How to Calculate Percentage Increase or Decrease

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.

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.