On This Page
- Percentage increase formula
- How to calculate percentage increase
- What is percentage increase?
- Percentage decrease and repeated changes
- Examples: salary, prices and growth
- Percentage increase in Excel
- How this calculator is verified
- FAQ
Percentage Increase Formula
How to Calculate Percentage Increase
- Subtract the old value from the new value.
- Divide that difference by the old value.
- Multiply by 100.
From $80 to $100: the difference is $20, $20 ÷ $80 = 0.25, and 0.25 × 100 = 25%.
Finding the New Value or the Original Value
The calculator has a mode for each of the three things you might not know:
| You know | You want | Formula | Example |
|---|---|---|---|
| Old and new values | % change | (New − Old) ÷ Old × 100 | $80 to $100 = +25% |
| Old value and % | New value | Old × (1 + % ÷ 100) | $50,000 + 8% = $54,000 |
| New value and % | Original value | New ÷ (1 + % ÷ 100) | $54,000 after +8% = $50,000 |
Enter a negative percentage for a decrease. Results are signed, so a positive answer is an increase and a negative one is a decrease, and a badge above the result shows which. The Percentage Calculator covers other percentage questions, such as what percent one number is of another.
What Is Percentage Increase?
Percentage increase is how much a value has grown, expressed as a percentage of its starting value. It measures growth relative to where you started. Adding 20 turns 20 into 40, a 100% increase, but turns 2,000 into 2,020, just 1%. The same arithmetic works for GDP, prices, test scores and grades. Raising a GPA between terms is the same calculation run backward, as what GPA you need to raise your cumulative GPA shows.
Percentage Decrease and Repeated Changes
A percentage decrease uses the same formula, and the answer comes out negative: $150 to $120 is (120 − 150) ÷ 150 × 100 = −20%. Each change applies to a new base, so work with multipliers: +25% is ×1.25 and −10% is ×0.90.
- They compound. Two 10% rises are 1.10 × 1.10 = 1.21, a 21% rise, not 20%.
- They do not reverse. $150 down 20% is $120, but $120 up 20% is only $144. A 50% fall needs a 100% gain to break even.
- Percent is not percentage points. A rate moving from 3.5% to 4.2% is a 0.7-point rise but a 20% increase.
Percentage Increase Examples: Salary, Prices and Growth
Salary and Pay Rise Calculations
| Question | Working | Answer |
|---|---|---|
| 5% raise on $65,000 | $65,000 × 1.05 | $68,250 (+$3,250 a year) |
| Raise needed to go from $65,000 to $72,000 | $7,000 ÷ $65,000 × 100 | 10.77% |
| Three yearly 4% raises on $60,000 | $60,000 × 1.04³ | $67,491.84, up 12.49%, not 12% |
| 6% then 4% raises on $45,000 | $45,000 × 1.06 × 1.04 | $49,608, up 10.24% |
Price Increase Calculations
| Question | Working | Answer |
|---|---|---|
| Supplier price from $4.20 to $4.85 | $0.65 ÷ $4.20 × 100 | +15.48% |
| Price $92 after a 15% rise; what was it? | $92 ÷ 1.15 | $80 |
| $100 after 5 years of 6% inflation | $100 × 1.065 | $133.82, not $130 |
Revenue Growth and Population Decline
| Question | Working | Answer |
|---|---|---|
| Revenue from $42,000 to $51,660 | $9,660 ÷ $42,000 × 100 | +23% |
| Population from 84,000 to 71,400 | −12,600 ÷ 84,000 × 100 | −15% |
To compare an hourly wage with a salary before applying a raise, the Work Hours Calculator gets you total hours. For how a price rise changes your margin, see the Markup Calculator.
Percentage Increase in Excel
With the old value in A2 and the new value in B2, =(B2-A2)/A2 formatted as a percentage gives the change. Excel handles the ×100 when the cell is formatted as a percentage. Wrap it in ABS() if you want the size without the sign. The new value from a percentage in C2 is =A2*(1+C2/100), or =A2*(1+C2) if C2 is already formatted as a percentage. Use IFERROR(...,"") to hide errors on blank rows.
How This Calculator Is Verified
A colored badge above the result tracks the sign of the percentage in real time (Increase, Decrease, or No change), and it updates the same way regardless of which of the three panels is active, whether the percentage came from direct input or was calculated from two values. Find Original Value divides by (1 plus percent/100); percentage-decrease's equivalent mode divides by (1 minus percent/100), so the sign is the only thing that changes between the two calculators' formulas, and this one blocks a -100% input specifically since that would divide by zero. Find Change and Find New Value run in opposite directions: one derives a percentage from old and new values, the other derives a new value from a base and a percentage, and neither shares intermediate results with the other.
Frequently Asked Questions
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 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 is (4.2 − 3.5) ÷ 3.5 × 100 = 20%. That's different from the 0.7 percentage point gap (4.2% minus 3.5%). See percentage points vs percent change for why the two numbers diverge and when to use each.
What is the percentage increase from zero?
Percentage increase from a starting value of zero is mathematically undefined: the formula divides by the old value, and division by zero has no defined result. If your baseline is zero (for example 0 sales last month, 12 this month), report the change as an absolute number rather than a percentage.
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.