Percentage Calculator
Calculate percentages.
RESULT
15% of 200 = 30
Percentage Calculator Explained
The Application of Percentage
A percentage is a fraction of a number expressed in terms of 100 units. For instance, an investor might want to know their profit as a percentage of their investment. If an investor puts in $12,000 and earns a profit of $3,000, the yield is 3,00012,000 which simplifies to ¼ of the investment. To express this as a percentage, we multiply by 100%.
3,00012,000 × 100% = 25%
This 25% means for every $100 invested, the investor earns $25 in profit. If T is the total investment (the base value), and p is the profit, the percentage is:
pT × 100%
How to Interpret Percentage Values
Percentages are always relative to a base value. Using the investment example:
- 0% means no profit; the amount realized equals the amount invested.
- 50% means the profit was half the amount invested.
- 100% means the profit was equal to the amount invested.
- Greater than 100% means the profit exceeded the investment amount.
- Less than 0% (negative) means the investment resulted in a loss.
The Detailed Percentage Formula
If an amount T is invested and a total of A is realized, the profit p is:
p = A - T
The percentage profit is:
A - TT × 100%
If the realized amount A is less than the investment T, it's a loss. The percentage loss is:
T - AT × 100%
How to Compute Percentage of a Number
If an investor with a $3,000 profit withdraws 20%, the amount is 20% of 3,000:
20100 × 3,000 = 600
The amount retained would be 80% of 3,000:
80100 × 3,000 = 2,400
How to Compute Percentage Increase or Decrease
Suppose an investment increases from $12,000 to $15,000. The increase is $3,000. The percentage increase is calculated based on the initial amount ($12,000):
15,000 - 12,00012,000 × 100% = 25%
The investment increased by 25%. You can use the "Percentage Change" mode in the calculator for this. Enter 12000 for the first value and 15000 for the second.
The History of the Percentage
The concept of expressing parts of a whole in consistent fractions dates back to ancient Babylon. The word "percent" itself comes from the Latin "pro centum," meaning "for a hundred." The Romans used this concept for calculating interest on loans.
During the Middle Ages, as trade expanded, calculating percentages became crucial. The modern percentage sign (%) is believed to have evolved from an abbreviation of the Latin "cento" (cto). By 1584, Belgian scientist Simon Stevin published tables for calculating percentages, popularizing their use in science and engineering.
Percentages are one of the most common mathematical concepts we encounter in our daily lives. From calculating a discount at a store to understanding interest rates or interpreting statistics in the news, a firm grasp of percentages is essential. A percentage calculator is a versatile tool designed to handle these calculations effortlessly. This guide will explain the different types of percentage problems this calculator can solve and the formulas behind them.
What is a Percentage?
The word "percent" originates from the Latin "per centum," meaning "by the hundred." A percentage is simply a fraction or a ratio where the value of the whole is always 100. For example, 25% is equivalent to the fraction 25/100, which simplifies to 1/4, or the decimal 0.25. It's a universal way to express a part of a whole, making it easy to compare different quantities.
How This Calculator Works: Four Modes Explained
This calculator is designed to solve the four most common percentage-related questions. You can switch between modes using the dropdown menu.
1. What is X% of Y?
This is the most straightforward percentage calculation. It's used to find a specific percentage of a given number. It's useful for tasks like calculating a tip or sales tax.
Formula:
Result = (X / 100) × Y
Example: What is 15% of 200?
Result = (15 / 100) × 200 = 0.15 × 200 = 30.
2. X is what % of Y?
This calculation determines what percentage one number represents of another. It's perfect for figuring out proportions, like what percentage of your monthly budget goes toward rent.
Formula:
Result (%) = (X / Y) × 100
Example: 40 is what percent of 200?
Result (%) = (40 / 200) × 100 = 0.2 × 100 = 20%.
3. Percentage Change
This mode calculates the percentage increase or decrease from an initial value to a final value. It's essential for tracking changes over time, such as stock price fluctuations, business growth, or changes in personal weight.
Formula:
Percentage Change (%) = ((Final Value - Initial Value) / Initial Value) × 100
A positive result indicates a percentage increase, while a negative result signifies a percentage decrease.
Example: What is the percentage change from 150 to 180?
Change (%) = ((180 - 150) / 150) × 100 = (30 / 150) × 100 = 0.2 × 100 = 20% increase.
Example: What is the percentage change from 50 to 40?
Change (%) = ((40 - 50) / 50) × 100 = (-10 / 50) × 100 = -0.2 × 100 = 20% decrease.
4. X is Y% of what?
This calculation helps you find the "whole" amount when you know a part of it and the percentage that part represents. This is useful for "reverse" calculations, like figuring out the original price of an item after you've been given a discount amount.
Formula:
Result (Whole Amount) = (X / Y) × 100
Example: 50 is 25% of what number?
Result = (50 / 25) × 100 = 2 × 100 = 200.
Practical Applications
Let's see how these calculations apply in the real world:
- Shopping: A shirt is $40, and it's on sale for 20% off. How much is the discount? Use mode 1: "What is 20% of 40?". The discount is $8.
- Finance: You invested $5,000 and it grew to $5,500. What was your return on investment? Use mode 3: "Percentage change from 5000 to 5500". The return was a 10% increase.
- Statistics: In a survey of 300 people, 120 preferred coffee. What percentage of people preferred coffee? Use mode 2: "120 is what % of 300?". The answer is 40%.
- Health & Fitness: You've lost 15 pounds, which you're told is 10% of your starting weight. What was your starting weight? Use mode 4: "15 is 10% of what?". Your starting weight was 150 pounds.
Conclusion
Percentages are a powerful tool for standardizing numbers and making them easier to understand and compare. By breaking down percentage problems into these four common types, this calculator provides a quick and reliable way to find the answers you need for a wide range of academic, financial, and everyday situations.