What Is Percentage Increase?
You got a raise. Your rent went up. Your investments grew. Every one of these is a percentage increase story — a way of describing how much something grew relative to where it started.
Here is why the “relative to where it started” part matters so much. Imagine two friends: one gets a $5,000 raise on a $50,000 salary, the other gets the same $5,000 on a $200,000 salary. Same dollars, completely different stories. The first friend got a 10% bump — life-changing. The second got 2.5% — barely noticeable. That is the power of learning how to calculate percentage increase: it turns raw numbers into meaning.
The Percentage Increase Formula
There is exactly one formula behind how to calculate percentage increase, and it never changes:
Percentage Increase = ((New Value − Old Value) ÷ Old Value) × 100
Memorize the rhythm of it — three steps, every single time:
- Subtract: new value minus old value. This gives you the raw difference.
- Divide: take that difference and divide it by the OLD (original) value.
- Multiply by 100: convert the decimal into a proper percentage.
That middle step is where almost everyone trips up, so burn it into memory: you always divide by where you started, never where you ended up.
Example 1: Calculating a Salary Raise
Let us walk through it slowly. Your salary moves from $50,000 to $55,000.
Step 1 — Subtract: 55,000 − 50,000 = 5,000
Step 2 — Divide by the old value: 5,000 ÷ 50,000 = 0.10
Step 3 — Multiply by 100: 0.10 × 100 = 10%
Your raise is 10%. Clean and simple. Now watch what happens if you make the classic mistake and divide by the new value instead: 5,000 ÷ 55,000 = 0.0909, or 9.09%. Wrong — and in a salary negotiation, that kind of error costs you real money.
Example 2: When Growth Passes 100%
Percentages above 100% make people’s brains short-circuit, but the formula does not care. You buy cryptocurrency for $2,000 and sell it later for $5,000.
Step 1: 5,000 − 2,000 = 3,000
Step 2: 3,000 ÷ 2,000 = 1.5
Step 3: 1.5 × 100 = 150%
A 150% increase. What does that actually mean? Your profit alone was one-and-a-half times your original investment — the money more than doubled. Anytime someone says “my investment grew 200%,” they mean it tripled: the original 100% plus 200% more on top.
Percentage Points vs. Percent: The Distinction Everyone Gets Wrong
This one deserves its own section because even news anchors butcher it. Going from 10% to 15% is a rise of 5 percentage points — that is simple subtraction. But as a percentage increase, it is (15 − 10) ÷ 10 × 100 = 50%. Saying “it went up 5%” would be flat wrong; it went up 50% relative to where it started.
Why does this matter? Because politicians, advertisers, and headlines exploit the confusion daily. “Unemployment rose 2%” sounds tiny — but if it rose from 4% to 6%, that is a 50% relative jump. Always ask: percent of what?
How to Calculate Percentage Decrease
Decreases use the identical formula — the answer simply comes out negative, which we read as a “decrease.” For clarity, most people flip it around:
Percentage Decrease = ((Old Value − New Value) ÷ Old Value) × 100
Same three steps, just starting from the old value in the subtraction.
Example 3: Spotting the Real Bargain
A jacket is marked down from $80 to $60.
Step 1: 80 − 60 = 20
Step 2: 20 ÷ 80 = 0.25
Step 3: 0.25 × 100 = 25%
A genuine 25% discount — you keep $20. Now here is a sharper shopping trick: store A offers “30% off” a $100 item ($70 final), store B offers “$25 off” the same item ($75 final). The percentage wins this round. Running this quick math before you buy is one of the highest-value habits in personal finance.
“Percent Of” vs. “Percent Change”: Don’t Mix Them Up
One more confusion to clear up, because search engines (and humans) treat these as different questions. “What is 20% of 80?” is a simple slice: 0.20 × 80 = 16. “What is the percentage change from 80 to 96?” is our formula: (96 − 80) ÷ 80 × 100 = 20%. Same 20%, totally different operations. If you ever catch yourself multiplying when you should be dividing by the original value, stop and ask: am I taking a slice of something, or measuring how much it moved? Slice → multiply. Movement → our three-step formula.
Working Backwards: Finding the Original Value
Here is the move most guides skip. Sometimes you know the NEW value and the percentage, but not where you started. Example: after a 10% raise, your salary is $66,000. What was it before?
Do not subtract 10% of $66,000 — that gives the wrong answer ($59,400). Instead, think in multipliers: a 10% increase means the new value is 110% of the old, or 1.10×. So:
Original Value = New Value ÷ (1 + Percentage Increase as a decimal)
Original Value = 66,000 ÷ 1.10 = $60,000
Check: 10% of 60,000 is 6,000, and 60,000 + 6,000 = 66,000. Correct. For a decrease, use (1 − decimal): a $45 sale price after 25% off means the original was 45 ÷ 0.75 = $60.
The Spreadsheet Method: Excel and Google Sheets
If you do this regularly, let the spreadsheet do it. Put the old value in cell A2 and the new value in B2, then in C2 type:
=(B2-A2)/A2
Then format C2 as a percentage (Format → Number → Percentage). That is it — one formula, reusable forever. For the reverse calculation (finding the original), use =B2/(1+0.10) where B2 is the new value and 0.10 is the increase as a decimal. Build this once into a small template and you will never do percentage math by hand again.
Real-Life Uses of Percentage Change
Once you see it, you cannot unsee it — percent change runs the modern world:
- Shopping: comparing “30% off” against “$25 off” to find the true bargain.
- Careers: evaluating raises, bonuses, and job offers on equal footing.
- Investing: reading portfolio returns, stock moves, and crypto swings honestly.
- Housing: making sense of rent hikes and home-price appreciation year over year.
- Business: tracking revenue growth, conversion-rate lifts, and churn.
- Health: measuring weight change or body-fat reduction over months.
- Everyday math: tips, taxes, discounts, and splitting bills fairly.
Common Mistakes to Avoid
- Dividing by the NEW value instead of the old one. The base is always your starting point.
- Forgetting to multiply by 100. A result of 0.25 is 25%, not 0.25%.
- Mixing up percentage points and percent (see the section above — it matters).
- Adding percentages directly. A 10% increase followed by a 10% decrease does NOT return you to the start: $100 → $110 → $99. Percentages compound on moving bases.
- Rounding too early. Keep full precision through the steps and round only the final answer.
Percentage Increase vs. Decrease: Quick-Reference Table
Bookmark this — it covers the situations you will run into most.
| Scenario | Old value | New value | Math | Result |
|---|---|---|---|---|
| Salary raise | $50,000 | $55,000 | (55,000−50,000)÷50,000×100 | +10% |
| Stock gain | $20 | $26 | (26−20)÷20×100 | +30% |
| Store discount | $80 | $60 | (80−60)÷80×100 | −25% |
| Rent hike | $1,200 | $1,320 | (1,320−1,200)÷1,200×100 | +10% |
| Weight loss | 180 lb | 162 lb | (180−162)÷180×100 | −10% |
| Investment triple | $2,000 | $6,000 | (6,000−2,000)÷2,000×100 | +200% |
Notice the pattern in every row: difference first, divided by the starting value, times one hundred. Once you have done it three times by hand, you will do it in your head.
Calculate It Instantly (Free Tool)
Understanding the math puts you ahead of 90% of people. But for daily life, just plug your numbers into our free percentage calculator — enter the old and new values and get the increase or decrease instantly, with every step of the working shown.
Frequently Asked Questions
What is the formula for percentage increase?
((New Value − Old Value) ÷ Old Value) × 100. Subtract the old from the new, divide by the old value, multiply by 100.
Can a percentage increase be more than 100%?
Absolutely. Anything beyond doubling exceeds 100% — tripling your money is a 200% increase.
What is the difference between percent and percentage points?
Percentage points are the plain arithmetic gap (10% to 15% = 5 points). Percent change is relative — that same move is a 50% increase.
How do I calculate percentage decrease?
Use ((Old − New) ÷ Old) × 100. An $80 jacket reduced to $60 is a 25% decrease.
How do I calculate percentage increase in Excel or Google Sheets?
With the old value in A2 and new in B2, enter =(B2-A2)/A2 and format the cell as a percentage.
How do I find the original value after a percentage increase?
Divide the new value by (1 + the increase as a decimal). A $66,000 salary after a 10% raise means the original was 66,000 ÷ 1.10 = $60,000.
Why is my percentage calculation slightly off from the store’s sign?
Usually rounding. Stores round to tidy numbers — a true 33.33% discount becomes “33% off” on the tag. For exact figures, always use the unrounded decimal through every step and round only at the end.
Conclusion
It all comes down to one formula: find the difference, divide by where you started, multiply by 100. With that — plus the reverse trick and the spreadsheet shortcut — you can decode raises, discounts, investments, and headlines like a pro. Now that you know how to calculate percentage increase, you’ll read every raise, discount, and return with confidence — and for the one-second answer, our free percentage calculator is always one click away.