Percentage Calculator

Quickly find percentages, percentage change, and the original value before or after a percentage increase or decrease.

What is P% of X?

Result -

P is what % of X?

Result -

Percentage Change

Result -

Percentages Explained: Concepts, Formulas, and Real-World Uses

Percentages describe parts of a whole using “per 100”, making comparisons, discounts, and growth rates easy to understand.

This guide mirrors your other calculator pages with structured boxes, examples, tables, pitfalls, and practice problems, focused on percentage values, reverse percentages, and percentage change.

What Is a Percentage?

A percentage is a way to express a number as a fraction of 100, written with the percent symbol %.

Key Ideas
  • Percent: “Per hundred”; 30% means 30 out of 100.
  • Fraction form: p% = p/100.
  • Decimal form: p% = p/100 as a decimal (e.g., 25% = 0.25).
Example 1: Simple percent
50% = 50/100 = 0.5, representing half of a whole.
Example 2: Converting a fraction
1/4 = 0.25 = 25%.
Fraction Decimal Percentage Description
1/2 0.5 50% Half
1/4 0.25 25% Quarter
3/4 0.75 75% Three quarters
1/10 0.1 10% Tenth
1/100 0.01 1% One per hundred

Core Percentage Formulas

Most percent problems reduce to three main types: “P% of X?”, “P is what % of X?”, and “How much did it change in %?”

1. What is P% of X?

Value = (P/100) × X

Example:
What is 20% of 150?
(20/100) × 150 = 0.2 × 150 = 30.
2. P is what % of X?

Percent = (P / X) × 100

Example:
30 is what percent of 200?
(30/200) × 100 = 0.15 × 100 = 15%.
3. Percentage change

Percentage change = (New − Old) / Old × 100
Positive result = increase; negative result = decrease.

Example:
Price goes from 80 to 100.
Change = (100 − 80)/80 × 100 = 20/80 × 100 = 25% increase.
Question Type Formula Example
P% of X (P/100) × X 25% of 200 = 50
P is what % of X? (P/X) × 100 50 of 200 = 25%
Increase % (New−Old)/Old × 100 80→100 = 25% ↑
Decrease % (Old−New)/Old × 100 100→80 = 20% ↓

Discounts, Markups, and Reverse Percentages

Many real problems involve working backwards from a final price or value to find the original before a percentage increase or decrease.

Discount (percentage decrease)

Final = Original × (1 − d/100)
Original = Final ÷ (1 − d/100)

Example 1: After discount
Original ₹200, discount 15%.
Final = 200 × (1 − 0.15) = 200 × 0.85 = ₹170.
Example 2: Reverse discount
Final price ₹850 after 15% off. Find original.
Original = 850 ÷ 0.85 = ₹1000.
Markup (percentage increase)

Final = Cost × (1 + m/100)
Cost = Final ÷ (1 + m/100)

Example 3: Markup
Cost ₹500, markup 20%.
Selling price = 500 × 1.2 = ₹600.
Example 4: Reverse markup
Selling price ₹720 with 20% profit. Cost = 720 ÷ 1.2 = ₹600.

Step-by-Step Worked Examples

These examples show how to set up and solve percentage problems by hand, then you can verify each using the calculator cards above.

Example 1: What is 18% of 250?
Solution:
Step 1: Convert percentage to decimal: 18% = 0.18.

Step 2: Multiply by the base: 0.18 × 250 = 45.

Answer: 18% of 250 is 45.
Example 2: 40 is what % of 160?
Solution:
Step 1: Divide part by whole: 40/160 = 0.25.

Step 2: Convert to percent: 0.25 × 100 = 25%.

Answer: 40 is 25% of 160.
Example 3: Percentage increase

A salary rises from ₹25,000 to ₹30,000. Find the percentage increase.

Solution:
Step 1: Difference = 30,000 − 25,000 = 5,000.

Step 2: Divide by original: 5,000 / 25,000 = 0.2.

Step 3: Convert to percent: 0.2 × 100 = 20%.

Answer: 20% increase.
Example 4: Percentage decrease

A phone price drops from ₹18,000 to ₹15,300. What is the percentage discount?

Solution:
Step 1: Drop = 18,000 − 15,300 = 2,700.

Step 2: Divide by original: 2,700 / 18,000 = 0.15.

Step 3: Convert: 0.15 × 100 = 15%.

Answer: 15% discount.

Real-World Applications of Percentages

Percentages appear in almost every practical context: money, data, measurements, and comparisons across different scales.

🛒 Shopping and Discounts

Sale tags show percentage reductions, and calculating “P% off” helps compare real savings between different offers.

💰 Finance and Interest

Bank interest rates, GST/VAT, and loan EMIs are expressed as yearly or monthly percentages of principal or price.

📊 Statistics and Data

Surveys, pass percentages, and success rates use percentages to summarize how many out of 100 meet a condition.

📈 Growth and Decay

Population growth, depreciation of assets, and performance changes are often reported as percentage increases or decreases.

🎯 Exams and Grades

Marks are converted to percentages to standardize scores across different tests and maximum marks.

📉 Probability and Risk

Chances of events (like 70% rain probability) are given in percentages to make probabilities easier to interpret.

Common Percentage Mistakes and Fixes

Most percentage errors come from mixing up base values, double-counting changes, or confusing percentage points with percent change.

❌ MISTAKE 1: Wrong base value
Calculating change using the new value instead of the old one gives incorrect percentages.
✅ Always divide by the original (old) value when computing percentage change.
❌ MISTAKE 2: Double percentage changes
A 20% discount followed by a 20% increase does not return to the original price.
✅ Apply each change step-by-step and avoid simply adding or subtracting percentages.
❌ MISTAKE 3: Confusing 10% of X with “X% more”
“10% more than X” is X + 0.10X, not 10% of X alone.
✅ Translate words carefully into formulas before calculating.
❌ MISTAKE 4: Ignoring decimal placement
Forgetting to divide or multiply by 100 leads to results that are 100 times too big or small.
✅ Remember: percent → decimal (÷100), decimal → percent (×100).

Practice Problems with Solutions

Use these problems to test your understanding, then verify your answers using the Percentage Calculator above.

Basic Level
Problem 1: What is 12% of 250?
Show Solution

12% = 0.12; 0.12 × 250 = 30.

Problem 2: 45 is what percent of 180?
Show Solution

(45/180) × 100 = 0.25 × 100 = 25%.

Intermediate Level
Problem 3: A number increases from 60 to 75. Find the percentage increase.
Show Solution

Change = 75 − 60 = 15; 15/60 × 100 = 25% increase.

Problem 4: After a 10% discount, a shirt costs ₹450. What was the original price?
Show Solution

Final = Original × 0.9 ⇒ Original = 450 ÷ 0.9 = ₹500.

Advanced Level
Problem 5: A value is first increased by 20% and then decreased by 20%. Is the final value equal to the original? If not, what percent of the original is it?
Show Solution

Start with 100 for simplicity: after +20% → 120; after −20% → 120 × 0.8 = 96.
Final is 96% of original, not 100%.

Problem 6: A student scores 72 out of 90 in a test. What is the percentage score?
Show Solution

(72/90) × 100 = 0.8 × 100 = 80%.