Percentage Calculator: X% of Y & Change

Percentage Calculator: What is X% of Y, Percent Change & Difference

Free percentage calculator for “what is X percent of Y,” “X is what percent of Y,” percent increase and decrease, and percent difference. How to calculate percentage and percent change formula with steps. Logic Trace and ratio visualizer. Trusted by students and educators. No sign-up; all calculations run locally.

What This Calculator Does and Who It’s For

This percentage calculator (also a percent calculator) handles four common percentage tasks in one tool: Value of % (what is X% of Y?), % Of (X is what percent of Y?), percent change (increase or decrease from initial to final), and percent difference (symmetric comparison of two values). Each mode shows a step-by-step Logic Trace and a Ratio visualizer so you can verify the math. Use it as a percent increase calculator, percent decrease calculator, or general percentage calculator with steps.

Who it’s for

Students and teachers (homework, tests); anyone needing how to calculate percentage or how to find percent increase between two numbers; analysts comparing metrics with percent difference. All calculations run in your browser; no data is sent to any server.
Trust and scope

Formulas follow standard algebra. Division by zero (e.g. whole = 0 in % Of, initial = 0 in Change) is detected and shown clearly in the Logic Trace.

How to Use This Calculator

Select the mode that matches your question. Use Value of % to answer "what is X% of Y?", enter the percentage and the whole number. Use % Of for "X is what percent of Y?", enter the part and the whole. Use Change for percent increase or decrease between two values, enter the initial (From) and new (To) amounts. Use Difference for a symmetric comparison when neither value is the "starting" point, enter both values. Results appear instantly alongside a step-by-step Logic Trace and a Ratio visualizer that shows the proportion graphically. Division by zero (whole = 0 in % Of, initial = 0 in Change, or average = 0 in Difference) is detected and displayed clearly. Use formatting options for decimal places when you need precision, such as reporting a test score percentage or a financial growth rate.

What Is a Percentage?

A percentage is a number expressed as a fraction of 100. So

X\% = \frac{X}{100}

For example, 20% = 0.20. To find what is 20% of 80, compute (20/100) × 80 = 16. Percentages are used for parts of a whole (e.g. 25% of a budget), rate of change (e.g. 10% increase), and comparisons (e.g. percent difference between two results). This calculator supports all of these in one interface

Percent Change vs Percent Difference: When to Use Which

Percent change answers “how much did it go up or down from a starting value?” It uses the initial value as the reference and is ideal for before/after cases: price changes, growth rates, salary increases. Formula:

\text{Percent Change} = \frac{\text{New} - \text{Initial}}{\text{Initial}} \times 100

Initial cannot be 0. Percent difference answers “how different are these two values, in percent?” It uses the average of the two values and is symmetric, there is no “from” or “to.” Use it when comparing two measurements, two options, or A/B test results. Formula:

\text{Percent Difference} = \frac{|V_1 - V_2|}{(V_1 + V_2)/2} \times 100

If the average is 0, the result is undefined. This calculator offers both modes so you can choose the right one for your question

Formulas: All Four Modes

All formulas are shown in the calculator’s Logic Trace when you enter values. Quick reference:

Value of % (what is X% of Y?)

$\text{Result} = \frac{P}{100} \times \text{Whole}$
Enter the percentage (P) and the whole. Example: 15% of 200 = 30
% Of (X is what percent of Y?)

$\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100$
Enter part and whole; whole cannot be 0. Example: 30 is 15% of 200
Change (percent increase or decrease)

$\text{Percent Change} = \frac{\text{New} - \text{Initial}}{\text{Initial}} \times 100$
Use Initial amount (From) and New amount (To). Initial cannot be 0
Difference (symmetric comparison)

$\text{Percent Difference} = \frac{|V_1 - V_2|}{(V_1 + V_2)/2} \times 100$
Use when there is no single “initial” value

How do I convert a percent to a decimal or a fraction for homework?

For percent to decimal, divide by 100: 62% → 0.62. For decimal to percent, multiply by 100: 0.62 → 62%. When a problem also wants a reduced fraction, move the decimal into a fraction with a power of 10 in the denominator, then simplify (for example 0.75 = 75/100 = 3/4). The fraction calculator handles that reduction in its Decimal ↔ Fraction tab so you can match workbook answers that insist on lowest terms.

Examples: Tip, Test Score, and Price Change

Real-world use cases show how to apply each mode and build trust in the result.

Tip on a bill (Value of %)

Bill is $45; you want to leave 18%. What is 18% of 45? Use Value of %: 18 and 45 → result 8.10. Tip = $8.10.
Test score as a percent (% Of)

You got 34 out of 40. What percent is that? Use % Of: 34 (part) and 40 (whole) → 85%.
Price increase (Change)

Item was $80, now $96. Percent increase? Use Change: Initial 80, New 96 → 20% increase. The Ratio visualizer shows the base (80) and growth (+16).

Percentage Calculator FAQ

How do I calculate what is X% of Y?

Use Value of % mode: enter X as the percentage and Y as the whole. Result = (X ÷ 100) × Y. Example: 20% of 100 = 20. The Logic Trace above shows the steps.

How do I find what percentage X is of Y?

Use % Of mode: enter X (part) and Y (whole). Result = (X ÷ Y) × 100. Example: 25 is 25% of 100. Whole cannot be 0.

What is the formula for percent change?

Percent change = (New − Initial) ÷ Initial × 100. Use Change mode; enter Initial amount (From) and New amount (To). Positive = increase, negative = decrease. Initial cannot be 0.

What is the difference between percent change and percent difference?

Percent change uses the initial value as the base, use it for before/after (e.g. price increase). Percent difference uses the average of the two values, use it when comparing two numbers with no “before” (e.g. two measurements). This calculator has both modes.

What is a percentage?

A percentage is a number out of 100. X% means X⁄100. So 20% of 50 = (20⁄100) × 50 = 10. Use this tool for “what is X% of Y,” “X is what % of Y,” percent change, and percent difference.

How do I convert a percent to a decimal?

Divide by 100: write the percent as a number and move the decimal two places left, same as (p / 100). Example: 37.5% = 0.375. To express that as a reduced fraction after you have the decimal, use the fraction calculator Decimal ↔ Fraction tab (e.g. 0.375 → 3/8).

How do I convert a decimal to a percent?

Multiply by 100 and attach the % symbol: 0.08 = 8%. Use % Of mode if you are checking what fraction of 100 a value represents, or compare with the fraction form on the fraction calculator when homework asks for both forms.

Percentage Calculator

Percentage Laboratory

Formatting

Using the Percentage Calculator (Percentage Laboratory)

At a glance

Value of %

% Of

Change

Difference