Free · no signup · signed result
Percent Change Calculator
One formula for both directions: (new − old) ÷ old × 100. Positive means growth, negative means decline — useful for prices, salaries, traffic, portfolios, anything measured twice.
Short answer
Percent change = (new − old) ÷ old × 100, keeping the sign: 100 → 125 is +25%, and 80 → 60 is −25%. The base is always the ORIGINAL value, which is why a rise and fall of the same dollar amount give different percentages. For changes between two percentages themselves, say whether you mean percent (relative) or percentage points (absolute) — 10% → 12% is +2 points but +20 percent.
change = (new − old) ÷ old × 100
From 100 to 125 is a change of
+25%
About the numbers
Where percent change misleads: tiny bases (going from 2 users to 10 is +400% and still tiny), chained changes (+10% then −10% lands at 99%, not 100%), and comparing across different bases. For repeated growth over time, an average per-period rate (geometric, like CAGR) is the honest summary — not the sum of the yearly changes.
Common percentages of common numbers
| Percent | of 20 | of 50 | of 80 | of 100 | of 250 | of 1000 |
|---|---|---|---|---|---|---|
| 5% | 1 | 2.5 | 4 | 5 | 12.5 | 50 |
| 10% | 2 | 5 | 8 | 10 | 25 | 100 |
| 15% | 3 | 7.5 | 12 | 15 | 37.5 | 150 |
| 20% | 4 | 10 | 16 | 20 | 50 | 200 |
| 25% | 5 | 12.5 | 20 | 25 | 62.5 | 250 |
| 30% | 6 | 15 | 24 | 30 | 75 | 300 |
| 40% | 8 | 20 | 32 | 40 | 100 | 400 |
| 50% | 10 | 25 | 40 | 50 | 125 | 500 |
| 75% | 15 | 37.5 | 60 | 75 | 187.5 | 750 |
| 90% | 18 | 45 | 72 | 90 | 225 | 900 |
Value = percent ÷ 100 × number. Mental shortcut: find 10% by moving the decimal, then scale (20% = 2×10%, 5% = half of 10%).
How we calculate this
Three formulas cover every percentage question:
- Percent of a number. value = percent ÷ 100 × number. 20% of 150 = 0.20 × 150 = 30.
- What percent. percent = part ÷ whole × 100. 30 out of 150 = 30 ÷ 150 × 100 = 20%.
- Percent change. change = (new − old) ÷ old × 100, keeping the sign. The base is always the original value.
Assumptions
- Results are rounded to 2 decimal places for display; the formulas themselves are exact.
- Percent change from a zero starting value is undefined (division by zero) — the calculator says so rather than inventing a number.
- Percent (relative) and percentage points (absolute difference between two rates) are different things; the change pages spell out which is which.
Last reviewed: July 22, 2026
Frequently asked questions
How do I calculate a percentage of a number?+
Divide the percent by 100 and multiply: 20% of 150 = 0.20 × 150 = 30. The fastest mental route is through 10% — move the decimal one place left (10% of 150 is 15), then scale: 20% is double that, 5% is half, 15% is one-and-a-half times. The calculator's first mode does this for any pair of numbers.
How do I work out what percent one number is of another?+
Divide the part by the whole and multiply by 100: 30 out of 150 = 30 ÷ 150 × 100 = 20%. This is the formula for test scores, discounts checked against receipts, and 'what share of the total' questions. Watch the order — part ÷ whole, not the reverse; getting 500% when you expected 20% usually means the numbers were swapped.
How is percentage increase calculated?+
(New − old) ÷ old × 100, always dividing by the ORIGINAL value: 80 → 100 is +25%, while 100 → 80 is −20%, and both statements are correct because the base changes. A doubling is a 100% increase, a tripling 200%. For a decrease, the same formula simply comes out negative.
What is the difference between percent and percentage points?+
Percentage points measure the absolute gap between two rates; percent measures the relative change. If an interest rate goes from 10% to 12%, it rose 2 percentage points — but 20 percent, because 2 is a fifth of 10. News reports mix these constantly; when the numbers being compared are themselves percentages, always ask which one is meant.
Why don't a 10% increase and a 10% decrease cancel out?+
Because the base changes between the two steps: 100 + 10% = 110, and 110 − 10% = 99. The decrease acts on the larger number, so you land below where you started — the same reason a 50% loss needs a 100% gain to recover. Chained percentage changes multiply (1.10 × 0.90 = 0.99); they never simply add.
How do I calculate a discount or reverse a percentage?+
A 25% discount on $80 is 0.25 × 80 = $20 off, so you pay $60 — or in one step, pay 75%: 0.75 × 80. Reversing is division: if $60 is the price AFTER a 25% discount, the original was 60 ÷ 0.75 = $80, not 60 + 25%. That last mistake — adding the percent back instead of dividing — is the most common percentage error in everyday math.
Also try the Percentage Calculator.