On This Page
- How to use this calculator
- What is percentage increase?
- Percentage increase formula
- Percentage decrease
- Salary and pay rise calculations
- Price increase calculations
- Percentage increase in Excel
- Worked examples
- Frequently asked questions
How to Use This Calculator
Three modes cover every common percentage change problem. Choose from the dropdown, enter your values, and the result appears instantly with a full step-by-step breakdown.
Find % change between two numbers
The default mode. Enter the original (old) value and the new value. The calculator finds the percentage increase or decrease between them, the absolute change, the multiplier, and the new value expressed as a percentage of the original. Use this when you have both numbers and need to know the percentage shift: price changes, sales figures, population data, test scores, or any before-and-after comparison.
Find new value after % increase
Enter the original value and a percentage change. Use a positive number for an increase, negative for a decrease. The calculator returns the new value and the absolute change amount. Use this for salary after a raise, a price after a markup, a population after growth, or any future-value question where you know the rate of change.
Find original value before % change
The reverse calculation. Enter the new value and the percentage change that produced it, and the calculator works backwards to find what the original value was. This is useful when you know the current figure and the rate of change but need to verify or audit the starting point, such as finding a pre-tax price from a post-tax price or finding last year's salary from this year's figure and the raise percentage.
What Is Percentage Increase?
Percentage increase measures how much a value has grown relative to its original amount, expressed as a percentage. It answers the question: by what fraction of the original did this value go up?
The key word is "relative." An increase of 20 units means very different things depending on the starting point. Going from 20 to 40 is a 100% increase. Going from 2000 to 2020 is a 1% increase. The absolute change is the same ($20), but the percentage increase reflects the size of the change in context.
Percentage increase appears in almost every area of quantitative reasoning: economics (GDP growth, inflation), business (revenue growth, margin expansion), personal finance (salary negotiation, investment returns), statistics (year-over-year comparisons), and science (experimental change measurement). The formula is the same across all of them.
Percentage Increase Formula
The formula has three components: the new value, the original (old) value, and 100 to convert the decimal fraction to a percentage.
Step through it: subtract the old value from the new to get the absolute change. Divide by the old value to express that change as a fraction of the original. Multiply by 100 to convert the fraction to a percentage.
Example: a product priced at $80 is now $100. Absolute change: $100 − $80 = $20. As a fraction of the original: $20 ÷ $80 = 0.25. As a percentage: 0.25 × 100 = 25% increase.
Finding the new value from a percentage increase
Rearrange to solve for the new value when you know the original and the percentage change.
Example: a salary of $50,000 increases by 8%. New salary = $50,000 × (1 + 8/100) = $50,000 × 1.08 = $54,000. The multiplier 1.08 means "100% of the original plus 8% more."
Finding the original value from a percentage increase
If you know the new value and the percentage change, you can reverse-engineer the original.
Example: a salary is now $54,000 after an 8% raise. Original = $54,000 ÷ 1.08 = $50,000. This is the exact reverse of the forward calculation. The Percentage Calculator covers this and four other percentage problem types if you need a different calculation mode.
The multiplier shortcut
For repeated or chained percentage changes, use multipliers instead of the full formula each time. A 25% increase has a multiplier of 1.25. A 10% decrease has a multiplier of 0.90. Two consecutive 10% increases: 1.10 × 1.10 = 1.21, so the total increase is 21%, not 20%. Percentages do not add directly when applied in sequence.
Percentage Decrease
The formula for percentage decrease is identical to percentage increase. When the new value is lower than the original, the result is negative, indicating a decrease.
Some textbooks write this formula with the subtraction reversed (old minus new) to get a positive number labeled "percentage decrease." This calculator uses the signed version: positive results are increases, negative results are decreases. Both conventions are correct as long as you are consistent.
Example: a stock falls from $150 to $120. Change: (120 − 150) ÷ 150 × 100 = −30 ÷ 150 × 100 = −20%. A 20% decrease. To find what price represents a 20% drop from $150, use the new-value formula: $150 × (1 − 0.20) = $150 × 0.80 = $120. ✓
But here's a catch that trips people up: a 20% decrease followed by a 20% increase does not get you back to the original. Starting at $150: after −20%, you have $120. After +20% on $120: $120 × 1.20 = $144, not $150. The percentage is applied to a different base each time. This is why index funds recovering from a 50% crash need a 100% gain just to break even.
Salary and Pay Rise Calculations
Salary negotiation is one of the most common real-life uses for the percentage increase formula. Knowing the math means you can quickly evaluate an offer, translate a percentage raise into actual dollars, or figure out what percentage rise you need to hit a target salary.
Calculating your pay rise amount
New salary = current salary × (1 + raise % ÷ 100). A 5% raise on $65,000: $65,000 × 1.05 = $68,250. The raise amount is $68,250 − $65,000 = $3,250 per year, or about $271 per month before tax.
Asking for a specific dollar amount
To figure out what percentage raise you need to reach a target, use the percentage increase formula with your current salary as "old" and your target as "new." If you earn $65,000 and want $72,000: ($72,000 − $65,000) ÷ $65,000 × 100 = $7,000 ÷ $65,000 × 100 = 10.77% raise required.
Year-over-year salary growth
For multi-year projections, chain the multipliers. Three consecutive 4% raises on a $60,000 salary: $60,000 × 1.04 × 1.04 × 1.04 = $60,000 × 1.04³ = $60,000 × 1.1249 = $67,493. The total increase is not 12% (3 × 4%) but 12.49% because each raise is applied to a slightly larger base than the last. The Work Hours Calculator converts your hourly wage to annual salary if you need to normalize a wage comparison before applying a percentage change.
Price Increase Calculations
Price changes in retail, supply chain, and product management require the same formula. The most common scenarios involve finding a percentage change from two known prices, or calculating a new price from a target percentage increase.
Supplier price increase
A supplier raises a component price from $4.20 to $4.85. What is the percentage increase? ($4.85 − $4.20) ÷ $4.20 × 100 = $0.65 ÷ $4.20 × 100 = 15.48% increase. This tells you exactly how much your input cost has grown, letting you decide whether to absorb, pass through, or partially offset the increase.
Setting a price after a target increase
A retailer needs to raise prices by 12% due to inflation. Current price: $29.99. New price = $29.99 × 1.12 = $33.59. Rounding to $33.99 adds a small additional margin. The Markup Calculator covers the related question of how markup percentage translates into gross margin, which is the other side of the pricing equation.
Compounding price increases over time
Inflation compounds. A product that costs $100 today at 6% annual inflation: after one year $106, after two years $112.36, after five years $133.82. The formula is $100 × 1.06^n where n is the number of years. Straight multiplication ($100 × 1.30 for 5 years of 6%) would give $130, understating the true compounded result by $3.82.
Percentage Increase in Excel
Excel handles percentage increase in a few different ways depending on what you need. All formulas assume old value is in cell A2 and new value is in B2.
Basic percentage change formula
=(B2-A2)/A2. Format the cell as "Percentage" to display the result as a percentage. Excel applies the ×100 conversion automatically when a cell is formatted as percentage. If you want the decimal result: =(B2-A2)/A2 gives 0.25 for a 25% increase.
Absolute percentage change (always positive)
=ABS((B2-A2)/A2). Use this when you want a number without a sign and will label increase/decrease separately.
New value after a percentage increase
If original value is in A2 and the percentage increase is in C2 (entered as 25, not 0.25): =A2*(1+C2/100). If C2 is already formatted as a percentage (i.e., you typed 25% into the cell): =A2*(1+C2).
Year-over-year change for a data column
If monthly revenue is in column B starting at B2, year-over-year change for B14 (this January vs last January in B2): =(B14-B2)/B2. To fill down automatically for a full year comparison, use =(B14-B2)/B2 and drag the formula down. Wrap in IFERROR(..., "") to suppress errors for blank cells at the end of the range.
For more percentage operations in Excel, the Percentage Calculator article covers Excel formulas for all five percentage problem types.
Worked Examples
Example 1: Monthly Revenue Growth
A business had $42,000 revenue in March and $51,660 in April. What is the percentage increase?
Change: ($51,660 − $42,000) ÷ $42,000 × 100 = $9,660 ÷ $42,000 × 100 = 23% increase. A strong month-on-month result. The absolute gain was $9,660.
Example 2: Salary After a 7% Raise
An employee earns $58,000. They receive a 7% pay rise. What is the new salary?
New salary = $58,000 × (1 + 7 ÷ 100) = $58,000 × 1.07 = $62,060. The raise adds $4,060 per year. Monthly: $62,060 ÷ 12 = $5,171.67.
Example 3: Finding the Original Price Before a 15% Increase
A product now sells for $92. The price was raised by 15% last quarter. What was the original price?
Original = $92 ÷ (1 + 15 ÷ 100) = $92 ÷ 1.15 = $80.00. The $12 increase was exactly 15% of the $80 original. Verify: $80 × 1.15 = $92. ✓
Example 4: Population Decline
A town's population fell from 84,000 to 71,400. What is the percentage decrease?
Change: (71,400 − 84,000) ÷ 84,000 × 100 = −12,600 ÷ 84,000 × 100 = −15% (a 15% decrease). The negative sign confirms the direction.
Example 5: Two-Year Compounded Salary Growth
A starting salary of $45,000 receives a 6% raise after year one and a 4% raise after year two. What is the salary after both raises?
After year one: $45,000 × 1.06 = $47,700. After year two: $47,700 × 1.04 = $49,608. Total percentage increase over two years: ($49,608 − $45,000) ÷ $45,000 × 100 = 10.24%, not 10% (6% + 4%), because the second raise is applied to the already-raised salary.
Frequently Asked Questions
How do you calculate percentage increase?
Subtract the old value from the new value, divide by the old value, then multiply by 100. Formula: ((New − Old) ÷ Old) × 100. Example: from 50 to 65, the increase is (65 − 50) ÷ 50 × 100 = 15 ÷ 50 × 100 = 30%.
How do you calculate percentage increase between two numbers?
Use the same formula: ((New − Old) ÷ Old) × 100. The "old" number is always the reference point (the denominator). Going from 200 to 250: (250 − 200) ÷ 200 × 100 = 50 ÷ 200 × 100 = 25%. Going from 250 to 200 (a decrease): (200 − 250) ÷ 250 × 100 = −50 ÷ 250 × 100 = −20%.
What is the formula for percentage increase?
% Increase = ((New Value − Old Value) ÷ Old Value) × 100. The formula works for any pair of numbers. If the result is positive, it is an increase. If negative, it is a decrease. The absolute value of the result gives the magnitude regardless of direction.
How do you calculate salary percentage increase?
Treat current salary as the old value and the new salary as the new value, then apply the formula. Current salary $62,000, new offer $67,000: ($67,000 − $62,000) ÷ $62,000 × 100 = $5,000 ÷ $62,000 × 100 = 8.06% raise. To find a new salary from a known raise percentage: new salary = current salary × (1 + raise% ÷ 100).
How do you calculate percentage increase in Excel?
With old value in A2 and new value in B2, use =(B2-A2)/A2 and format the cell as percentage. Excel multiplies by 100 automatically when you apply percentage formatting. To display as a decimal: leave the cell unformatted and the result is between −1 and 1 (e.g., 0.25 = 25% increase).
How do you calculate percentage increase in salary?
If you already have both salaries: ((New Salary − Old Salary) ÷ Old Salary) × 100. If you have the old salary and the raise percentage: new salary = old salary × (1 + raise% ÷ 100). If you have the new salary and the raise percentage: old salary = new salary ÷ (1 + raise% ÷ 100). All three modes are available in this calculator.
How do you calculate price percentage increase?
Same formula as any other percentage increase: ((New Price − Old Price) ÷ Old Price) × 100. Old price $24.99, new price $27.99: ($27.99 − $24.99) ÷ $24.99 × 100 = $3.00 ÷ $24.99 × 100 = 12.0%.
What is the difference between percentage increase and percentage change?
"Percentage change" is the general term that covers both increases and decreases. "Percentage increase" specifically implies the change is positive (upward). Both use the same formula. The result of the formula tells you which one applies: positive = increase, negative = decrease. Many people use the terms interchangeably in everyday language.
Can percentage increase be more than 100%?
Yes. If a value doubles, the percentage increase is 100%. If it triples, the increase is 200%. If it goes from 10 to 150, the increase is (150 − 10) ÷ 10 × 100 = 1400%. There is no upper limit on percentage increase. However, percentage decrease is capped at 100% (you cannot decrease by more than the full original value, assuming the value cannot go below zero).
How do you calculate percentage increase year over year?
Use the same formula with this year's value as "new" and last year's value as "old." Revenue this year $2.4M, last year $2.1M: ($2.4M − $2.1M) ÷ $2.1M × 100 = $0.3M ÷ $2.1M × 100 = 14.3% year-over-year growth. For multi-year compound annual growth rate (CAGR), use the formula: CAGR = (End Value ÷ Start Value)^(1/years) − 1.
How do you calculate a percentage increase of a percentage?
Treat the original percentage as a regular number. If interest rates rise from 3.5% to 4.2%, the percentage change in the rate is (4.2 − 3.5) ÷ 3.5 × 100 = 20%. Note the difference between "percentage points" (4.2% − 3.5% = 0.7 percentage points, an absolute difference) and "percentage change" (20%, a relative change). A rate rising from 3.5% to 4.2% is a 0.7 percentage point increase and a 20% percentage change in the rate itself.
References
- Khan Academy: Percent Change Review: Clear explanation of percentage change with worked examples and practice problems.
- Microsoft Support: Calculate Percentage Change in Excel: Official Microsoft documentation on percentage change formulas in Excel with step-by-step instructions.
- U.S. Bureau of Labor Statistics: Computing Price Changes: How the BLS calculates inflation as a percentage change, with real-world application of the formula.