How to Calculate Percentage Increase: Formula, Steps and Examples
Working out a percentage increase comes down to one formula and three steps. This guide shows you the formula, walks through each step with real numbers, and then applies it to the five situations people actually need it for: price rises, pay raises, sales growth, investment returns and inflation. Every example is verified against the free percentage increase calculator.
Percentage Increase = ((New Value − Old Value) ÷ Old Value) × 100.
Example: from $50 to $65 → ((65 − 50) ÷ 50) × 100 = 30% increase. Always divide by the old value — that is the base you are measuring the growth against.
The Percentage Increase Formula
Some textbooks write the same thing as (Difference ÷ Original) × 100, or as (New ÷ Old − 1) × 100. All three are identical — pick whichever you find easiest to remember. The second version is often quicker on a calculator: 65 ÷ 50 = 1.3, subtract 1 to get 0.3, multiply by 100 to get 30%.
How to Work It Out in 3 Steps
- Subtract the old value from the new value: New − Old = the growth.
- Divide that growth by the old value. You now have a decimal.
- Multiply by 100 to turn the decimal into a percentage.
Worked through with numbers, going from 80 to 100:
- 100 − 80 = 20
- 20 ÷ 80 = 0.25
- 0.25 × 100 = 25%
Note that the same 20-unit gain would be a 20% increase if you started at 100, and a 40% increase if you started at 50. The starting point decides the percentage — that is the whole point of the measure.
What Percentage Increase Actually Means
Percentage increase tells you how much a value has grown relative to where it started, rather than in raw units. That relative framing is what makes it useful for comparison.
A $10 rise on a $20 item is a 50% increase. The same $10 on a $1,000 item is a 1% increase. The absolute change is identical; the significance is not even close.
The bigger the starting value, the smaller the same absolute rise looks in percentage terms.
1. Price Increase
A product went from $40 to $52. What is the percentage increase?
- Difference: $52 − $40 = $12
- Divide: $12 ÷ $40 = 0.30
- Multiply: 0.30 × 100 = 30%
The same method handles rent. Rent going from $1,200 to $1,350: $150 ÷ $1,200 = 0.125 → 12.5%.
If you need to go the other way — applying a known increase to a price — multiply by (1 + rate). A 7% rise on $89 is 89 × 1.07 = $95.23. Retailers use the same arithmetic when they set a selling price from cost, which is covered in margin vs markup.
2. Salary and Pay Raises
Your salary went from $55,000 to $60,500:
- Difference: $60,500 − $55,000 = $5,500
- Divide: $5,500 ÷ $55,000 = 0.10
- Multiply: 0.10 × 100 = 10%
Two things worth knowing when you judge a raise. First, the number that matters is the raise net of inflation: a 4% raise in a year with 3% inflation is roughly a 1% real increase. Second, hourly workers should compare hourly rates, not annual totals, because a change in hours will distort the percentage.
Percentage raises compound year over year, which is why an early raise is worth more than the same raise later.
More on brackets, deductions and take-home effects in percentages in tax and salary.
3. Sales and Revenue Growth
Sales grew from 2,400 units last month to 3,000 this month: 600 ÷ 2,400 = 0.25 → 25% increase.
For year-over-year growth, use last year's figure as the old value. Revenue of $500,000 rising to $650,000: 150,000 ÷ 500,000 = 0.30 → 30% YoY.
When growth spans several periods, don't average the individual percentages — that overstates the result. Use the compound growth rate instead, which is explained in percentage change over time.
4. Investment Returns
A stock bought at $45 now trades at $63: 18 ÷ 45 = 0.40 → 40% return.
Percentage return is the only fair way to compare investments of different sizes. A $900 gain on a $3,000 position (30%) beats a $1,200 gain on a $12,000 position (10%), even though the second number is bigger.
Over multiple years, returns compound rather than add — see what compound interest is.
5. Inflation and Cost of Living
Inflation is a percentage increase in a price index. If a basket cost 261.6 last year and 271.5 this year: 9.9 ÷ 261.6 = 0.0378 → 3.78% inflation.
The same arithmetic tells you what an old price is worth today. A $20 lunch with 3.8% annual inflation costs $20 × 1.038 = $20.76 a year later, and $20 × 1.038³ = $22.37 after three years.
Inflation compounding on a $20 purchase
At 3.8% per year, each year's increase is applied to the already-increased price:
| Year | Calculation | Price | Check it |
|---|---|---|---|
| Year 1 | $20.00 × 1.038 | $20.76 | Open |
| Year 2 | $20.76 × 1.038 | $21.55 | Open |
| Year 3 | $21.55 × 1.038 | $22.37 | Open |
| Year 5 | $20.00 × 1.038⁵ | $24.10 | Open |
Total increase after five years is 20.5%, not 19% (5 × 3.8%), because each year compounds on the last.
Quick Reference Table
Common percentage increases at a glance
Each row opens the calculator with the values already filled in.
| Increase | From → To | Growth | Open |
|---|---|---|---|
| 5% | 100 → 105 | +5 | Open |
| 10% | 100 → 110 | +10 | Open |
| 12.5% | 1200 → 1350 | +150 | Open |
| 25% | 80 → 100 | +20 | Open |
| 30% | 50 → 65 | +15 | Open |
| 40% | 45 → 63 | +18 | Open |
| 100% | 50 → 100 | +50 | Open |
| 200% | 50 → 150 | +100 | Open |
In Excel and Google Sheets
With the old value in A2 and the new value in B2, the formula is:
Then format the cell as a percentage (Ctrl+Shift+% in both Excel and Google Sheets) — do not multiply by 100 as well, or you will get 2500% instead of 25%. To guard against a zero starting value, wrap it: =IF(A2=0,"n/a",(B2-A2)/A2). Full spreadsheet walkthrough in percentages in Excel and Google Sheets.
Doing It in Your Head
Anchor on 10% and build from there. 10% of the old value is the old value with the decimal point moved one place left; 5% is half of that; 1% is a tenth of it.
- From 200 to 230? 10% of 200 is 20, and the growth is 30 — one and a half tens, so 15%.
- From 40 to 46? 10% of 40 is 4, growth is 6, so 1.5 × 10% = 15%.
- From 60 to 63? 10% of 60 is 6, growth is 3, half a ten → 5%.
More shortcuts in percentages in your head.
Can It Be Over 100%?
Yes. Once a value more than doubles, the increase passes 100%:
- 50 → 100 = 100% increase (doubled)
- 50 → 150 = 200% increase (tripled)
- 50 → 200 = 300% increase (quadrupled)
Percentage Increase vs Percentage Points
These are constantly mixed up, including in the news.
- An interest rate moving from 2% to 3% is a 1 percentage point rise.
- As a percentage increase it is ((3 − 2) ÷ 2) × 100 = 50%.
Both statements are true and they sound wildly different, which is why the distinction gets exploited. When the underlying value is itself a percentage, always say which one you mean. See percent vs percentage vs percentage points.
Reversing a Percentage Increase
To find the original value after a known increase, divide — don't subtract the percentage. A price of $126 after a 5% rise was 126 ÷ 1.05 = $120. Subtracting 5% from $126 would give $119.70, which is wrong.
Use the reverse percentage calculator for this, or read how reverse percentages work.
Common Mistakes to Avoid
- Using the new value as the base. Always divide by the original. Using 100 instead of 80 in the 80 → 100 example gives 20% — plausible and wrong.
- Adding chained increases. +10% then +10% is +21%, not +20%.
- Assuming +50% and −50% cancel. They leave you at 75% of the start.
- Starting from zero. Percentage increase is undefined when the old value is 0 — report the absolute change instead.
- Rounding too early. Round only the final answer; rounding the intermediate decimal can move the result by a full point.
- Reporting a negative as an increase. A negative result is a percentage decrease.
- Confusing points and percent. 10% to 15% is 5 percentage points and a 50% increase.
Practice Questions
Work each one out before revealing the answer.
- A subscription rose from $12 to $15 per month. What is the increase?
- Website visitors went from 8,000 to 12,400.
- A house bought for $320,000 is now worth $416,000.
- A price rises 8% two years running from $250. What is the final price?
- After a 15% raise you earn $69,000. What was the old salary?
Check any of them in the percentage increase calculator — it shows the full step-by-step working for whatever numbers you enter.
Related Calculations
- How to calculate percentage decrease — the same formula in the other direction
- Percentage change over time — chaining growth and CAGR
- Percentage difference vs percentage change — when there is no "before" value
- The percentage formula — all five versions in one place
- Percentage difference calculator — compare two values symmetrically
- Markup calculator — cost-to-price increases in retail
Frequently Asked Questions
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