Percentage Calculator

Free percentage calculator to quickly compute percentage increases, decreases, differences, and fractions with instant results.

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Core Percentage Formulas & Equations

Last reviewed: September 2026

Calculation Formula

P% of Y = (P ÷ 100) × Y | X is % of Y = (X ÷ Y) × 100 | % Change = ((New − Old) ÷ |Old|) × 100

Variables & Definitions

P%:
Percentage rate per one hundred parts (e.g. 15% = 0.15)
X, Y:
Given base numbers or quantities
% Change:
Relative difference indicating markup/increase (+) or discount/decrease (-)
% Difference:
Absolute difference divided by average: (|X − Y| ÷ ((X + Y) ÷ 2)) × 100

Core Assumptions

  • Denominators must not equal zero (division by zero is undefined).
  • Percentage change uses the initial (old) value as the relative denominator base.
  • Percentage difference treats both numbers symmetrically using their average as the denominator base.
Disclaimer: Percentage calculations assume linear relationships. When analyzing compound interest, inflation, or multi-step compounding markups, chained formulas must be evaluated sequentially.

Worked Example: Retail Markup vs. Subsequent Clearance Discount

A shop owner buys goods for $80.00 wholesale, applies a 50% markup for the retail price, and later runs a 25% clearance discount:

Step 1: 50% Markup on Wholesale$80.00 + (50% of $80.00) = $80.00 + $40.00 = $120.00 Retail Price
Step 2: 25% Clearance Discount$120.00 − (25% of $120.00) = $120.00 − $30.00 = $90.00 Final Sale Price
Step 3: Final Net Margin vs Wholesale(($90.00 − $80.00) ÷ $80.00) × 100 = +12.5% Net Profit Margin

💡 Notice that a 50% increase followed by a 25% decrease does not equal a net 25% gain. Because the discount base ($120) is larger than the original wholesale base ($80), the final return is 12.5%.

How to use Percentage Calculator

  1. 1

    Select the calculation card matching your problem: "What is X% of Y?" for tips and taxes, "X is what % of Y?" for grades and shares, "Increase/Decrease by X%" for price adjustments, or "Percentage Difference" between two numbers.

  2. 2

    Enter your values in the input fields — calculations update in real time as you type.

  3. 3

    Review the result and step-by-step mathematical formula explanation to copy into spreadsheets or reports.

Why use this tool?

4 Common Percentage Modes in One View

Solve discounts, exam scores, sales growth, tips, and comparative variance on a single responsive interface without switching pages.

Formula Explanations for Spreadsheets & Verification

Every calculation displays the exact mathematical equation applied, making it effortless to audit homework, verify invoices, or write Excel/Google Sheets formulas.

Handles Negative & Decimal Values Accurately

Whether you need to compute fractional interest rates (0.375%), market declines (-14.2%), or large ratios (350%), numbers format cleanly with configurable decimal precision.

Continue your workflow

Shopping sales or comparing sticker prices? Use the Calculate retail discounts and coupon codes.

Need to add or separate consumption tax from a subtotal? Try the Calculate sales tax, VAT, and gross totals.

Measuring investment returns that compound across multiple years? Use the Calculate compound annual growth rate (CAGR).

Frequently asked questions

How do I calculate 20% off a $45 item?

Use "What is X% of Y?": enter 20 for X and 45 for Y. The discount amount is $9.00, meaning the final discounted price is $36.00.

How do I calculate what percentage my score is out of total points?

Use "X is what % of Y?": enter your points as X and the maximum points as Y. For example, 72 out of 90 is (72 ÷ 90) × 100 = 80%.

How do I find percentage increase from $50,000 to $57,500?

Use "Percentage Change": enter 50000 as From and 57500 as To. The result is +15.0% increase. The formula is ((57500 − 50000) ÷ 50000) × 100.

What is the difference between Percentage Change and Percentage Difference?

Percentage Change compares an old value to a new value chronologically using the old value as the base (e.g. population growth or salary increase). Percentage Difference compares two numbers without order or hierarchy by dividing the absolute difference by their average.

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