Calculate the percentage increase or decrease between two values instantly with detailed step-by-step solutions. This advanced calculator helps students, business professionals, and anyone needing to understand percent change between an original value and a new value.
Input Values
Quick Examples:
50 → 65
120 → 150
80 → 72
10k → 12.5k
Results
Enter values to see results
How to Calculate Percentage Increase
Calculating percentage increase helps you understand the relative change between two values. Follow these steps:
Find the difference: Subtract the original value from the new value to get the absolute change.
Divide by the original: Take the difference and divide it by the original (old) value to get the rate of change.
Convert to percentage: Multiply the rate by 100 to express it as a percentage.
This method works for any scenario where you need to measure growth, such as salary increases, population growth, revenue changes, or price adjustments.
Percentage Increase Formula
The mathematical formula for calculating percentage increase is:
Where:
New Value is the final or current value
Old Value is the original or initial value
Δ (Delta) represents the absolute change
For percentage decrease, the formula remains the same, but the result will be negative. The absolute value is often used to express decrease as a positive number with "decrease" label.
Worked Examples
Example 1: Salary Increase
A teacher's salary increases from AED 8,000 to AED 9,200. What is the percentage increase?
Step 1: Find the change:
Step 2: Calculate the rate:
Step 3: Convert to percentage:
Answer: The salary increased by 15%
Example 2: Student Enrollment
A school in Dubai had 450 students last year and now has 540 students. Calculate the percentage increase in enrollment.
Step 1: Change = 540 - 450 = 90 students
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. What is the percentage decrease?
Dividing by the new value instead of the old: Always divide by the original (old) value, not the new value. This is the most common error.
Forgetting to multiply by 100: The result of dividing the change by the original is a decimal rate. Don't forget to multiply by 100 to get a percentage.
Confusing percentage points with percentage change: A change from 20% to 25% is a 5 percentage point increase, but a 25% relative increase.
Handling zero as original value: If the original value is 0, percentage increase is mathematically undefined. Use absolute change instead.
Negative values without context: When working with negative numbers (debts, temperatures below zero), ensure you understand the direction of change.
Rounding too early: Round only the final answer to avoid accumulating rounding errors in multi-step calculations.
Frequently Asked Questions
What is percentage increase?
Percentage increase is the relative change between an original value and a new higher value, expressed as a percentage of the original value. It shows by what percent the original value has grown.
How do you calculate percent increase between two numbers?
Subtract the old value from the new value to find the change, divide the change by the old value, then multiply by 100. Formula: ((New - Old) / Old) × 100%
What's the difference between percentage increase and percentage change?
Percentage increase specifically refers to when the new value is greater than the old value (positive change). Percentage change is a broader term that includes both increases (positive) and decreases (negative).
Can percentage increase be negative?
No, by definition percentage increase is always positive or zero. If the calculation yields a negative result, it's actually a percentage decrease, not an increase.
What if the original value is zero?
When the original value is zero, percentage increase is mathematically undefined (division by zero). Instead, report the absolute change (e.g., "increased from 0 to 50") or state the new value directly.
How is percentage increase used in business?
Businesses use percentage increase to track revenue growth, sales performance, profit margins, customer acquisition rates, and market share expansion. It provides a standardized way to compare performance across different time periods and metrics.
What's the difference between absolute change and percentage increase?
Absolute change is the numerical difference between two values (New - Old), while percentage increase expresses this change relative to the original value. For example, a change from 50 to 75 has an absolute change of 25 but a percentage increase of 50%.
Can you calculate percentage increase with negative numbers?
Yes, but interpretation requires care. For example, if a debt changes from -$100 to -$150, the formula works, but you're increasing in a negative direction. Context matters for interpreting whether this is good or bad.
How do you calculate percentage decrease?
The formula is identical to percentage increase: ((New - Old) / Old) × 100%. If the result is negative, it indicates a decrease. Many people prefer to report decrease as a positive number with the label "decrease" for clarity.
Is percentage increase the same as multiplier?
They're related but different. A multiplier shows how many times the original value the new value represents (New/Old). A 25% increase corresponds to a multiplier of 1.25, while a 100% increase means a multiplier of 2.0.
How accurate should percentage increase calculations be?
For most educational and general business purposes, 2 decimal places (e.g., 15.75%) is sufficient. Financial reporting may require more precision, while informal communication might round to whole numbers.
Can I use this calculator for exam preparation?
Yes! This calculator is perfect for students preparing for GCSE, IGCSE, IB, AP, or A-Level exams. Use it to check your work and understand the step-by-step process, but always show your working in exams.
About the Author: This calculator and educational content is provided by Numbers Institutes and Education LLC, a leading tutoring center in Dubai, UAE, specializing in mathematics, statistics, physics, chemistry, and biology. We serve students from primary through high school, offering both in-center and online tutoring services.
