What This Calculator Does
This all-in-one percentage calculator handles five common percentage operations: finding X% of a number, what percent X is of Y, percentage increase, percentage decrease, and percentage difference between two values. Perfect for homework, business, shopping discounts, and statistics.
Inputs Explained
- Operation: Choose which percentage calculation you need.
- Values: Enter the two numbers required by the chosen operation.
How It Works
Each operation uses a standard percentage formula. The calculator shows the formula, the substituted values, and the final result so you can learn the math, not just the answer.
Formula / Logic Used
Percentage Calculator
Calculate percentage increase, decrease, of a number, or what percent X is of Y.
Step-by-Step Example
Op: What is 20% of 500?
Formula: (20 ÷ 100) × 500 = 100
Result: 100
Op: Percentage increase from 80 to 100
Formula: ((100 − 80) ÷ 80) × 100 = 25%
Use Cases
- Shopping discounts: Calculate sale prices — '40% off ₹2,500' = save ₹1,000.
- Exam scores: Convert raw marks to percentages or check what percentage you need on the next test.
- Salary hikes: Compute the percentage increase from your old to new salary.
- Tip calculation: Find 10%, 15%, or 18% of your restaurant bill.
- Statistics: Calculate percentage difference for comparing two measurements in lab work or surveys.
Assumptions and Limitations
- Percentage difference uses the average of two values as the base, which is only meaningful when neither value is zero or negative.
- For complex compound percentage calculations (e.g., compound interest), use a dedicated calculator.
- Be careful with successive percentage changes — a 20% decrease followed by 20% increase does not return to the original value.
- Negative percentages are mathematically valid but interpretation depends on context.
Frequently Asked Questions
What is the difference between percentage change and percentage difference?
Percentage change uses the original value as the base ((new − old) / old × 100). Percentage difference uses the average of both values as the base — useful when neither is the 'original' (e.g., comparing two methods of measurement).
Why is 20% off and 20% on different from each other?
Because the base changes. ₹100 with 20% off = ₹80. ₹80 with 20% added = ₹96, not ₹100. Successive percentages compound multiplicatively, not additively.
How do I calculate a tip?
Use 'What is X% of Y?' — enter the tip percentage and the bill amount. For 15% on a ₹2,000 bill: 0.15 × 2,000 = ₹300 tip.
Is X% of Y the same as Y% of X?
Yes mathematically. 20% of 50 = 10, and 50% of 20 = 10. This commutative property is sometimes useful for mental math.
How do I find the original price before discount?
If sale price is ₹800 after 20% off: original = sale ÷ (1 − discount/100) = 800 ÷ 0.8 = ₹1,000. The calculator's percentage operations help work backwards similarly.
Can I use this for marks percentage?
Yes. Use 'X is what percent of Y?' — enter your obtained marks as X and total marks as Y. Example: 380 out of 500 = 76%.
Is my data saved?
No. Calculations run entirely in your browser. Numbers are never logged or transmitted.
What's the formula for percentage error?
|Measured − True| ÷ True × 100. Use the 'percentage difference' operation for absolute difference; for percentage error specifically, use percentage decrease (true to measured) and take the absolute value.
Sources and References
- Khan Academy — Percentages — Comprehensive percentage tutorials and exercises.
- Math Is Fun — Percentage Calculator — Visual explanations of percentage concepts.
- NCERT Class 7 Maths — Comparing Quantities — Indian curriculum source for percentage basics.
- Wikipedia — Percentage — Background on percentage notation and uses.