Percentage Increase Calculator
Calculate percentage increase, percentage decrease, and overall percent change between two values with step-by-step working. Use it for exam practice, prices, salary changes, sales growth, enrollments, marks, and everyday percentage questions.
Quick Answer
Percentage increase = ((new value - old value) / old value) x 100. For example, if a value rises from 50 to 65, the increase is 15. Divide 15 by the old value 50, then multiply by 100: 30%.
The original value is always the denominator. Using the new value gives a different result.
If the answer is negative, the change is a percentage decrease, not an increase.
Percentage increase is undefined when the old value is zero because the formula divides by zero.
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How to Calculate Percentage Increase
Calculating percentage increase shows the relative change between an original value and a new value.
- Find the difference: subtract the original value from the new value.
- Divide by the original: take the difference and divide it by the original value.
- Convert to a percentage: multiply the result by 100.
Percentage Increase Formula
The standard formula is:
Where the old value is the original starting point and the new value is the final value.
| Scenario | Old Value | New Value | Change | Result |
|---|---|---|---|---|
| Price rises | 100 | 125 | +25 | 25% increase |
| Score improves | 60 | 72 | +12 | 20% increase |
| Price falls | 80 | 72 | -8 | 10% decrease |
Percentage Increase vs Percentage Change
Percentage increase is used only when the new value is higher than the old value. Percentage change is the broader term because it includes both increases and decreases. This calculator auto-detects the direction of change, then labels the result as an increase, decrease, or no change.
Worked Examples
Example 1: Salary Increase
A teacher's salary increases from AED 8,000 to AED 9,200. What is the percentage increase?
Worked Steps
Step 1: Change = 9,200 − 8,000 = 1,200
Step 2: Rate = 1,200 ÷ 8,000 = 0.15
Step 3: Percentage = 0.15 × 100 = 15%
Example 2: Student Enrollment
A school had 450 students last year and now has 540 students.
Step 1: Change = 540 − 450 = 90
Step 2: Rate = 90 ÷ 450 = 0.2
Step 3: Percentage = 0.2 × 100 = 20%
Example 3: Price Decrease
A laptop price drops from AED 3,500 to AED 2,800.
Step 1: Change = 2,800 − 3,500 = −700
Step 2: Rate = −700 ÷ 3,500 = −0.2
Step 3: Percentage = −0.2 × 100 = −20%, which is a 20% decrease
When to Use This Calculator
This calculator is useful when the question asks how much something grew or shrank compared with its starting value. Common uses include price changes, salary increases, business growth, population changes, test-score improvement, school enrollment, marks comparison, and finance homework.
Check percent change problems in GCSE, IGCSE, IB, AP, A-Level, SAT, and school math practice.
Measure sales growth, traffic changes, revenue increases, cost changes, or customer growth.
Compare discounts, rent changes, salary raises, savings growth, or price changes over time.
Common Mistakes to Avoid
- Dividing by the new value instead of the old value
- Forgetting to multiply by 100
- Confusing percentage points with percentage change
- Trying to calculate percentage increase when the original value is zero
- Rounding too early in a multi-step solution
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Percentage Increase GuideRead the full lesson-style explanation with more formula notes and examples.