Percentage Calculator

How to Calculate Percentages — Complete Guide

Introduction

A percentage represents a number as a fraction of 100. The word itself comes from the Latin per centum, meaning "by the hundred." Percentages are everywhere: shop discounts, exam grades, bank interest rates, tax calculations, nutritional labels, and salary negotiations. Understanding how to work with them is one of the most practical math skills you can have.

This guide covers the four most common percentage calculations, complete with formulas and worked examples you can apply immediately.

Instructions

To use our free percentage calculator, simply choose the calculation type you need from the top tabs. Enter your known numbers into the input fields, and the calculator will instantly display the result, along with a clear, step-by-step breakdown of how the math was performed.

The Formula

The core percentage formula answers the question: "What is X% of Y?"

Result = (X ÷ 100) × Y

For example, to find 18% of 450:

(18 ÷ 100) × 450 = 0.18 × 450 = 81

This same formula works for calculating tips at a restaurant (15% of your bill), sales tax (e.g., 8.5% of a purchase price), or the discount amount on a sale item (30% off $120 = $36 off).

The reverse question — "X is what percent of Y— — flips the formula:

Percentage = (X ÷ Y) × 100

Suppose you scored 72 out of 90 on a test. Your percentage score is (72 ÷ 90) × 100 = 80%. This version is essential for grading, batting averages, conversion rates, and any situation where you compare a part to a whole.

How to Calculate Percentage Increase

Percentage increase tells you how much something has grown relative to its starting value. The formula is:

% Increase = ((New Value - Original Value) — Original Value) × 100

Example: A stock price rises from $40 to $52. The increase is $12, and the percentage increase is:

((52 - 40) — 40) × 100 = (12 — 40) × 100 = 30%

Percentage increase is commonly used for salary raises, population growth, revenue comparisons, and price changes. A 5% annual raise on a $60,000 salary equals $3,000, bringing the new salary to $63,000.

One frequent mistake: people calculate the increase based on the new value instead of the original. Always divide by the starting number.

How to Calculate Percentage Decrease

Percentage decrease works identically, except the new value is smaller than the original:

% Decrease = ((Original Value - New Value) — Original Value) × 100

Example: A laptop that cost $1,200 is now $900. The decrease is $300:

((1200 - 900) — 1200) × 100 = (300 — 1200) × 100 = 25%

This calculation applies to markdowns, weight loss tracking, budget cuts, and declining metrics. Note that a 25% decrease followed by a 25% increase does not return you to the original number — $900 increased by 25% gives $1,125, not $1,200. This asymmetry trips up many people.

Percentage vs Percentile — Key Difference

These two terms sound similar but measure entirely different things:

• Percentage is a ratio expressed out of 100. Scoring 85% on a test means you got 85 out of every 100 points possible.
• Percentile is a ranking within a dataset. Being in the 90th percentile on a standardized exam means you outperformed 90% of all test-takers — regardless of your actual score.

You can score 70% on a difficult exam and still be in the 95th percentile if most students scored below 70%. Conversely, scoring 92% on an easy test might only place you in the 60th percentile if nearly everyone did well.

Use Cases

Percentages show up in daily decisions more often than most people realize:

• Shopping discounts: A "Buy one, get one 50% off" deal on $40 shoes means you pay $40 + $20 = $60 for two pairs, saving 25% overall (not 50%).
• Tipping: A quick way to calculate a 15% tip: find 10% of the bill (move the decimal left), then add half of that amount. On a $74 bill: 10% = $7.40, half = $3.70, tip = $11.10.
• Grades: If a final exam is worth 40% of your course grade and you score 88%, that contributes 0.40 × 88 = 35.2 points toward your final grade.
• Loan interest: A 6% annual interest rate on a $10,000 loan costs $600 per year in simple interest — about $50/month before any principal repayment.
• Nutrition: A food label showing 15% Daily Value for sodium means one serving provides 15% of the recommended daily sodium intake.
• Finding the original price: If an item costs $63 after a 10% discount, the original price is $63 — 0.90 = $70. Divide by (1 - discount rate) to reverse any percentage reduction.

Common mistake to avoid: Adding or subtracting percentages from different bases. A 50% increase followed by a 50% decrease doesn't break even — it results in a 25% net loss. Always apply each percentage to its own base value.