Percentage Calculator

Solve common percentage problems

Other Titles
Mastering Percentages
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, '%'.

Solving the Three Main Types of Percentage Problems

  • This calculator handles the three most common percentage calculations you'll encounter.
  • Each calculation solves for a different unknown variable in the percentage equation.
Understanding percentages is a fundamental life skill, essential for everything from shopping to finance. The core relationship can be expressed as: (Part / Whole) * 100 = Percentage. This calculator helps you solve for any one of these three values when you know the other two.
The Three Problems:

Core Formulas

  • 1. What is 20% of 150? Answer: 30
  • 2. 30 is what percent of 150? Answer: 20%
  • 3. 30 is 20% of what? Answer: 150

How to Use the Calculator: A Step-by-Step Guide

  • Select the type of problem you want to solve from the dropdown menu.
  • Enter your two known values into the corresponding input fields.
  • Click 'Calculate' to see the instant result.
The calculator is designed to be intuitive. First, identify what you are trying to find (the part, the percentage, or the whole). Then, select that scenario from the dropdown list. The labels on the input fields will change to guide you.

Practical Example

  • Scenario: A shirt costs $40 and is on sale for 25% off. How much do you save?
  • 1. Select: 'What is X% of Y?'
  • 2. Enter 25 in the 'Percentage (%)' field.
  • 3. Enter 40 in the 'Total Number' field.
  • 4. Result: 10. You save $10.

Percentages in Everyday Life

  • Calculating discounts and sales tax while shopping.
  • Figuring out tips at a restaurant.
  • Understanding interest rates on loans, mortgages, and savings accounts.
Retail and Shopping:
When a store advertises '30% off', you're calculating the part that is subtracted from the whole. If an item is $80, the discount is (30 / 100) * 80 = $24. The final price is $80 - $24 = $56. Sales tax is similar, but it's a percentage added to the total.
Finance and Investment:
Interest rates are a crucial application of percentages. If you have a savings account with a 2% annual interest rate, you can calculate your earnings. If you have $5,000 in the account, your annual interest would be (2 / 100) * 5000 = $100. Conversely, for loans, this represents the extra amount you pay back.

Common Scenarios

  • A 15% tip on a $50 meal is $7.50.
  • If you answer 45 out of 50 questions correctly on a test, you scored (45/50)*100 = 90%.

Common Mistakes to Avoid

  • Forgetting to convert the percentage to a decimal before calculating.
  • Mixing up the 'part' and the 'whole'.
  • Misinterpreting percentage points vs. percentage change.
Percentage to Decimal Conversion:
The most common error is forgetting that the '%' sign means 'per 100'. Before you multiply or divide in a percentage calculation, you must convert the percentage to a decimal or a fraction. For example, 25% becomes 0.25 (by dividing by 100). If you multiply by 25 instead of 0.25, your result will be 100 times too large.
Identifying Part vs. Whole:
In the problem 'X is what percent of Y?', the number that follows the word 'of' is almost always the 'whole' or the denominator. The 'part' is the subset or portion of that whole. Getting these two mixed up will lead to an incorrect answer. For example, '9 is what percent of 36?' is (9/36)100, not (36/9)100.

Calculation Accuracy

  • Incorrect: 50 * 20% = 1000
  • Correct: 50 * (20/100) = 50 * 0.2 = 10

The History and Importance of Percentages

  • The concept of percentages originated in ancient Rome.
  • The '%' symbol evolved from an Italian term, 'per cento'.
  • Percentages provide a universal standard for comparing fractions and proportions.
The idea of expressing parts of a whole in terms of 100 has ancient roots. Roman emperors would levy taxes as a fraction of 1/100 of the value of goods sold at auction. The term 'percent' comes from the Latin 'per centum', meaning 'by the hundred'.
The '%' symbol we use today is believed to have evolved from a 15th-century Italian manuscript. It started as 'p.c.' (for 'per cento'), then the 'p' disappeared and the 'c' was often accompanied by a small circle or 'o', which eventually morphed into the / sign with two zeros. Percentages are invaluable because they standardize comparisons. It is easier to understand that 13% is more than 11% than it is to compare 17/131 and 21/191.

Context and Standardization

  • A score of 40/50 is 80%. A score of 42/60 is 70%. The percentage makes the comparison immediate.