Percentage Increase Formula with Examples
What Is Percentage Increase?
Percentage increase measures how much a value has grown compared to its original value, expressed as a percentage. It tells you not just by how much something went up, but by how much it went up relative to where it started.
This makes percentage increase far more meaningful than a raw number. For example, a salary raise of $500 means something very different if your original salary was $1,000 versus $50,000. The percentage increase captures that context clearly.
Percentage increase is used in almost every field — finance, economics, science, health, business, and everyday life. Whether you are tracking price changes, population growth, revenue gains, or exam score improvements, this formula gives you the answer.
The Percentage Increase Formula
The standard formula for percentage increase is:
Percentage Increase = [(New Value − Old Value) / Old Value] × 100
Where:
- New Value = the value after the increase
- Old Value = the original value before the increase
The result is always expressed as a percentage (%). A positive result confirms an increase. If your result is negative, the value actually decreased — use the percentage decrease formula instead.
Step-by-Step Examples
Example 1 — Price Increase
Problem: The price of a product increased from $80 to $100. What is the percentage increase?
Old Value = 80, New Value = 100
Percentage Increase = [(100 − 80) / 80] × 100
= [20 / 80] × 100
= 0.25 × 100
Answer: 25% increase
Example 2 — Salary Increase
Problem: An employee's salary increased from $3,200 to $4,000 per month. What is the percentage increase in salary?
Old Value = 3200, New Value = 4000
Percentage Increase = [(4000 − 3200) / 3200] × 100
= [800 / 3200] × 100
= 0.25 × 100
Answer: 25% increase
Example 3 — Population Growth
Problem: A city's population grew from 1,200,000 to 1,380,000 in five years. What is the percentage increase in population?
Old Value = 1,200,000, New Value = 1,380,000
Percentage Increase = [(1,380,000 − 1,200,000) / 1,200,000] × 100
= [180,000 / 1,200,000] × 100
= 0.15 × 100
Answer: 15% increase
Example 4 — Exam Score Improvement
Problem: A student scored 60 marks in the first test and 78 marks in the second test. By what percentage did their score increase?
Old Value = 60, New Value = 78
Percentage Increase = [(78 − 60) / 60] × 100
= [18 / 60] × 100
= 0.30 × 100
Answer: 30% increase
Example 5 — Finding the New Value After a Percentage Increase
Problem: A laptop costs $750. Its price increases by 20%. What is the new price?
Old Value = 750, Percentage Increase = 20%
Increase Amount = (20 / 100) × 750 = 150
New Value = Old Value + Increase Amount
New Value = 750 + 150
Answer: $900
Or using the direct formula:
New Value = Old Value × (1 + Percentage Increase / 100)
New Value = 750 × (1 + 20/100)
New Value = 750 × 1.20
Answer: $900
Example 6 — Finding the Original Value Before an Increase
Problem: After a 25% increase, the price of a item is $500. What was the original price?
New Value = 500, Percentage Increase = 25%
Old Value = New Value / (1 + Percentage Increase / 100)
Old Value = 500 / (1 + 25/100)
Old Value = 500 / 1.25
Answer: $400
Percentage Increase vs Percentage Decrease
It is important to know when to use which formula.
Percentage Increase is used when the new value is greater than the old value.
Formula: [(New − Old) / Old] × 100
Percentage Decrease is used when the new value is less than the old value.
Formula: [(Old − New) / Old] × 100
Percentage Change is the general formula that works for both. A positive result means increase. A negative result means decrease.
Formula: [(New − Old) / Old] × 100
| Situation | Old Value | New Value | Result |
|---|---|---|---|
| Price goes up | $200 | $250 | +25% increase |
| Price goes down | $200 | $150 | −25% decrease |
| No change | $200 | $200 | 0% change |
Common Mistake to Avoid
Many people accidentally calculate the percentage increase based on the new value instead of the old value. This gives a wrong answer.
Wrong: [(New − Old) / New] × 100
Correct: [(New − Old) / Old] × 100
Always divide by the original (old) value — not the new one.
Quick Reference — Percentage Increase Formulas
| What to Find | Formula |
|---|---|
| Percentage Increase | [(New − Old) / Old] × 100 |
| New Value | Old Value × (1 + % / 100) |
| Old Value | New Value / (1 + % / 100) |
| Increase Amount | (Percentage / 100) × Old Value |
Related Formulas
Percentage increase connects directly to several other important formulas:
- Percentage Decrease Formula — Used when a value falls instead of rises. The reverse of percentage increase. [See Percentage Decrease Formula →]
- Percentage Formula — The foundation of all percentage calculations including increase and decrease. [See Percentage Formula →]
- Percentage Change Formula — A general formula that covers both increase and decrease in one calculation. [See Percentage Change Formula →]
- Profit and Loss Formula — Profit percentage is essentially a percentage increase over the cost price. [See Profit and Loss Formula →]
- Compound Interest Formula — Compound growth uses repeated percentage increase applied over multiple periods. [See Compound Interest Formula →]
- Simple Interest Formula — Interest earned on a deposit is a type of percentage increase on the principal. [See Simple Interest Formula →]
Related Calculators and Pages
Frequently Asked Questions (FAQ )
Q1. What is the percentage increase formula?
The percentage increase formula is: Percentage Increase = [(New Value − Old Value) / Old Value] × 100. It measures how much a value has grown relative to its original amount, expressed as a percentage.
Q2. How do you calculate percentage increase in price?
Subtract the old price from the new price, divide the result by the old price, then multiply by 100. For example, if a price goes from $50 to $60: [(60 − 50) / 50] × 100 = 20% increase.
Q3. What is the difference between percentage increase and percentage change?
Percentage change is the general formula that works for both increases and decreases. A positive result is a percentage increase. A negative result is a percentage decrease. The formula is the same: [(New − Old) / Old] × 100.
Q4. How do you find the new value after a percentage increase?
Multiply the old value by (1 + percentage / 100). For example, if the original price is $200 and it increases by 15%: New Value = 200 × 1.15 = $230.
Q5. How do you find the original value before a percentage increase?
Divide the new value by (1 + percentage / 100). For example, if a price after a 20% increase is $240: Old Value = 240 / 1.20 = $200.
Q6. Can percentage increase be more than 100%?
Yes. A percentage increase greater than 100% means the value more than doubled. For example, if a value goes from $50 to $150, the increase is [(150 − 50) / 50] × 100 = 200%. This is perfectly valid and common in areas like investment returns and business growth.
Summary
The percentage increase formula — [(New Value − Old Value) / Old Value] × 100 — is one of the most widely used calculations in mathematics, finance, and everyday life. It tells you exactly how much a value has grown in percentage terms relative to where it started.
Always remember to divide by the old value, not the new one. Use the rearranged versions of the formula to find the new value, the original value, or the amount of increase when needed.
Paired with the percentage decrease formula and the general percentage change formula, you have a complete toolkit for analyzing any change in value — whether it is a price, a salary, a population, or a test score.