Few math skills feel as immediately useful as knowing how to calculate a percentage increase. Whether you’re negotiating a raise, comparing grocery prices, or figuring out how much a 5% jump really costs, this simple formula puts real numbers behind everyday decisions.
5% increase of $100: $5 ·
2% increase on $80,000: $1,600 ·
3% increase on $20: $0.60 ·
Typical annual salary raise percentage: 3–5%
Quick snapshot
- Formula: (New – Original) / Original × 100 (Britannica (educational publisher))
- Negative result means decrease (Britannica (educational publisher))
- Historical average salary raise percentages vary by industry and year (Paycor (HR and payroll platform))
- Use when comparing old and new values over time — salary reviews, price changes, investment returns
- Apply formula to your own numbers: salary negotiations, budgeting, cost comparisons
Four numbers, one pattern: formula stays the same whether you’re working out a raise or a grocery price jump.
| Label | Value |
|---|---|
| Formula | (New – Original) / Original × 100 |
| Example: 5% of $100 | $5 increase, new total $105 |
| Example: 2% of $80,000 | $1,600 increase |
| Typical annual raise | 3–5% (BLS data) |
Why this matters: A 2% raise on $80,000 adds $1,600 — enough to cover a month’s rent in many markets. Knowing the math puts you in control.
How do I calculate a percentage increase?
Percentage increase formula
The standard formula is straightforward: subtract the original value from the new value, divide by the original value, then multiply by 100. According to Britannica (educational publisher), the formula is:
(New Value – Original Value) ÷ Original Value × 100
Always divide by the starting number — a common mistake is dividing by the new value instead. The result is a percentage without a unit.
Step-by-step example: from $50 to $65
- New value: $65, Original value: $50
- Difference: $65 – $50 = $15
- Divide by original: $15 ÷ $50 = 0.3
- Multiply by 100: 0.3 × 100 = 30% increase
This is the same approach used by Omni Calculator (online calculation tool) for their pay raise calculator: new salary = old salary + (old salary × raise %). The difference ($15) is 30% of the original $50.
Anyone negotiating a pay rise who can show the math as a percentage — not just a dollar figure — looks more informed. A 30% increase sounds more concrete than “fifteen bucks more.”
The pattern: The formula is indifferent to context. Whether it’s dollars, kilograms, or exam points, the arithmetic stays identical. The only variable is which value you call “original.”
How do I calculate the percentage change between two numbers?
Distinguishing percentage increase vs decrease
The same formula handles both directions. If the result is positive, it’s an increase; if negative, a decrease. Britannica (educational publisher) notes that a negative final value indicates a decrease, not an increase. For example, a price drop from $80 to $60 gives:
- ($60 – $80) ÷ $80 × 100 = -25%
That minus sign signals a 25% decrease, not an increase.
Interpreting negative results
A negative percentage change is perfectly valid — it means the new value is smaller. When using the formula for salary comparisons or budget tracking, the sign shows the direction. As Patriot Software (payroll software provider) explains, the percent raise formula is [(New Salary – Old Salary) / Old Salary] × 100, and a negative result would mean a pay cut.
Don’t drop the sign. Many people mistakenly use the absolute difference, which makes every change look like an increase. That erases the most important information: whether you’re gaining or losing.
The trade-off: The formula is blind to context — a 5% salary increase and a 5% price hike use the same math, but their real-world implications are opposite. Always pair the number with the context.
How much is a 5% increase on $20?
Let’s walk through a concrete monetary example. You want to know the new total after a 5% increase on $20. First, find 5% of $20:
- 5% means 5 per hundred, or 0.05 as a decimal
- 0.05 × $20 = $1 increase
- New total: $20 + $1 = $21
Alternatively, multiply the original by 1.05 (1 + 0.05): $20 × 1.05 = $21. This shortcut works for any percentage increase — multiply by (1 + percentage/100). The same method is used by Inch Calculator (calculation resource) for salary calculations.
Why this matters: A 5% increase on $20 is only $1, but applied to a $200,000 mortgage payment it’s $10,000. The percentage is constant; the dollar impact scales with the base. For a real-world example, see our guide on How Much Mortgage Can I Get to see how interest rate changes affect borrowing power.
How to calculate salary raise percentage?
Salary negotiations often hinge on a single percentage. Knowing how to calculate it — and what it means for your take-home pay — is essential.
Calculating a raise from current salary to new salary
The formula is the same: (new salary – old salary) ÷ old salary × 100. ADP (payroll and HR provider) gives an example: a $65,000 salary with a 4% raise becomes $67,600. Working backwards, ($67,600 – $65,000) / $65,000 × 100 = 4%.
- Example: $50,000 to $52,000 → ($2,000 ÷ $50,000) × 100 = 4% increase
- Example from AV Trinity (UK finance news): a £5,000 raise on £50,000 gives (5,000 ÷ 50,000) × 100 = 10%.
Comparing raise percentages across different salary levels
A 2% raise on $80,000 yields $1,600; a 3% raise on $30,000 yields $900. The percentage feels similar but the absolute difference matters. Paycor (HR and payroll platform) notes that HR pay raises often include merit increases benchmarked against market data.
- 2% increase on $80,000 = $1,600 extra annually (AV Trinity (UK finance news) example for £30k shows £600 for 2%)
- 3% increase on $20/hour = $0.60/hour rise
Inch Calculator (calculation resource) adds that annual salary can be approximated by multiplying hourly wage by 2,080 (40 hours × 52 weeks).
When comparing raise offers across employers, the percentage is only half the story. A 5% raise at a low base may be less in dollar terms than a 3% raise at a high base. Always convert to dollars to compare buying power.
The implication: A typical annual raise of 3-5% may feel modest, but over a career those percentages compound. Knowing the math helps you push for a number backed by data, not emotion.
How to calculate percentage increase or decrease?
This section covers both directions and common pitfalls.
Common mistakes when working with percentage decrease
- Dividing by the new value: Always divide by the original. Using $40 instead of $50 in the earlier example would give -25% instead of the correct -25%? Actually dividing by original gives correct -25%; dividing by new gives different. The mistake leads to wrong percentages.
- Forgetting to multiply by 100: The raw decimal (e.g., 0.25) is not a percentage — it’s 25% only after multiplying.
- Using absolute value: The sign matters. A -25% signals a decrease; ignoring the sign hides the direction.
Britannica (educational publisher) cautions that when the starting value is zero, percentage change is undefined — you cannot divide by zero.
Real-world examples: discounts, population change
- Discount: $50 item on sale for $40 → (40-50)/50 × 100 = -20% (20% discount)
- Population: Town grows from 2000 to 2600 → (600/2000)×100 = 30% increase
Population growth in biology uses the same formula, often written as (final – initial)/initial × 100. The same math applies whether you’re tracking bacteria cultures or company revenue.
The catch: Percentage decrease can never exceed 100% (that would mean the value goes to zero or below). But percentage increase has no upper limit — a tripling is a 200% increase.
Step-by-Step Calculation Guide
- Identify the two numbers: Original (starting) value and New (final) value.
- Subtract original from new: New – Original = Difference.
- Divide the difference by the original: Difference ÷ Original = Decimal.
- Multiply by 100: Decimal × 100 = Percentage increase (or decrease if negative).
For salary raises, Patriot Software (payroll software provider) recommends also converting the percentage to a decimal, multiplying by current pay, and adding the result to the old salary to get the new pay.
What We Know and What’s Unclear
Confirmed facts
- Formula is mathematically correct: (New – Original) / Original × 100 (Britannica (educational publisher))
- Percentage increase can exceed 100% (e.g., tripling = 200% increase)
- Negative result = decrease (Britannica (educational publisher))
What’s unclear
- Historical average salary raise percentages vary significantly by industry and year (Paycor (HR and payroll platform))
- Whether the formula using absolute value for the starting value (as Britannica does) is always appropriate for negative baselines
- Exact median raise percentage across all US private-sector jobs in 2024
Insights from Experts
“To calculate percentage increase, subtract the original number from the new number, divide that difference by the original number, and then multiply by 100. It’s a method that works for everything from exam scores to house prices.”
“Percent increase expresses the magnitude of change from a starting point to a final point. The larger the percentage, the greater the magnitude of change.”
— Britannica (educational publisher)
With the cost of living putting pressure on household budgets, understanding percentage increase helps you evaluate whether a raise truly keeps pace with inflation. For a broader look at the financial landscape, see our analysis of the Cost of Living Crisis UK.
For a broader understanding, you can also refer to our guide on general percentage calculation to see how the same formula applies to various scenarios.
Frequently asked questions
How to calculate percentage increase in Excel?
In Excel, subtract the old value from the new value, divide by the old value, then format as percentage. Example: =(B2-A2)/A2 and format cell as %.
What is the percentage increase from 0 to 10?
Undefined. Division by zero is not possible. Percentage change requires a non-zero starting point.
How to calculate percentage increase without a calculator?
Use pen and paper: subtract, divide, multiply by 100. For simple numbers like 20 to 25, find the fraction (5/20 = 0.25 = 25%) mentally.
Can percentage increase be more than 100%?
Yes. A tripling of value yields a 200% increase. There is no upper bound for percentage increase.
What is the difference between percentage increase and percentage point increase?
A percentage increase is relative to the original number. A percentage point increase is an absolute change in a percentage value. For example, a rise from 4% to 6% is a 2 percentage point increase but a 50% increase.
How to calculate a 10% increase on a price?
Multiply the price by 1.10. Example: $80 × 1.10 = $88.
How to calculate percentage increase in biology (e.g., population growth)?
Use same formula: (final population – initial population) / initial population × 100. Example: 200 to 280 = (80/200)×100 = 40% increase.
For the millions of workers negotiating raises and families budgeting against rising costs, the percentage increase formula is more than a math trick — it’s a tool for real-world decisions. The choice is clear: learn the formula, or let others calculate your numbers for you.
Harriet Langford is Editor-in-Chief at WordPatch.co.uk, overseeing editorial policy, corrections, standards, submissions policy and publication decisions. She writes occasional editorial columns and covers major publishing stories.