How to Calculate Percentage: The Complete Step-by-Step Guide

The word percentage comes from the Latin per centum, which literally translates to "by the hundred." A percentage is simply a ratio or fraction expressed with 100 as its denominator.

Whether you are calculating a discount at a grocery store, examining exam scores, or budgeting your expenses, understanding how percentages work is one of the most practical mathematical skills you can develop.

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The Fundamental Percentage Formula

At its core, calculating what percentage a number is of another number relies on one simple equation:

Percentage = (Part ÷ Whole) × 100

Where:

• Part: The specific portion or subset you are measuring.
• Whole: The total base value or reference amount.

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3 Common Percentage Problems (With Solutions)

Problem 1: Finding the Percentage of a Given Number

Question: What is 20% of 150?

Method:

1. Convert the percentage to a decimal by dividing by 100: 20 ÷ 100 = 0.20
2. Multiply that decimal by the whole number: 0.20 × 150 = 30

Answer: 20% of 150 is 30.

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Problem 2: Finding What Percentage One Number Is of Another

Question: You scored 42 points out of 50 on a test. What percentage is that?

Method:

1. Divide the score (part) by the maximum possible score (whole): 42 ÷ 50 = 0.84
2. Multiply by 100 to convert to a percentage: 0.84 × 100 = 84%

Answer: You achieved an 84% score.

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Problem 3: Working Backwards to Find the Whole

Question: 30 is 15% of what number?

Method:

1. Convert 15% to a decimal: 0.15
2. Divide the part by the decimal: 30 ÷ 0.15 = 200

Answer: The whole number is 200.

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Quick Mental Math Shortcuts

When you do not have a calculator handy, use these reliable mental shortcuts:

• To find 10%: Move the decimal point one place to the left. (10% of 240 = 24)
• To find 5%: Find 10%, then divide by 2. (10% of 240 = 24 → 5% is 12)
• To find 20%: Find 10%, then double it. (10% of 240 = 24 → 20% is 48)
• To find 1%: Move the decimal point two places to the left. (1% of 350 = 3.5)

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Instant Online Calculation

Need an immediate result with step-by-step breakdowns and base increase/decrease values? Use our free, browser-based Percentage Calculator. All calculations happen instantly on your device with 100% privacy.