How to Calculate Percentage Increase or Decrease
Master the formula with clear examples from salaries, prices, exam scores, and weight tracking.
Calculating percentage change is one of the most frequently needed maths skills in daily life — whether you are comparing product prices, understanding a salary hike, tracking weight loss progress, or evaluating investment returns. This guide covers the complete formula, worked examples across different contexts, and the most common mistakes to avoid.
The percentage increase and decrease formula
Both percentage increase and decrease use the same core formula:
Percentage Change = [(New Value – Old Value) / Old Value] × 100
- If the result is positive, it is a percentage increase
- If the result is negative, it is a percentage decrease
The old value (also called the base value) is always the denominator. Getting this right is the most common error — always divide by the starting value, not the ending value.
Example 1 – Salary hike calculation
Your salary increased from ₹40,000 to ₹46,000 per month. What is the percentage increase?
= [(46,000 – 40,000) / 40,000] × 100 = [6,000 / 40,000] × 100 = 15%
Your salary increased by 15%.
Example 2 – Price discount calculation
A jacket was priced at ₹2,500 and is now on sale for ₹1,875. What is the percentage decrease?
= [(1,875 – 2,500) / 2,500] × 100 = [–625 / 2,500] × 100 = –25%
The price decreased by 25% (a 25% discount).
Example 3 – Exam score change
A student scored 68 out of 100 in the first test and 85 in the second. What is the percentage improvement?
= [(85 – 68) / 68] × 100 = [17 / 68] × 100 = 25%
Example 4 – Weight loss percentage
Someone weighed 90 kg and now weighs 81 kg. What percentage of their starting weight have they lost?
= [(81 – 90) / 90] × 100 = [–9 / 90] × 100 = –10%
They have lost 10% of their body weight.
How to calculate a new value after a percentage change
If you know the original value and the percentage change, and want to find the new value:
New Value = Old Value × (1 + Percentage Change / 100)
- 20% increase on ₹500: ₹500 × 1.20 = ₹600
- 15% decrease on ₹800: ₹800 × 0.85 = ₹680
Percentage points vs percentage change — an important distinction
This is one of the most misunderstood concepts in percentage calculations. If an interest rate rises from 5% to 7%, it has increased by 2 percentage points but by 40% in relative terms. Always clarify which one is being used in financial discussions, especially for loans and investments.
Reverse percentage – finding the original value
If a product costs ₹1,200 after a 20% price increase, what was the original price?
Original = New Value / (1 + Percentage / 100) = 1,200 / 1.20 = ₹1,000
This reverse calculation is useful for finding the pre-tax or pre-discount price of any item.
Common mistakes when calculating percentage change
- Dividing by the new value instead of the old value — always use the starting value as denominator
- Confusing percentage points with percentage change (as explained above)
- Forgetting to multiply by 100 at the end
- Applying successive discounts incorrectly — two 10% discounts do not equal a 20% discount
Two successive 10% discounts on ₹1,000 = ₹1,000 × 0.90 × 0.90 = ₹810 — a 19% total discount, not 20%.
Frequently asked questions about percentage increase and decrease
What is the formula for percentage increase? Percentage Increase = [(New Value – Old Value) / Old Value] × 100.
How do you calculate a 20% increase on a price? Multiply the original price by 1.20. For example, 20% increase on ₹500 = ₹600.
Is a 100% increase the same as doubling? Yes. A 100% increase means the value has increased by an amount equal to itself, which doubles the original figure.
What is the difference between percentage increase and markup? Markup is calculated on cost price, while selling price percentage increase is calculated on the original retail price. They use the same formula but with different base values.
Practical checklist for percentage calculations
- Identify clearly which value is the original (base) value
- Subtract old from new before dividing
- Divide by the old value — never the new value
- Multiply by 100 to express as a percentage
- Verify your answer with a quick sanity check — does the direction and size make logical sense?
Final takeaway
Percentage change calculations follow one consistent formula regardless of whether you are comparing prices, scores, weights, or financial figures. Once you internalise that the old value is always the denominator, most percentage problems become straightforward. Use the percentage calculator below to verify your calculations instantly.