Percentage Increase & Decrease Guide

Understanding Percentage Change

Percentage change measures how much a value has increased or decreased relative to its original value. It's one of the most useful calculations in everyday life, from tracking price changes to analyzing business growth.

The Percentage Change Formula

The universal formula for calculating percentage change is:

Percentage Change = ((New Value - Original Value) ÷ Original Value) × 100

Important: A positive result indicates an increase, while a negative result indicates a decrease.

Calculating Percentage Increase

Example 1: Salary Increase

Question: Your salary increased from R25,000 to R28,000. What's the percentage increase?

Solution:
Step 1: Find the difference: R28,000 - R25,000 = R3,000
Step 2: Divide by original value: R3,000 ÷ R25,000 = 0.12
Step 3: Multiply by 100: 0.12 × 100 = 12%
Answer: Your salary increased by 12%

Example 2: Population Growth

Question: A town's population grew from 50,000 to 62,500. What's the percentage increase?

Solution:
Step 1: Find the difference: 62,500 - 50,000 = 12,500
Step 2: Divide by original: 12,500 ÷ 50,000 = 0.25
Step 3: Multiply by 100: 0.25 × 100 = 25%
Answer: The population increased by 25%

Example 3: Stock Price Increase

Question: A stock rose from R45 to R54. What's the percentage gain?

Solution:
Step 1: Find the difference: R54 - R45 = R9
Step 2: Divide by original: R9 ÷ R45 = 0.20
Step 3: Multiply by 100: 0.20 × 100 = 20%
Answer: The stock increased by 20%

Calculating Percentage Decrease

Example 4: Sales Discount

Question: A laptop was R12,000, now on sale for R9,600. What's the discount percentage?

Solution:
Step 1: Find the difference: R12,000 - R9,600 = R2,400
Step 2: Divide by original: R2,400 ÷ R12,000 = 0.20
Step 3: Multiply by 100: 0.20 × 100 = 20%
Answer: The discount is 20%

Example 5: Weight Loss

Question: Someone's weight decreased from 90kg to 81kg. What's the percentage decrease?

Solution:
Step 1: Find the difference: 90 - 81 = 9
Step 2: Divide by original: 9 ÷ 90 = 0.10
Step 3: Multiply by 100: 0.10 × 100 = 10%
Answer: Weight decreased by 10%

Example 6: Business Revenue Decline

Question: Revenue dropped from R500,000 to R425,000. What's the percentage decrease?

Solution:
Step 1: Find the difference: R500,000 - R425,000 = R75,000
Step 2: Divide by original: R75,000 ÷ R500,000 = 0.15
Step 3: Multiply by 100: 0.15 × 100 = 15%
Answer: Revenue decreased by 15%

Special Cases & Common Mistakes

Mistake 1: Using the Wrong Base Value

Always divide by the original (starting) value, not the new value.

Wrong: (New - Old) ÷ New × 100
Correct: (New - Old) ÷ Old × 100

Mistake 2: Percentage vs Percentage Points

If interest rates go from 5% to 7%, that's NOT a 2% increase.

The change is 2 percentage points, but the percentage increase is:
(7 - 5) ÷ 5 × 100 = 40% increase

Case 3: 100% Increase = Doubling

A 100% increase means the value doubled.
Example: R100 increased by 100% = R200

Case 4: Maximum Decrease is 100%

You can't decrease by more than 100% (that would mean going below zero).
If something goes from R100 to R0, that's a 100% decrease.

Reverse Calculations

Finding Original Value After Increase

Question: After a 20% increase, a price is R120. What was the original price?

Solution:
If 120% = R120, then 100% = R120 ÷ 1.20 = R100
Answer: Original price was R100

Finding Original Value After Decrease

Question: After a 25% discount, an item costs R300. What was the original price?

Solution:
If 75% = R300, then 100% = R300 ÷ 0.75 = R400
Answer: Original price was R400

Real-World Applications

Retail & Shopping: Compare sale prices, calculate actual savings, determine if a discount is worthwhile.

Business & Finance: Track revenue growth, analyze profit margins, measure investment returns, monitor expenses.

Personal Finance: Calculate salary increases, track savings growth, monitor debt reduction, analyze spending changes.

Health & Fitness: Measure weight loss progress, track workout improvements, monitor calorie reduction.

Real Estate: Analyze property value changes, calculate appreciation rates, assess market trends.

Quick Reference Table

Common Percentage Changes:

• 25% increase: Multiply original by 1.25
• 50% increase: Multiply original by 1.50
• 100% increase: Multiply original by 2
• 10% decrease: Multiply original by 0.90
• 25% decrease: Multiply original by 0.75
• 50% decrease: Multiply original by 0.50

Practice Problems

Problem 1: A product price increased from R80 to R100. What's the percentage increase?
Answer: 25%

Problem 2: Sales decreased from 2,000 units to 1,500 units. What's the percentage decrease?
Answer: 25%

Problem 3: After a 15% increase, a salary is R34,500. What was it before?
Answer: R30,000

Use Our Calculator

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