Online Percentage Calculator
A comprehensive suite of percentage calculators to solve all your math problems. Whether you need to calculate discounts, find the percentage increase between two values, or determine what percentage one number is of another, we have a specific tool for you.
What is a Percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%". Percentages are used to express how large or small one quantity is relative to another.
How much is
What percentage is the value of ?
A value of that INCREASED to . What was the percentage increase?
A value of that DECREASED to . What was the percentage decrease?
The value over the value is what percent?
I have a value of and want to INCREASE it by
I have a value of and want to DECREASE it by
I have an initial value that INCREASED by
I have an initial value that DECREASED by
Understanding Percentages: A Complete Guide
A percentage is a mathematical concept that expresses a number as a fraction of 100. The word comes from the Latin phrase "per centum", meaning "by the hundred." Percentages are one of the most commonly used mathematical concepts in everyday life, appearing in shopping discounts, interest rates, statistics, nutrition labels, tax calculations, and much more.
The Basic Percentage Formula
The fundamental percentage formula is: Percentage = (Part ÷ Whole) × 100. From this single formula, we can derive all nine calculations available in our tool. For example, finding "what is 15% of 200" rearranges to: Part = (Percentage ÷ 100) × Whole = (15 ÷ 100) × 200 = 30.
Percentage Increase and Decrease
Percentage change measures how much a value has increased or decreased relative to its original value. The formula is: Change% = ((New Value − Old Value) ÷ Old Value) × 100. A positive result indicates an increase; a negative result indicates a decrease.
For example, if a product's price goes from $80 to $100, the percentage increase is: ((100 − 80) ÷ 80) × 100 = 25%. Conversely, if it drops from $100 to $80, the decrease is: ((100 − 80) ÷ 100) × 100 = 20%. Notice that the same $20 change represents different percentages depending on the direction — this is because the base (denominator) changes.
Real-World Applications
- Shopping and discounts: A 30% off sale on a $50 item saves you $15 (30% × 50 = 15), making the final price $35.
- Finance and investment: A stock that rises from $10 to $15 has gained 50%. Annual interest rates, inflation, and returns are all expressed as percentages.
- Statistics: Poll results, survey data, and probability are typically reported as percentages for easy comprehension.
- Health and nutrition: Daily Value percentages on nutrition labels tell you what portion of your recommended daily intake a food provides.
- Taxes: Sales tax, income tax brackets, and VAT rates are all percentage-based calculations.
Frequently Asked Questions
Why is percentage increase different from percentage decrease for the same amount?
This is because the base value changes. A $20 increase on a $80 base is 25% (20/80). But a $20 decrease on a $100 base is only 20% (20/100). The base is always the original value, and since the original value is different in each direction, the percentages differ.
How do I calculate reverse percentages?
Reverse percentage (finding the original value) uses this formula: Original = Final ÷ (1 ± Percentage/100). For example, if a price after a 20% increase is $120, the original was: 120 ÷ 1.20 = $100. Our calculator handles this in options 8 and 9.
What is the difference between percentage points and percentages?
Percentage points measure the arithmetic difference between two percentages. For example, if interest rates go from 3% to 5%, that's a 2 percentage point increase, but a 66.7% relative increase ((5-3)/3 × 100). This distinction is important in finance and statistics.
Can a percentage be more than 100%?
Yes. A percentage greater than 100% simply means the part is larger than the whole reference. For example, if a company's revenue grows from $1 million to $3 million, that's a 200% increase. If you invest $100 and it becomes $250, you've earned a 150% return.