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. Every number in this guide can be reproduced with the percentage calculator and the age calculator — open them alongside as you read.
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%. When you finish here, the guides on how to calculate TDEE and how to lose weight by walking continue the series.
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.
The universal percentage change formula
All percentage increase and decrease calculations use one core formula, applied in the correct direction. The key principle that most errors violate: always divide by the original (old) value, never the new value.
Percentage Change = [(New Value – Old Value) ÷ Old Value] × 100
- Positive result = percentage increase
- Negative result = percentage decrease
This single formula handles both directions. The sign of the result tells you which direction the change went.
10 real-world worked examples
1. Salary increment: Salary rose from $52,000 to $59,800.
Change = [(59,800 – 52,000) ÷ 52,000] × 100 = [7,800 ÷ 52,000] × 100 = 15%
2. Price discount: Original price $3,200, sale price $2,560.
Change = [(2,560 – 3,200) ÷ 3,200] × 100 = [–640 ÷ 3,200] × 100 = –20% (20% discount)
3. Investment return: Invested $80,000, current value $112,000.
Change = [(1,12,000 – 80,000) ÷ 80,000] × 100 = [32,000 ÷ 80,000] × 100 = 40% return
4. Weight loss progress: Started at 94 kg, now 84.6 kg.
Change = [(84.6 – 94) ÷ 94] × 100 = [–9.4 ÷ 94] × 100 = –10% (10% body weight lost)
5. Website traffic: Last month 12,400 visitors, this month 15,500.
Change = [(15,500 – 12,400) ÷ 12,400] × 100 = [3,100 ÷ 12,400] × 100 = 25% increase
6. Exam score improvement: First test 58, second test 72 (both out of 100).
Change = [(72 – 58) ÷ 58] × 100 = [14 ÷ 58] × 100 = 24.1% improvement
7. Petrol price change: Price was $96/litre, now $103.68/litre.
Change = [(103.68 – 96) ÷ 96] × 100 = [7.68 ÷ 96] × 100 = 8% increase
8. Company revenue decline: Revenue fell from $24,000,000 to $19,200,000.
Change = [(1.92 – 2.4) ÷ 2.4] × 100 = [–0.48 ÷ 2.4] × 100 = –20% decline
Finding the new value after a percentage change
If you know the original value and the percentage change, the new value is:
New Value = Old Value × (1 + Percentage ÷ 100)
- $45,000 salary with a 12% hike: $45,000 × 1.12 = $50,400
- $2,500 product with a 25% discount: $2,500 × 0.75 = $1,875
- $120,000 investment with a 15% return: $120,000 × 1.15 = $138,000
Finding the original value (reverse percentage)
When you know the final value after a percentage change and need the original:
Original = Final ÷ (1 + Percentage ÷ 100)
- Final price $5,900 includes 18% GST. Original: $5,900 ÷ 1.18 = $5,000
- Sale price $1,360 after a 15% discount. Original: $1,360 ÷ 0.85 = $1,600
Percentage points vs percentage change — critical distinction
If loan interest rates rise from 7% to 10%, they have increased by 3 percentage points but by 42.9% in relative terms (3 is 42.9% of 7). Financial media often use "percentage points" when discussing interest rate, tax rate, or inflation changes. Always clarify which measure applies before drawing conclusions.
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Successive percentage changes: why they don't add up
Two successive changes of the same percentage do not cancel out. A 20% increase followed by a 20% decrease: Start ₹100. After +20%: ₹120. After −20%: ₹120 × 0.80 = ₹96. Net result: −4%, not zero. Formula for two successive changes of x% and y%: Net change = x + y + (xy/100). For +20% then −20%: 20 + (−20) + (20 × −20/100) = 0 − 4 = −4%. This is why stock market gains and losses are asymmetric: a 50% loss requires a 100% gain to break even.
Percentage points vs percentage: a crucial distinction
Interest rates rising from 5% to 8% is a 3 percentage point increase — but a 60% increase in the interest rate. "Percentage point" describes the absolute difference between two percentages. "Percent change" describes the relative change. This distinction matters enormously in finance and policy: a tax rate increasing from 20% to 22% is a 2 percentage point increase (absolute) but a 10% tax increase (relative). Use our percentage calculator for all three types of percentage calculation.
Percentage change in Indian financial contexts
Percentage change calculations appear throughout Indian personal finance. Salary negotiation: if offered ₹12L and requesting ₹14L, percentage increase = (14−12)÷12 × 100 = 16.7%. Inflation-adjusted salary: if you earned ₹10L in 2020 and earn ₹14L in 2026, at 6% average inflation your real salary growth = [(14÷10) ÷ (1.06)^6 − 1] × 100 = (1.4 ÷ 1.4185 − 1) × 100 = −1.3% real terms — you actually lost purchasing power despite a 40% nominal raise. Sensex performance: if Sensex was at 50,000 in January and is now at 62,500, the percentage gain = (62,500−50,000)÷50,000 × 100 = 25%. If it then drops to 55,000: percentage loss from peak = (55,000−62,500)÷62,500 × 100 = −12%. Note the asymmetry: a 25% gain followed by a 12% loss does not return to the starting point — 50,000 × 1.25 × 0.88 = 55,000 — a net 10% gain, not zero.
Quick reference: percentage calculator quick reference guide
This guide covers the essential concepts and practical steps for how to calculate percentage increase decrease. Bookmark this page and use the interactive calculators linked throughout to apply every concept to your specific numbers. The calculators handle all the arithmetic — your job is to understand the principles, ask the right questions, and make informed decisions with the results.
Key takeaways from this guide: understand the formula before trusting any calculator output. Use real numbers from your own situation, not example numbers. Revisit your calculations when circumstances change — income, expenses, goals, and market conditions all shift over time. Share results with a qualified professional (CA, financial planner, doctor) before making major decisions based on calculator outputs.
All calculators on iCalcApp are free, require no signup, and use formulas cited from authoritative sources. Results are updated instantly as you type. For questions about specific formulas or data sources, see the Methodology page or email hello@icalcapp.com.
How do you calculate percentage change when the original value is zero?
Percentage change is undefined when the original value is zero because you cannot divide by zero. If a metric was zero last month and is 100 this month, the conventional description is "increased from zero" or "new" rather than a percentage. Some analysts use absolute change in this case, or report it as an N/A percentage change.
What is the percentage change formula in Microsoft Excel?
In Excel: =(B2-A2)/ABS(A2)*100 where A2 is the old value and B2 is the new value. ABS() handles negative original values correctly. For a simple increase from A2 to B2: =(B2-A2)/A2 formatted as percentage. Use the TEXT() function if you need to display the % symbol in a combined text string.
Sources & references
Sources: NCERT Mathematics standards; ISO 80000-1 quantities and units conventions.