Percentage Calculator
The percentage calculator covers the 4 most common percentage calculations in finance and everyday life: finding X% of a number, determining what percentage one number is of another, calculating percentage change (increase/decrease), and increasing or decreasing a number by a given percentage.
Illustrative scenario:
- 15% of 1.000.000.000 = 150.000.000
- 250.000.000 is what % of 1.000.000.000? = 25%
- Change from 800.000.000 to 1.000.000.000 = +25.0%
Percentages are one of the most fundamental mathematical concepts, used everywhere from bank interest rates and income tax to product discounts and investment returns.
The four percentage formulas
1. Find X% of Y (Percentage of a number)
Result = Y × (X / 100)
Example: 15% of 1.000.000.000 = 1.000.000.000 × 15/100 = 150.000.000
Applications: calculating tax, interest, or discounts.
2. A is what % of B? (Find the percentage ratio)
% = (A / B) × 100
Example: 250.000.000 / 1.000.000.000 × 100 = 25%
Applications: cost-to-income ratio, ROI, profit margins.
3. % change from A to B (Percentage increase/decrease)
% change = ((B − A) / |A|) × 100
Example: (1.000.000.000 − 800.000.000) / 800.000.000 × 100 = +25.0%
Positive = increase, negative = decrease. Applications: stock returns, salary raises, inflation.
4. Increase/Decrease a number by X%
Increase = Y × (1 + X/100) | Decrease = Y × (1 − X/100)
Example: 500.000.000 increased by 10% = 550.000.000, decreased by 10% = 450.000.000
Applications: computing post-discount prices, post-raise salaries, or capital after gains/losses.
Common percentage mistakes
Many people confuse "increase by X%" with "increase to X%". Increasing by 10% from 100 gives 110. Increasing to 10% is ambiguous. Always clarify whether you mean "by" or "to" when discussing percentage changes.
Worked example: Real estate investment profit
| Parameter | Value |
|---|---|
| Purchase price | 800.000.000 |
| Sale price after 2 years | 1.000.000.000 |
| Profit | 200.000.000 |
| Return % | +25.0% |
Applying all 4 formulas
- 2% tax on profit: 200.000.000 × 2% = 4.000.000
- Agent fee as % of sale price: 10.000.000 / 1.000.000.000 = 1.00%
- % price increase: (1.000.000.000 − 800.000.000) / 800.000.000 = +25.0%
- If price drops 5%: 1.000.000.000 × (1 − 5%) = 950.000.000
Frequently asked questions
How to calculate percentages quickly without a calculator?
To find X% of Y: divide Y by 100, then multiply by X. Or use tricks: 10% = move decimal one place left, 5% = half of 10%, 1% = move two places. Example: 15% of 1 billion = 10% (100M) + 5% (50M) = 150M.
Does a percentage increase followed by the same decrease cancel out?
No. Increasing by 20% then decreasing by 20% does not return to the original value. Example: 100 + 20% = 120, then − 20% = 96 (lower than the original 100). This is the compounding effect.
What is the difference between percentage points and percent?
Percentage points are an absolute unit; percent is relative. Interest rates rising from 5% to 7% = a 2 percentage point increase = a 40% increase (because (7-5)/5 = 40%).
How to calculate bank interest rate as a percentage?
Annual rate × deposit amount / 12 = monthly interest. Example: 1.000.000.000 at 6%/year: monthly interest = 1.000.000.000 × 6% / 12 = 5.000.000.
How to calculate a discount percentage?
Original price × discount % = discount amount. Sale price = original − discount. Example: a 1.000.000 item at 30% off = 1.000.000 × 30% = 300.000 discount. Sale price = 700.000.
How is ROI calculated as a percentage?
ROI = (Profit / Investment) × 100. Example: invest 800.000.000, get back 1.000.000.000, profit 200.000.000. ROI = (200.000.000 / 800.000.000) × 100 = 25.0%.