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Percentage Calculator

Percentage Calculator

Find percentages, increases, decreases, ratios & reverse percentages instantly

Find out what a given percentage of a number is. Example: 25% of 200.
%
Find what percentage one number is of another. Example: 50 is what % of 200.
Find the percentage increase or decrease between two values. Example: from 80 to 100.
Find the original number when you know a value and the percentage it represents. Example: 50 is 25% of what number?
%
Convert a ratio or fraction (A : B) into a percentage and simplified form.
Apply a discount or sales tax to a price and see the final amount.
%
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Result
Detailed Breakdown

About the Percentage Calculator

This free percentage calculator handles six common percentage problems in one place — finding a percentage of a number, working out what percentage one number is of another, calculating percentage increase or decrease, reversing a percentage to find the original value, converting a ratio to a percentage, and applying discounts or sales taxes to a price.

  • Switch between six calculation modes using the tabs — no need to remember different formulas.
  • Get a clear breakdown showing the formula used and step-by-step values.
  • Percentage change mode automatically detects whether a value increased or decreased.
  • Discount and sales tax mode shows the final price and the exact amount added or removed.
  • Works with decimals and negative numbers for accurate real-world results.

How to Calculate a Percentage

Quick Answer

To find a percentage of a number, divide the percentage by 100 and multiply it by the number: percentage ÷ 100 × number. To find what percentage one number is of another, divide the part by the whole and multiply by 100.

"Percent" literally means "per hundred" — a percentage is simply a fraction expressed out of 100. Whether you're calculating a discount at checkout, working out exam scores, comparing year-over-year revenue growth, or splitting a restaurant bill, the underlying math is always the same: converting between a part, a whole, and a ratio expressed as a fraction of 100.

This calculator covers the six most common percentage problems people search for, each with its own formula and a step-by-step breakdown so you can see exactly how the result was reached.

The Six Percentage Formulas Explained

1. Finding a Percentage of a Number

Formula
Result = (Percentage ÷ 100) × Number

Example: What is 25% of 200? → (25 ÷ 100) × 200 = 0.25 × 200 = 50.

2. Finding What Percentage One Number Is of Another

Formula
Percentage = (Part ÷ Whole) × 100

Example: 50 is what percent of 200? → (50 ÷ 200) × 100 = 0.25 × 100 = 25%.

3. Percentage Increase or Decrease

Formula
% Change = ((New Value − Old Value) ÷ Old Value) × 100

Example: A value rises from 80 to 100 → ((100 − 80) ÷ 80) × 100 = (20 ÷ 80) × 100 = 25% increase. A positive result means an increase; a negative result means a decrease.

4. Reverse Percentage (Finding the Original Number)

Formula
Original Number = Value ÷ (Percentage ÷ 100)

Example: 50 is 25% of what number? → 50 ÷ (25 ÷ 100) = 50 ÷ 0.25 = 200. This is useful when you know a discounted price or a partial amount and need to work backward to the full value.

5. Ratio to Percentage

Formula
Percentage = (A ÷ (A + B)) × 100

Example: A ratio of 3:4 → 3 ÷ (3 + 4) × 100 = 3 ÷ 7 × 100 ≈ 42.86% for the first part, and the remainder for the second.

6. Discount and Sales Tax Calculations

Formula
Discount: Final Price = Price × (1 − Percentage ÷ 100)
Sales Tax / Markup: Final Price = Price × (1 + Percentage ÷ 100)

Example: A $1,000 item with a 20% discount → $1,000 × (1 − 0.20) = $1,000 × 0.80 = $800, a savings of $200. To add a 8.5% sales tax to a $50 item → $50 × 1.085 = $52.50.

Common Real-World Uses for Percentage Calculations

ScenarioMode to Use
Working out a discount or sale priceDiscount / Tax
Adding U.S. sales tax to a priceDiscount / Tax
Calculating a test score from correct answersX is what %
Comparing salary, revenue, or population growth% Change
Finding the original price before a discount was appliedReverse %
Splitting a budget or converting odds/ratiosRatio → %
Calculating commission or interest on an amount% of a Number

Tips for Working with Percentages

  • Percentage points vs. percent: Going from 20% to 25% is a 5 percentage point increase, but it's a 25% relative increase (5 ÷ 20 × 100). These two phrasings describe different things and are often confused — particularly in financial and political reporting.
  • Negative percentages in change calculations: A negative result in the percentage change formula means the value decreased — for example, going from 100 to 80 gives −20%, a 20% decrease.
  • Order matters for sequential percentages: Applying a 10% increase followed by a 10% decrease does not return you to the original number, because the second percentage is calculated on a different base value.
  • U.S. sales tax varies by state: Unlike a fixed national rate, U.S. sales tax rates differ by state and sometimes by county or city. Five states — Alaska, Delaware, Montana, New Hampshire, and Oregon — have no statewide sales tax.
  • Rounding: For financial calculations, round only at the final step to avoid compounding small rounding errors across multiple calculations.

Frequently Asked Questions

Subtract the old value from the new value, divide that difference by the old value, then multiply by 100. For example, going from 50 to 75 is ((75 − 50) ÷ 50) × 100 = 50% increase. Use the "% Change" mode to calculate this automatically — it also tells you whether the result is an increase or decrease.
If you know the discounted price and the discount percentage, divide the discounted price by (1 − discount ÷ 100). For example, if an item costs $80 after a 20% discount, the original price was 80 ÷ (1 − 0.20) = 80 ÷ 0.80 = $100. Note this is different from the "Reverse %" mode, which assumes the value you enter represents the percentage directly (i.e., Value ÷ (Percentage ÷ 100)) — for discounted prices specifically, use this division-by-(1 − rate) approach.
A percentage point is a simple arithmetic difference between two percentages — moving from 30% to 35% is a 5 percentage point change. A percentage change describes that same move relative to the starting value — 5 ÷ 30 × 100 ≈ 16.7% relative increase. The two numbers describe the same change but from different perspectives, and mixing them up is a common source of confusion in U.S. financial news and political reporting.
Yes. All six modes accept decimal values, and the percentage change mode also accepts negative starting or ending values where mathematically valid (the old value cannot be zero, since dividing by zero is undefined). Results are automatically rounded for readability while preserving precision in the underlying calculation.
A ratio A:B is converted by dividing each part by the total (A + B) and multiplying by 100. For a ratio of 1:3, part A represents 1 ÷ 4 × 100 = 25% and part B represents 3 ÷ 4 × 100 = 75%. The "Ratio → %" mode also shows the simplified ratio using the greatest common divisor of the two numbers.
Use the "Discount / Tax" mode and select "Sales Tax / Markup." Enter your pre-tax price and the applicable sales tax rate for your state or locality. The calculator adds the tax amount to give you the total price. U.S. sales tax rates vary widely — for example, California's statewide rate is 7.25% (with local additions often making the combined rate 8.5–10.25%), while states like Oregon and New Hampshire have no sales tax at all. Check your state's department of revenue website for the exact rate in your area.

About This Tool & Editorial Standards

Toolriz Calculators Team
Content reviewed for accuracy of mathematical formulas and worked examples
Last updated: June 2026

This percentage calculator uses standard arithmetic formulas for percentage, ratio, and proportional calculations. The educational content on this page is written and periodically reviewed by the Toolriz tools team for accuracy. This tool is provided for general informational purposes only and is not a substitute for professional financial, tax, or accounting advice. For tax-related questions, consult a CPA or refer to the IRS website at irs.gov.

Sources & Further Reading

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