Percentage Calculator — Percentage of Number, Change & What Percent Is

Complete Guide to Percentage Calculations — Formulas, Examples & Tricks

A practical guide for students, professionals, and creators — learn the math behind percentages, common use cases, and how to avoid errors.

Introduction

Percentages are everywhere — from discounts and interest rates to test scores and statistics. Understanding how to calculate percentages quickly and accurately is a valuable life-skill. This guide breaks down three common percentage problems: (1) Percentage of a number, (2) Percentage change, and (3) What percent one number is of another. We also include practical tips, quick mental shortcuts, and real-world examples to make percentage math simple and reliable.

1. Percentage of a Number

This is the most common question: “What is X% of Y?” The formula is straightforward:

Result = (Percentage / 100) × Number

Example: 15% of 2000 → 15/100 × 2000 = 0.15 × 2000 = 300. Use this to calculate discounts (e.g., price after 15% discount = price − 15% of price).

Tip: To find 10% of a number, move the decimal one place left (10% of 200 = 20). To find 5%, divide the 10% by 2 (5% of 200 = 10).

2. Percentage Change (Increase or Decrease)

When comparing two values you often need the percentage change:

Percentage Change = ((New − Old) / Old) × 100

Example: Old price ₹150, New price ₹180 → Change = (180 − 150) / 150 × 100 = 30 / 150 × 100 = 20% increase. If the result is negative, it’s a percentage decrease.

Tip: For small changes, approximate the percentage by dividing the difference by the old value and multiply by 100 — mental math methods help for quick estimates.

3. What Percent Is One Number of Another?

Use this when you want to know what share one number is of the total:

Percent = (Part / Total) × 100

Example: 45 of 200 → (45 / 200) × 100 = 0.225 × 100 = 22.5%.

Practical Examples & Use Cases

Percentages are used in finance (interest rates, returns), shopping (discounts, VAT), education (grades), analytics (conversion rates), and more. A common practical workflow:

1. Use percentage of number for discounts and tax computations.
2. Use percentage change for month-over-month growth or shrinkage.
3. Use ‘what percent is’ for share, composition or ratio analysis.

Common Mistakes to Avoid

• Confusing percentage points with percent change (e.g., 5% rise from 20% is not 25 percentage points but a relative change).
• Using the wrong denominator in percentage change (always divide by the original/old value).
• Rounding too early — carry precision in your calculations, round only for display.

Quick Mental Shortcuts

– 10% = divide by 10 – 5% = half of 10% – 1% = divide by 100 – To get 20% quickly, double 10% – For 15%: 10% + 5%

How This Tool Helps

This calculator prevents input errors, gives instant results, and supports three common percentage operations in one place. Use it for shopping, billing, exam grading, analytics, or budgeting.

Frequently Asked Questions (FAQ)

Q: Should I use the original value or new value for percent change?

A: Always divide the difference by the original (old) value, then multiply by 100.

Q: How do I show increases vs decreases?

A: Positive result = increase; negative result = decrease. You can show an arrow or sign in UI if desired.

Q: Can this tool handle negative numbers?

A: Yes — percentage change uses the numeric difference and handles negative values correctly, but interpret results carefully.

Conclusion

Percentages are fundamental and appear in many areas of life. With simple formulas and careful attention to the denominator, you can solve most percentage problems quickly. Use this Percentage Calculator for fast, accurate answers and keep the mental shortcuts in your toolkit for quick estimates.