Percentage Increase vs Decrease — Formula and Real-World Examples

Introduction

Percentage increase and percentage decrease are among the most commonly used calculations in everyday life — from understanding your salary hike to calculating how much a product’s price has dropped during a sale. Despite the simplicity of the formulas, many students and professionals make errors by using the wrong base number.

This guide covers both formulas with clear real-world examples, a side-by-side comparison, and tips to avoid the most common mistakes.

🔧 Calculate instantly: Percentage Calculator — find percentage increase, decrease, and more with step-by-step working.

Percentage Increase Formula

Use this when a value goes UP from an original amount to a new (higher) amount.

Formula:

Percentage Increase = ((New Value − Old Value) / Old Value) × 100

Key point: you always divide by the old (original) value, not the new value.

Percentage Decrease Formula

Use this when a value goes DOWN from an original amount to a new (lower) amount.

Formula:

Percentage Decrease = ((Old Value − New Value) / Old Value) × 100

Same principle: divide by the original value.

Comparison Table

Aspect	Percentage Increase	Percentage Decrease
When to use	Value went up	Value went down
Formula	((New−Old)/Old) × 100	((Old−New)/Old) × 100
Denominator	Always the OLD value	Always the OLD value
Result	Positive number	Positive number
Example	Price ₹100 → ₹120 = 20% increase	Price ₹100 → ₹80 = 20% decrease

Worked Examples: Percentage Increase

Example 1: Salary Hike

Your monthly salary increased from ₹45,000 to ₹52,200.

Percentage Increase = ((52,200 − 45,000) / 45,000) × 100 = (7,200 / 45,000) × 100 = 16% increase

Example 2: Population Growth

A city’s population grew from 12,00,000 to 13,80,000 over 5 years.

Percentage Increase = ((13,80,000 − 12,00,000) / 12,00,000) × 100 = (1,80,000 / 12,00,000) × 100 = 15% growth

Example 3: Stock Price Rise

A stock price went from ₹850 to ₹1,020.

Percentage Increase = ((1,020 − 850) / 850) × 100 = (170 / 850) × 100 = 20% increase

Worked Examples: Percentage Decrease

Example 1: Sale Price Drop

A phone’s price dropped from ₹25,000 to ₹21,250 during a sale.

Percentage Decrease = ((25,000 − 21,250) / 25,000) × 100 = (3,750 / 25,000) × 100 = 15% decrease

Example 2: Weight Loss

A person’s weight dropped from 82 kg to 73.8 kg.

Percentage Decrease = ((82 − 73.8) / 82) × 100 = (8.2 / 82) × 100 = 10% decrease

Example 3: Revenue Decline

Annual revenue fell from ₹50,00,000 to ₹42,50,000.

Percentage Decrease = ((50,00,000 − 42,50,000) / 50,00,000) × 100 = (7,50,000 / 50,00,000) × 100 = 15% decrease

Common Mistakes to Avoid

1. Dividing by the new value instead of old — The denominator must ALWAYS be the original/starting value, not the final value
2. Confusing increase with decrease — If the new value is higher, it’s increase; if lower, it’s decrease. Check your subtraction direction.
3. A 50% increase then 50% decrease does NOT return to original — ₹100 + 50% = ₹150; then ₹150 − 50% = ₹75 (not ₹100). The base changes.
4. Mixing up “percentage points” and “percent change” — An interest rate going from 6% to 8% is a 2 percentage point increase but a 33.3% relative increase.
5. Rounding too early — Calculate the full division before rounding to avoid compounding errors in multi-step problems.

Percentage Change Shortcut

You can use a single universal formula for both directions:

Percentage Change = ((New − Old) / Old) × 100

• If the result is positive → it’s an increase
• If the result is negative → it’s a decrease (just report the magnitude)

Frequently Asked Questions

What is the percentage increase from 200 to 250?

((250 − 200) / 200) × 100 = (50/200) × 100 = 25% increase.

If something decreases by 20% and then increases by 20%, do I get back to the original?

No. Example: ₹100 − 20% = ₹80. Then ₹80 + 20% = ₹96 (not ₹100). The 20% decrease and 20% increase apply to different bases.

How do I find the original price before a percentage increase?

Original = New Value / (1 + Rate/100). For example, if final price is ₹1,200 after a 20% increase: Original = 1200 / 1.20 = ₹1,000.

What is the difference between “percent” and “percentage points”?

If inflation goes from 4% to 6%, it increased by 2 percentage points. But the percentage increase is ((6−4)/4) × 100 = 50%. They measure different things.

Can percentage increase be more than 100%?

Yes. If a value doubles (₹100 → ₹200), the increase is 100%. If it triples (₹100 → ₹300), the increase is 200%. There is no upper limit.

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