To calculate a percentage, divide the part by the whole and multiply by 100 — percentage = (part ÷ whole) × 100. For example, 30 out of 150 is (30 ÷ 150) × 100 = 20%. This same core idea also lets you find "X% of Y," work out what percent one number is of another, and measure percentage increase or decrease between two values.
The 3 core percentage formulas:
1. X% of Y = (X ÷ 100) × Y
2. X is what % of Y = (X ÷ Y) × 100
3. % change from A to B = ((B − A) ÷ A) × 100
Below, each formula is broken down with fully worked examples, plus common mistakes to avoid and a free tool that calculates all three instantly.
How Do You Calculate X% of Y?
This is the most common percentage question: "what is 20% of 150?" To find X% of Y, convert the percentage to a decimal by dividing by 100, then multiply by Y.
Formula: X% of Y = (X ÷ 100) × Y
Worked example: What is 20% of 150?
- (20 ÷ 100) × 150 = 0.2 × 150 = 30
Another example: What is 15% of 200?
- (15 ÷ 100) × 200 = 0.15 × 200 = 30
This formula is used everywhere — calculating a discount at checkout, a tip on a restaurant bill, GST on an invoice, or interest on a loan.
How Do You Find What Percent One Number Is of Another?
This answers questions like "45 is what percent of 180?" Here you're finding the percentage relationship between a part and a whole. Divide the part by the whole, then multiply by 100.
Formula: X is what % of Y = (X ÷ Y) × 100
Worked example: 45 is what percent of 180?
- (45 ÷ 180) × 100 = 0.25 × 100 = 25%
Another example: 12 is what percent of 48?
- (12 ÷ 48) × 100 = 0.25 × 100 = 25%
This is the formula you need for test scores (e.g., "38 out of 40 questions correct"), survey results, and comparing any part of a total against the whole.
How Do You Calculate Percentage Increase or Decrease?
Percentage change tells you how much a value has grown or shrunk relative to its starting point. Subtract the old value from the new value, divide by the old value, then multiply by 100. A positive result means an increase; a negative result means a decrease.
Formula: % change from A to B = ((B − A) ÷ A) × 100
Worked example (increase): A price rises from 80 to 100.
- ((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = +25%
Worked example (decrease): A price falls from 120 to 90.
- ((90 − 120) ÷ 120) × 100 = (−30 ÷ 120) × 100 = −25%
Notice the denominator is always the original (starting) value — not the new value. This is the single most common source of errors when calculating percentage change by hand.
Tip — reversing a percentage: If you know a part and its percentage but need the whole, use Y = X ÷ (percentage ÷ 100). For example, if 25 is 20% of a number, then the number is 25 ÷ 0.20 = 125. Check: 20% of 125 = (20 ÷ 100) × 125 = 25. ✓
How to Use the UtilityX Percentage Calculator
Doing this math by hand works fine for quick checks, but for speed and zero risk of arithmetic slips, the UtilityX Percentage Calculator does all three calculations instantly as you type.
- Open the tool — visit utilityx.co.in/text-tools/percentage-calculator/. No sign-up required.
- Pick a mode tab — choose "% of" for X% of Y, "what % of" for X is what percent of Y, or "% change" for percentage increase/decrease.
- Enter your numbers — type the two values into the input fields.
- See the instant result — the answer updates live as you type, with no button to click and no page reload.
Calculate Any Percentage Instantly
Free, private, no sign-up. All three formulas in one tool.
Open Percentage Calculator →Common Percentage Calculation Mistakes
1. Confusing percentage change with percentage points
These are not the same thing. If an interest rate rises from 5% to 8%, that's a 3 percentage point increase (8 − 5 = 3), but a 60% relative increase, since ((8 − 5) ÷ 5) × 100 = 60%. Mixing these up leads to very different — and often misleading — numbers.
2. Using the wrong base value in percentage change
Always divide by the original value, not the new one. Going from 80 to 100 is a +25% increase using 80 as the base. Calculating it backwards from 100 to 80 gives a different magnitude: ((80 − 100) ÷ 100) × 100 = −20%. Increase and decrease percentages between the same two numbers are not symmetric.
3. Forgetting to convert the percentage to a decimal
When finding X% of Y, remember to divide X by 100 before multiplying. A common slip is multiplying by the raw percentage number (e.g., 20 × 150 = 3000) instead of the decimal form (0.2 × 150 = 30) — the answer ends up 100 times too large.
4. Rounding too early
If a calculation involves multiple steps, round only your final answer, not intermediate results. Rounding early can shift the final percentage by a noticeable margin, especially with larger numbers.
Watch out: "Percent" and "percentage points" are the most commonly confused terms in reporting on rates, taxes, and statistics. Always check which one a figure is referring to before drawing conclusions.
Frequently Asked Questions
How do I calculate 20% of 150?
Use X% of Y = (X ÷ 100) × Y. So 20% of 150 = (20 ÷ 100) × 150 = 0.2 × 150 = 30. You can verify this instantly with the UtilityX Percentage Calculator's "% of" tab.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100: (X ÷ Y) × 100. For example, to find what percent 45 is of 180: (45 ÷ 180) × 100 = 0.25 × 100 = 25%. This works for any two positive numbers.
How do I calculate percentage increase?
Percentage increase = ((New − Old) ÷ Old) × 100. For example, going from 80 to 100: ((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = 25%. The result is positive because the value went up.
How do I calculate percentage decrease?
Use the same formula as increase: ((New − Old) ÷ Old) × 100. For example, from 120 to 90: ((90 − 120) ÷ 120) × 100 = (−30 ÷ 120) × 100 = −25%. The negative sign shows it's a 25% decrease.
What is the difference between percentage points and percent?
A percentage point is a simple difference between two percentages, while percent change is a relative change. If an interest rate rises from 5% to 8%, that's a 3 percentage point increase, but a 60% relative increase, since ((8 − 5) ÷ 5) × 100 = 60%.
How do I reverse a percentage to find the original number?
If X is a known percentage of an unknown number Y, use Y = X ÷ (percentage ÷ 100). For example, if 25 is 20% of a number, then Y = 25 ÷ 0.20 = 125. Check: 20% of 125 = (20 ÷ 100) × 125 = 25, which confirms the answer.
Summary
Every percentage question boils down to one of three formulas: X% of Y, X is what % of Y, or percentage change between two numbers. Once you know which formula applies, the arithmetic is simple — and the UtilityX Percentage Calculator handles all three instantly, so you never have to second-guess your math.