Percentage Calculator
Six modes: find a percentage, % of total, % change, % difference, % error, and reverse percentage. Instant results.
💯 What is Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word itself comes from the Latin per centum, meaning "by the hundred." When you say 35 percent, you mean 35 out of every 100, or equivalently the decimal 0.35 or the fraction 35/100.
Percentages are used everywhere in daily life - from exam scores and discounts to tax rates, interest rates, and nutritional information on food labels. They provide a universal, normalised way to compare proportions. Instead of saying "42 out of 150 customers complained," you can say "28% of customers complained," which is immediately comparable regardless of the total sample size.
This calculator covers six distinct percentage operations in one place. First, finding a percentage of a number (for example, calculating a 15% tip on a bill). Second, finding what percentage one number is of another (for example, expressing exam marks as a percentage of the total). Third, calculating percentage change between an old and new value - useful for salary increases or stock returns. Fourth, percentage difference between two values where neither is the "original" - used when comparing two measurements or two stores' prices. Fifth, percentage error for science and engineering experiments, where you know both the theoretical value and your measured result. Sixth, reverse percentage - working backwards to find the original value before a percentage was applied (for example, finding the pre-tax price from a final total).
A common source of confusion is the difference between a percentage and a percentage point. If a bank's interest rate rises from 4% to 6%, it has risen by 2 percentage points - but by 50% in relative terms (since 2 is 50% of 4). News and financial reports frequently conflate these two concepts, so it is important to know the distinction when reading about interest rates, election polling, or economic statistics.
📐 Percentage Formulas
X% of Y = (X ÷ 100) × Y
Example: 15% of 200 = (15 ÷ 100) × 200 = 30
X is what % of Y = (X ÷ Y) × 100
Example: 45 is what % of 180 = (45 ÷ 180) × 100 = 25%
% Change = [(New − Old) ÷ Old] × 100
Positive result = percentage increase
Negative result = percentage decrease
Example: Price goes from 80 to 100: change = [(100 - 80) / 80] × 100 = 25% increase
% Difference = |V1 − V2| ÷ [(V1 + V2) ÷ 2] × 100
V1, V2 = the two values being compared (neither is the "original")
Used when both values are measurements or observations - not before/after
Example: Store A charges 120, Store B charges 150: difference = |120 - 150| / ((120 + 150) / 2) × 100 = 30 / 135 × 100 = 22.2%
% Error = |Experimental − Theoretical| ÷ |Theoretical| × 100
Theoretical = the known or accepted true value
Experimental = the value you measured in the lab or experiment
Example: Theoretical speed of sound = 343 m/s, measured = 355 m/s: error = |355 - 343| / 343 × 100 = 3.50%
Reverse %: Original = Final ÷ (1 + change%÷100) [increase]
Original = Final ÷ (1 − change%÷100) [decrease]
Use when you know the value after a percentage change and need the original
Example (increase): A price is now 1,440 after a 20% increase: original = 1,440 / 1.20 = 1,200
Example (decrease): A salary is now 34,000 after a 15% cut: original = 34,000 / 0.85 = 40,000
📖 How to Use This Calculator
Steps to Calculate Percentages
1
Select the mode using the tabs at the top of the widget. Choose from: "X% of Y" (find a percentage of a number), "X is ?% of Y" (find what percentage), "% Change" (increase or decrease over time), "% Difference" (compare two values where neither is the reference), "% Error" (science and lab measurements), or "Reverse %" (find the original value before a known percentage change).
2
Enter your values in the fields shown for the selected mode. All inputs accept decimals (e.g. 8.5%).
3
Click Calculate to see the result. The label above the result tells you exactly what was computed.
💡 Example Calculations
Example 1 — Find X% of Y (GST Calculation)
Calculate 18% GST on ₹2,400
1
Convert GST rate to decimal: 18 ÷ 100 = 0.18
2
Multiply: 0.18 × 2,400 = 432
3
Total amount: 2,400 + 432 = 2,832
GST amount = ₹432 | Total payable = ₹2,832
Try this example →Example 2 — Marks to Percentage
A student scored 347 out of 500 in board exams. What is their percentage?
1
Divide scored marks by total: 347 ÷ 500 = 0.694
2
Multiply by 100: 0.694 × 100 = 69.4%
Board exam percentage = 69.4%
Try this example →Example 3 — Percentage Change
A product's price went from ₹1,200 to ₹960. What is the percentage decrease?
1
Difference: 960 − 1,200 = −240
2
Change: (−240 ÷ 1,200) × 100 = −20%
Price decreased by 20%
Try this example →Example 4 — Percentage Difference
Store A sells a phone for ₹18,500; Store B sells the same phone for ₹21,000. What is the percentage difference?
1
Absolute difference: |18,500 − 21,000| = 2,500
2
Average: (18,500 + 21,000) ÷ 2 = 19,750
3
Difference: 2,500 ÷ 19,750 × 100 = 12.66%
Percentage difference between the two prices = 12.66%
Try this example →Example 5 — Reverse Percentage
A shop lists a product as "20% off." The sale price is 960. What was the original price?
1
The sale price is 80% of the original (100% − 20% = 80%)
2
Original = 960 ÷ 0.80 = 1,200
Original price = 1,200
Try this example →Example 6 — Percentage Error
The theoretical density of copper is 8.96 g/cm³. A lab measurement gives 8.72 g/cm³. What is the percentage error?
1
Absolute error: |8.72 − 8.96| = 0.24
2
Divide by theoretical: 0.24 ÷ 8.96 = 0.02679
3
Multiply by 100: 0.02679 × 100 = 2.68%
Percentage error = 2.68%
Try this example →❓ Frequently Asked Questions
What is the formula for percentage?
Percentage = (Part ÷ Whole) × 100. For example, if you scored 72 out of 90 on a test, your percentage is (72 ÷ 90) × 100 = 80%. This formula finds what fraction a part is of the whole, expressed as a number per hundred.
How do I calculate percentage increase or decrease?
Percentage change = ((New Value - Old Value) / Old Value) × 100. If the result is positive, it is an increase. If negative, it is a decrease. For example, a salary increase from ₹40,000 to ₹46,000 is ((46,000 - 40,000) / 40,000) × 100 = 15% increase.
How do I find what percentage one number is of another?
Divide the first number by the second and multiply by 100. For example, 45 is what percentage of 180? = (45 / 180) × 100 = 25%. This is useful for calculating exam scores, conversion rates, market share, and similar proportions.
How do I calculate a percentage of a number?
Multiply the number by the percentage divided by 100. For example, 15% of 240 = (15 / 100) × 240 = 0.15 × 240 = 36. A quick mental trick: to find 10%, just move the decimal point one place left. To find 5%, halve that. To find 15%, add them together.
What is percentage point vs percentage change?
A percentage point is the simple arithmetic difference between two percentages. If a tax rate changes from 18% to 28%, it increased by 10 percentage points. However, in relative terms, it increased by (10 / 18) × 100 = 55.6%. Financial media often use these terms loosely, so always check which one is meant when reading about rate changes.
How do I calculate a percentage discount on a product?
Discount % = ((Original Price - Sale Price) / Original Price) × 100. For example, a product originally at ₹2,500 selling at ₹1,750: discount = ((2,500 - 1,750) / 2,500) × 100 = 30%. To find the sale price when you know the discount: Sale Price = Original Price × (1 - Discount%/100). So 25% off ₹3,000 = ₹3,000 × 0.75 = ₹2,250.
What is 15% of 1200?
15% of 1200 = (15 / 100) × 1200 = 180. A quick mental method: 10% of 1200 = 120, and 5% = 60, so 15% = 120 + 60 = 180. This approach works well for common percentages like 5%, 10%, 15%, 20%, and 25% - useful for quick mental calculations of tips, discounts, or tax amounts.
How do you find the original price before a percentage increase or decrease?
To reverse a percentage change: Original = Final ÷ (1 ± change%). If a price rose by 20% to reach ₹1,800: original = 1,800 ÷ 1.20 = ₹1,500. If a price fell by 15% to reach ₹850: original = 850 ÷ 0.85 = ₹1,000. This is called reverse percentage calculation and is useful when you know the result but not the starting value - common in GST calculations and salary negotiation.
What is percentage difference between two numbers?
Percentage difference = |V1 - V2| / ((V1 + V2) / 2) × 100. Use this when neither value is the "original" or "reference" - for example, comparing the price of the same item at two stores, or two separate measurements of the same quantity. The result is symmetric: it doesn't matter which value is V1 and which is V2. This is mathematically different from percentage change, which requires a clear "old" and "new" value and produces a different number.
What is percentage error and how do I calculate it?
Percentage error = |Experimental - Theoretical| / |Theoretical| × 100. It measures the accuracy of a measured or estimated value relative to a known true value. For example, if the accepted boiling point of ethanol is 78.37°C and your experiment gives 80.1°C: % error = |80.1 - 78.37| / 78.37 × 100 = 2.21%. Always divide by the theoretical value, never the experimental one. The result is always a positive number representing how far off the measurement was.
How do I convert marks to percentage in India?
Marks percentage = (Total scored marks / Total maximum marks) × 100. For a single subject: if you scored 76 out of 100, your percentage is 76%. For aggregate across subjects (e.g. CBSE Class 10 or 12): add all scored marks and divide by the sum of all maximum marks. For 5 subjects with max 100 each - if you scored 82+78+91+74+85 = 410 out of 500: percentage = (410 / 500) × 100 = 82%. Use the "X is ?% of Y" mode in this calculator - enter scored marks as X and total marks as Y.
How is percentage used in everyday life?
Percentages appear in almost every area: bank interest rates, loan EMIs, tax calculations (GST, income tax slabs), exam scores, stock market returns, sale discounts, inflation rates, nutrition labels (% daily value), opinion polls, and sports statistics. Understanding how to calculate and interpret percentages is one of the most practical math skills for personal finance and everyday decisions.