Saved calculators
Saved calculators
Math

Percentage of a number calculator

Share calculator

Add our free calculator to your website

Please enter a valid URL. Only HTTPS URLs are supported.
Use as default values for the embed calculator what is currently in input fields of the calculator on the page.
Input border focus color, switchbox checked color, select item hover color etc.
Please agree to the Terms of Use.
Preview

Save calculator

What is a percentage?

A percentage represents a fraction of 100. Derived from the Latin term per centum (“by the hundred”), it is denoted using the symbol %. Percentages simplify comparisons by standardizing values relative to a whole. For example, saying “25%” is equivalent to stating “25 out of every 100 units.”

Key formulas for percentage calculations

1. What percentage of Y is X?

Result=X100×Y\text{Result} = \frac{X}{100} \times Y

Example: What is 20% of 150?

20100×150=30\frac{20}{100} \times 150 = 30

2. Determine what percentage one number (X) is of another (Y)?

Percentage=(XY)×100%\text{Percentage} = \left( \frac{X}{Y} \right) \times 100\%

Example: 45 is what percentage of 180?

(45180)×100%=25%\left( \frac{45}{180} \right) \times 100\% = 25\%

3. Increase a number (Y) by a certain percentage (X)

New Value=Y+(X100×Y)=Y×(1+X100)\text{New Value} = Y + \left( \frac{X}{100} \times Y \right) = Y \times \left(1 + \frac{X}{100}\right)

Example: Add 15% to 200.

200×1.15=230200 \times 1.15 = 230

4. Decrease a number (Y) by a certain percentage (X)

New Value=Y−(X100×Y)=Y×(1−X100)\text{New Value} = Y - \left( \frac{X}{100} \times Y \right) = Y \times \left(1 - \frac{X}{100}\right)

Example: Subtract 30% from 500.

500×0.70=350500 \times 0.70 = 350

5. By what percentage is one number (X) greater than another (Y)?

Increase %=(X−YY)×100%\text{Increase \%} = \left( \frac{X - Y}{Y} \right) \times 100\%

Example: 75 is what percentage greater than 50?

(75−5050)×100%=50%\left( \frac{75 - 50}{50} \right) \times 100\% = 50\%

6. By what percentage is one number (X) less than another (Y)?

Decrease %=(Y−XY)×100%\text{Decrease \%} = \left( \frac{Y - X}{Y} \right) \times 100\%

Example: 30 is what percentage less than 60?

(60−3060)×100%=50%\left( \frac{60 - 30}{60} \right) \times 100\% = 50\%

7. Find the original number if a certain percentage (X) is equal to another number (Y)

Original Number=YX×100\text{Original Number} = \frac{Y}{X} \times 100

Example: If 40% of a number is 80, what is the original number?

8040×100=200\frac{80}{40} \times 100 = 200

8. Percentage change between two values

Change %=(New Value−Original ValueOriginal Value)×100%\text{Change \%} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100\%

Example: A stock price rises from $50 to $65. What is the percentage change?

(65−5050)×100%=30%\left( \frac{65 - 50}{50} \right) \times 100\% = 30\%

Historical context

Percentages date back to ancient civilizations. Roman tax calculations used fractions of 100, while medieval merchants applied percentage-based profit margins. The symbol ”%” evolved from the Italian per cento abbreviation “p.c.” in the 15th century.

Common mistakes and how to avoid them

  1. Misplacing decimal points: Always divide percentages by 100 before calculating.
    Incorrect: 20% of 50 = 20×5020 \times 50.
    Correct: 0.20×50=100.20 \times 50 = 10.

  2. Confusing percentage increase/decrease: Ensure the denominator is the original value, not the new one.
    Example: If a price drops from $200 to $150:

    (200−150200)×100%=25% decrease.\left( \frac{200 - 150}{200} \right) \times 100\% = 25\% \text{ decrease}.

  3. Forgetting units: Label results with ”%” to avoid ambiguity.

Applications in daily life

  • Budgeting: Calculate sales tax (e.g., 7% on a $1,000 purchase = $70).
  • Fitness: Track weight loss (e.g., losing 5% of body weight).
  • Education: Determine exam scores (e.g., 85% correct answers).
  • Investing: Analyze returns (e.g., a 12% annual gain on $10,000 = $1,200).

Frequently Asked Questions

How to calculate a 20% tip on a $45 restaurant bill?

Tip=45×20100=9Total=45+9=$54\text{Tip} = 45 \times \frac{20}{100} = 9 \quad \text{Total} = 45 + 9 = \$54

If a product’s price increases from $80 to $100, what is the percentage increase?

(100−8080)×100%=25%\left( \frac{100 - 80}{80} \right) \times 100\% = 25\%

A population decreases from 5,000 to 4,500. What is the percentage decrease?

(5000−45005000)×100%=10%\left( \frac{5000 - 4500}{5000} \right) \times 100\% = 10\%

How much is 150% of 80?

150100×80=120\frac{150}{100} \times 80 = 120

After a 30% discount, a jacket costs $70. What was its original price?

Original Price=701−0.30=700.70=$100\text{Original Price} = \frac{70}{1 - 0.30} = \frac{70}{0.70} = \$100

Notes

  • Percentages greater than 100% represent values exceeding the original amount.
  • Negative percentage changes indicate a decrease.
  • Use parentheses in formulas to ensure correct order of operations.

Advanced scenarios

  • Compound interest: Combine percentage growth over multiple periods.
    Example: $1,000 at 5% annual interest for 3 years: 1000×(1.05)3≈$1157.631000 \times (1.05)^3 \approx \$1157.63
  • Statistical analysis: Use percentages to compare demographic data (e.g., 60% of survey respondents prefer Option A).

For compound interest calculations, use our compound interest calculator.

Similar calculators

Privacy policy Terms of use

Report a bug