Math

Free Percentage Calculator

Percent of a number, percent change, and reverse percent problems.

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Inputs

Result

20.00% of 150.00

30.00

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Short answer

A percentage is a ratio expressed per hundred. 'X percent of Y' equals (X ÷ 100) × Y. Percent change equals (new − old) ÷ |old| × 100.

What is the Percentage Calculator?

The percentage calculator resolves the three most common percent problems: finding a percentage of a number, finding what percent one number is of another, and computing percent change between two values.

How does the Percentage Calculator work?

Divide by 100 to convert a percent to a decimal; multiply to convert back. For percent change, subtract old from new, divide by the absolute value of the old, and multiply by 100.

Formula

percent of: X% of Y = (X/100)·Y change: (B − A)/|A| · 100

Variables

  • XPercent value
  • YBase amount
  • AOriginal value
  • BNew value

Explanation

A percentage is a fraction with denominator 100. Multiplying by 100 converts a decimal ratio to a percent.

Examples

Example 1: 20% of 150

(20/100) × 150 = 30.

Example 2: 45 is what % of 180

45 ÷ 180 × 100 = 25%.

Example 3: % change from 80 to 100

(100 − 80) ÷ 80 × 100 = +25%.

Applications

  • Sales tax and tip calculation
  • Discount and markup pricing
  • Grade and score conversion
  • Financial return reporting

Advantages

  • Instantly handles the three main percent problems
  • Signed percent change distinguishes gains from losses

Limitations

  • Percent change is undefined when the base value is zero

Common mistakes

  • Confusing 'X% of Y' with 'X is what % of Y'
  • Dividing by the new value instead of the old value in percent change

Tips

  • To increase a number by P%, multiply by (1 + P/100)
  • To reverse a P% increase, divide by (1 + P/100), not subtract P%

Related concepts

The Percentage Calculator sits inside the Math Calculators hub, in the algebra & equations cluster. Solving for unknowns and manipulating expressions. Understanding the terms below makes the output easier to interpret and easier to compare against neighbouring measures.

equationrootexponentlogarithmsequenceproportion

Practical use cases and industry applications

Understanding Percentage

The percentage calculator resolves the three most common percent problems: finding a percentage of a number, finding what percent one number is of another, and computing percent change between two values. Within math calculators, percentage belongs to the algebra & equations cluster, where it shares terminology and assumptions with closely related tools.

Learning how percentage is calculated

A percentage is a fraction with denominator 100. Multiplying by 100 converts a decimal ratio to a percent. Working through the variables one at a time — X, Y, A, B — makes the result reproducible by hand and easier to sanity-check.

Using percentage to make a decision

Sales tax and tip calculation Discount and markup pricing Grade and score conversion Because outputs depend on the assumptions you enter, run more than one scenario before committing to a figure.

How percentage compares with related measures

equation, root, exponent, logarithm all describe adjacent aspects of algebra & equations. Comparing this calculator's output against those measures — using the related tools listed on this page — prevents a single metric from being read in isolation.

Frequently asked questions

How do I remove a discount?

If a price after a P% discount is X, the original price is X ÷ (1 − P/100).

Is percent change symmetric?

No. Going from 100 to 120 is +20%, but going from 120 to 100 is −16.7%.

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