Percentage Calculator: The Complete Guide
Learn what a percentage is, how every common percentage formula works, and how to apply percentages to exam marks, discounts, tax, tips, salaries, profits and everyday decisions.
What Is a Percentage?
A percentage expresses a number as a fraction of 100. The word percent means per hundred, so 50% is 50 out of 100, 25% is 25 out of 100, and 100% is the complete amount. Scoring 85% on an exam means answering correctly 85 marks out of every 100.
Because percentages are always based on 100, they let you compare values of completely different sizes. Student A scoring 45 out of 60 and Student B scoring 72 out of 90 look hard to compare, until you convert them to 75% and 80%.
What Is a Percentage Calculator?
A Percentage Calculator applies the standard percentage formulas automatically. You enter the numbers, choose the type of calculation, and the answer appears instantly. This calculator handles the three calculations people search for most:
- What is X% of Y?
- X is what percent of Y?
- Percentage increase and percentage decrease between two values
How to Find X% of a Number
Formula: Percentage Value = (Percentage x Number) / 100
What is 20% of 500? 20 x 500 = 10,000, then 10,000 / 100 = 100. So 20% of 500 is 100. What is 35% of 800? 35 x 800 = 28,000, then 28,000 / 100 = 280.
This is the calculation behind discounts, tax amounts, commissions, tips and marks awarded out of a total.
X Is What Percent of Y?
Formula: Percentage = (Part / Whole) x 100
75 is what percent of 300? 75 / 300 = 0.25, then 0.25 x 100 = 25%. Similarly, 48 out of 60 is 80%. Use it for exam percentages, attendance, goal completion and sales performance.
Percentage Increase
Formula: ((New Value - Original Value) / Original Value) x 100
A score rising from 70 to 84 is an increase of 14. 14 / 70 = 0.2, so the score increased by 20%. Percentage increase is used for salary raises, revenue, population, website traffic and investment returns.
Percentage Decrease
Formula: ((Original Value - New Value) / Original Value) x 100
A price falling from $250 to $200 is a drop of 50. 50 / 250 = 0.2, so the product is 20% cheaper. Percentage decrease covers discounts, price cuts, weight loss, revenue decline and energy savings.
Percentage Difference and Percentage Change
Percentage change tracks how one value moved over time. Percentage difference compares two separate values without treating either as the starting point, which is useful for comparing prices, temperatures, populations and measurements.
Every Formula at a Glance
| Calculation | Formula | Example |
|---|---|---|
| X% of Y | (P x N) / 100 | 20% of 500 = 100 |
| X is what % of Y | (Part / Whole) x 100 | 75 of 300 = 25% |
| Percentage increase | ((New - Old) / Old) x 100 | 70 to 84 = 20% |
| Percentage decrease | ((Old - New) / Old) x 100 | 250 to 200 = 20% |
| Exam percentage | (Marks / Total) x 100 | 425 of 500 = 85% |
| Attendance | (Attended / Total) x 100 | 92 of 100 = 92% |
How to Calculate Exam Percentage
Exam Percentage = (Marks Obtained / Total Marks) x 100. Scoring 425 out of 500 gives 85%. Once you have your subject percentages you can convert them with the Percentage to CGPA Calculator or work out your overall standing with the GPA Calculator.
How to Calculate Attendance Percentage
Attendance Percentage = (Classes Attended / Total Classes) x 100. Attending 92 of 100 classes gives 92%, comfortably above the 75% minimum most institutions require.
Discounts, Tax and Tips
Discount: a 25% discount on a $120 item saves $30, so you pay $90.
Sales tax: 8% tax on a $500 product adds $40, so the final price is $540.
Tip: a 15% tip on an $80 bill is $12, so you pay $92.
| Situation | Original | Percentage | Result |
|---|---|---|---|
| Discount | $200 | 25% off | $150 final price |
| Black Friday | $800 TV | 40% off | $480 final price |
| Sales tax | $900 laptop | 8% tax | $972 total |
| Restaurant tip | $125 bill | 20% tip | $150 total |
| Salary raise | $3,000 | 10% raise | $3,300 per month |
| Investment | $10,000 | 15% return | $11,500 value |
Where Percentages Are Used
Percentages appear in nearly every field because they standardise values for fair comparison:
- Education: exam scores, assignments, attendance, scholarship cut offs, GPA and CGPA conversions
- Shopping: discounts, coupons, cashback, clearance sales, sales tax
- Banking: savings interest, loan APR, mortgages, fixed deposits
- Business: profit margin, revenue growth, market share, retention
- Healthcare: body fat, nutrition daily values, recovery rates
- Sports: win rate, shooting percentage, pass completion
- Marketing and SEO: click through rate, conversion rate, bounce rate, traffic growth
- Government: inflation, unemployment, economic growth, election results
Percentages beat raw numbers for comparison. School A passing 400 of 450 students (88.9%) outperforms School B passing 800 of 1,200 students (66.7%), even though School B has the bigger number.
Mental Math Percentage Tricks
| Percentage | Shortcut | Example |
|---|---|---|
| 1% | Move the decimal two places left | 1% of 900 = 9 |
| 10% | Move the decimal one place left | 10% of 650 = 65 |
| 5% | Half of 10% | 5% of 650 = 32.5 |
| 25% | Divide by 4 | 25% of 200 = 50 |
| 50% | Divide by 2 | 50% of 800 = 400 |
| 75% | 50% plus 25% | 75% of 400 = 300 |
Common Percentage Mistakes to Avoid
- Dividing the whole by the part instead of the part by the whole
- Forgetting to multiply by 100 after dividing
- Confusing percentage increase with percentage difference
- Comparing values measured in different units
- Rounding halfway through instead of at the end
Manual Calculation vs Percentage Calculator
| Manual calculation | Percentage Calculator |
|---|---|
| Requires formulas | No formulas needed |
| Easy to make mistakes | Accurate every time |
| Slower | Instant answers |
| Needs math confidence | Beginner friendly |
| Time consuming | Saves time |
Percentage Glossary
- Percentage: a value expressed out of 100
- Percentage increase: how much a value grew from its original value
- Percentage decrease: how much a value fell from its original value
- Percentage difference: a comparison between two separate values
- Percentage change: the overall rise or fall over time
- Discount: a reduction applied to an original price
- Interest rate: the percentage charged or earned on money
- Profit margin: the percentage of revenue kept as profit
Key Takeaways
- A percentage is simply a part of 100, which makes different values comparable.
- Almost every percentage problem is one of six calculations: percent of a number, part of a whole, increase, decrease, difference and change.
- Percentages drive decisions in education, shopping, banking, business, health and sport.
- Mental shortcuts cover simple cases, while the calculator handles large numbers and repeated calculations without errors.