided by the starting value, which is the reference. A price that goes from $80 to $100 has increased by 20 ÷ 80 = 25%. If the final value is smaller, the result is negative and means a decrease.
Increasing a value by X%: multiply it by the growth factor 1 + X ÷ 100. A 3% increase means multiplying by 1.03; a 20% increase by 1.2. A $52,000 salary with a 3% raise becomes 52,000 × 1.03 = $53,560.
Finding the value before the increase: divide the final value by the same factor, rather than taking X% off the result. An item priced $120 after a 20% increase was 120 ÷ 1.2 = $100, while 120 minus 20% gives $96. The same reasoning takes you from a tax-inclusive price back to the price before tax.
Successive increases multiply, they do not add up. Two 10% increases give 1.1 × 1.1 = 1.21, or +21%, not +20%. For an average change over several years, you need a compound annual growth rate (CAGR), calculated with a dedicated tool.
How to use this tool
Choose your question
% change, Increase by X% or Value before increase.
Enter the two numbers
Amounts, quantities or index values: only their shared unit matters, the tool does not change it.
Read the result
The rate is shown with its sign, or the calculated value rounded to two decimal places; it updates as you type.
Percentage increase formulas
Three calculations linked by the growth factor k = 1 + t ÷ 100.
Value after a t% increase
VA = VD × (1 + t ÷ 100)
Multiply by the growth factor.
Value before the increase
VD = VA ÷ (1 + t ÷ 100)
Reverse percentage: divide by the same factor.
Successive increases
k = (1 + t₁ ÷ 100) × (1 + t₂ ÷ 100)
The factors multiply.
- VD
- starting (original) value, the reference
- VA
- final value
- t
- rate of change, in %
- k
- growth factor (multiplier)
Example: a 15% increase means k = 1.15; 200 becomes 230.
Use cases
Salaries and negotiation
Turn a proposed raise into dollars, or measure the percentage difference between two paychecks.
Prices, rent and fees
Check an increase announced by a supplier, a landlord or a subscription, and work back to the old price from the new one.
Performance tracking
Measure growth in revenue, traffic, customer numbers or any metric from one period to the next.
School and exams
Practice percentage change, growth factors and reverse percentages, from middle school to college.
Examples
Price increase rate
(100 − 80) ÷ 80 × 100 = 25%.
Input
from $80 to $100Result
+25%Salary raise
52,000 × 1.03 = $53,560, or $1,560 more per year.
Input
$52,000 + 3%Result
$53,560Price before increase
120 ÷ 1.2 = $100; taking 20% off 120 would give $96, which is wrong.
Input
$120 after +20%Result
$100Audience growth
3,100 more visitors compared with the starting 12,400.
Input
from 12,400 to 15,500 visitorsResult
+25%Two successive increases
50 × 1.1 × 1.1 = $60.50, an overall increase of 21%.
Input
+10% then +10% on $50Result
$60.50Tips and best practices
- Always divide by the starting value: from 80 to 100 is +25%; from 100 to 80 is −20%.
- To remove an increase, divide by the factor (1 + t): do not subtract the same percentage.
- Successive increases combine by multiplying their factors.
- Tell percentages and percentage points apart: a rate going from 2% to 3% rises by one point, but by 50%.
- A 100% increase doubles the value, a 200% increase triples it.
Sources and references
- Weisstein E.W., Percentage Change (opens in a new tab), Wolfram MathWorldPage in English
- Weisstein E.W., Percent (opens in a new tab), Wolfram MathWorldPage in English
Frequently asked questions
How do I calculate a percentage increase?
Subtract the starting value from the final value, divide by the starting value, then multiply by 100. From 250 to 300: (300 − 250) ÷ 250 × 100 = 20%.
How do I increase a price by 10%?
Multiply it by 1.10. A $45 price increased by 10% becomes $49.50. In the same way, a 5% increase means × 1.05 and a 25% increase means × 1.25.
How do I find the price before an increase?
Divide the final price by 1 + the rate. After an 8% increase, a rent of $1,512 was 1,512 ÷ 1.08 = $1,400.
Why don't two 10% increases make 20%?
Because the second increase applies to a value that has already gone up. The factors multiply: 1.1 × 1.1 = 1.21, a total increase of 21%.
What is a growth factor?
It is the number you multiply the starting value by to get the final value: k = 1 + t ÷ 100 for a t% increase. It also equals final value ÷ starting value; when it is greater than 1, the change is an increase.
Does a 50% increase followed by a 50% decrease bring you back to the start?
No: 100 becomes 150, then 75. After a t% increase, you need a smaller decrease, t ÷ (1 + t), to get back to the start: here 33.33%.
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