Percentage Formula with Examples
What Is a Percentage?
percentage is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin phrase per centum, meaning "per hundred." When you say 40%, you mean 40 out of every 100, or 40/100 = 0.40.
Percentages are used everywhere — from calculating a discount at a store, to finding your exam score, to understanding a tax rate. Knowing the percentage formula is one of the most practical math skills you can have.
The Basic Percentage Formula
The core formula for calculating a percentage is:
Percentage = (Part / Whole) × 100
This formula answers the question: "What percent of the whole is this part?"
You can rearrange the same formula to find the Part or the Whole, depending on what is unknown:
- To find the Part: Part = (Percentage / 100) × Whole
- To find the Whole: Whole = (Part / Percentage) × 100
These three versions of the formula cover almost every percentage problem you will encounter.
Step-by-Step Examples
Example 1 — Finding the Percentage
Problem: A student scored 45 out of 60 marks. What is their percentage?
Part = 45, Whole = 60
Percentage = (45 / 60) × 100
Percentage = 0.75 × 100
Answer: 75%
Example 2 — Finding the Part
Problem: What is 30% of 250?
Percentage = 30, Whole = 250
Part = (30 / 100) × 250
Part = 0.30 × 250
Answer: 75
Example 3 — Finding the Whole
Problem: 18 is 45% of what number?
Part = 18, Percentage = 45
Whole = (18 / 45) × 100
Whole = 0.40 × 100
Answer: 40
Percentage Increase Formula
Use this formula when a value goes up — for example, a price increase or a salary raise.
Percentage Increase = [(New Value − Old Value) / Old Value] × 100
Example: A product's price increased from $80 to $100.
% Increase = [(100 − 80) / 80] × 100
= [20 / 80] × 100
= 0.25 × 100
Answer: 25% increase
Percentage Decrease Formula
Use this when a value goes down — such as a discount or a drop in temperature.
Percentage Decrease = [(Old Value − New Value) / Old Value] × 100
Example: A salary dropped from $5,000 to $4,000.
% Decrease = [(5000 − 4000) / 5000] × 100
= [1000 / 5000] × 100
= 0.20 × 100
Answer: 20% decrease
Percentage Change Formula
This is a general formula that works for both increases and decreases. A positive result means an increase; a negative result means a decrease.
Percentage Change = [(New Value − Old Value) / Old Value] × 100
Quick Reference — All Percentage Formulas
| What to Find | Formula |
|---|---|
| Percentage | (Part / Whole) × 100 |
| Part | (Percentage / 100) × Whole |
| Whole | (Part / Percentage) × 100 |
| % Increase | [(New − Old) / Old] × 100 |
| % Decrease | [(Old − New) / Old] × 100 |
| % Change | [(New − Old) / Old] × 100 |
Related Formulas
Understanding percentages connects directly to several other important math topics:
- Simple Interest Formula — SI = (P × R × T) / 100 — uses percentage to calculate interest on a loan or deposit. [See Simple Interest Formula →]
- Compound Interest Formula — A = P(1 + r/n)^nt — calculates growth where interest is added back to the principal. [See Compound Interest Formula →]
- Profit and Loss Percentage — Profit % = (Profit / Cost Price) × 100 — essential for business and commerce. [See Profit and Loss Formula →]
- Discount Formula — Discount % = (Discount / Marked Price) × 100 — used in retail and sales. [See Discount Formula →]
Related Calculators and Pages
Frequently Asked Questions (FAQ)
Q1. What is the basic percentage formula?
The basic formula is: Percentage = (Part / Whole) × 100. It expresses one value as a fraction of another, scaled to per hundred. For example, 30 out of 50 = (30/50) × 100 = 60%.
Q2. How do you calculate what percentage one number is of another?
Divide the first number by the second number, then multiply by 100. For example, to find what percent 15 is of 60: (15 / 60) × 100 = 25%.
Q3. What is the formula for percentage increase?
Percentage Increase = [(New Value − Old Value) / Old Value] × 100. If a price goes from $50 to $65, the increase is [(65 − 50) / 50] × 100 = 30%.
Q4. How do you find a percentage of a number?
Use: Part = (Percentage / 100) × Whole. To find 15% of 300: (15/100) × 300 = 45.
Q5. How do you convert a fraction to a percentage?
Divide the numerator by the denominator, then multiply by 100. For example, 3/8 = 0.375 × 100 = 37.5%.
Q6. What is the difference between percentage and percentile?
A percentage is a value out of 100 (e.g., you scored 80%). A percentile is a rank showing what share of a group scored below you (e.g., the 90th percentile means you scored higher than 90% of people).
Summary
The percentage formula — Percentage = (Part / Whole) × 100 — is the building block for dozens of real-world calculations. Whether you need to find a discount, track growth, or calculate interest, this formula is the starting point. Mastering its three forms (finding the percentage, the part, and the whole) along with the increase and decrease variants gives you a complete toolkit for any percentage problem.