Percentage Calculator: Formulas, Examples & Common Uses

# Percentage Calculator: 3 Formulas, Examples & Quick Tricks

Percentages show up everywhere — discount prices, tax rates, test scores, investment returns, tip calculations, and salary negotiations. There are three core percentage calculations, each with its own formula. Once you know which one to use, the math is straightforward.

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The 3 Core Percentage Formulas#

Formula 1: What is X% of Y? (Find the Part)#

Part = (Percentage ÷ 100) × Whole

This is the most common calculation — finding a percentage of a given number.

Example: What is 15% of $240?

• Part = (15 ÷ 100) × 240 = 0.15 × 240 = $36

Real-world uses: Calculating a tip, a sales tax, a commission, or a discount amount.

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Formula 2: X is what percent of Y? (Find the Percentage)#

Percentage = (Part ÷ Whole) × 100

Use this when you know both numbers and want to express their relationship as a percentage.

Example: 45 out of 60 questions answered correctly — what percent is that?

• Percentage = (45 ÷ 60) × 100 = 0.75 × 100 = 75%

Real-world uses: Test scores, conversion rates, market share, batting averages.

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Formula 3: Percentage Change (Increase or Decrease)#

Percentage Change = [(New Value − Old Value) ÷ Old Value] × 100

A positive result is a percentage increase; a negative result is a percentage decrease.

Example (increase): Stock price went from $80 to $96. What's the percent change?

• Percentage Change = [(96 − 80) ÷ 80] × 100 = [16 ÷ 80] × 100 = +20%

Example (decrease): Product price dropped from $50 to $42. What's the percent decrease?

• Percentage Change = [(42 − 50) ÷ 50] × 100 = [−8 ÷ 50] × 100 = −16%

Real-world uses: Year-over-year revenue growth, price changes, inflation rates, weight loss tracking.

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Percentage Difference vs. Percentage Change#

These are not the same thing:

Example: Comparing the price of two TVs — $500 and $650. There's no "old" and "new," just two prices. Use percentage difference:

• Difference = [|500 − 650| ÷ ((500 + 650) ÷ 2)] × 100 = [150 ÷ 575] × 100 = 26.1% difference

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Quick Mental Math Tricks#

10% shortcut: Move the decimal one place left. 10% of $340 = $34.

Build from 10%:

• 5% = half of 10% ($34 ÷ 2 = $17)
• 20% = double 10% ($34 × 2 = $68)
• 15% = 10% + 5% ($34 + $17 = $51)
• 25% = one quarter of the number ($340 ÷ 4 = $85)

Reverse tip trick: To find 18% mentally, find 20% (double of 10%) then subtract 10% of that. 20% of $65 = $13; 10% of $13 = $1.30; 18% ≈ $13 − $1.30 = $11.70.

The flip trick: "What percent of A is B?" gives the same answer as "What percent of B is A?" — just inverted. 25% of 80 = 20; and 20 is 25% of 80, which means 80 is 400% of 20. If you need a quick sanity check, flip the fraction.

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Common Percentage Calculations Reference#

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Frequently Asked Questions#

How do I calculate a percentage without a calculator?

The 10% method works for most situations: divide the number by 10 (move the decimal left one place), then scale up or down. For 15%, add 10% + 5%. For 25%, divide by 4. For 30%, triple 10%. For irregular percentages like 17%, find 10% + 5% + 2% (which is 10% ÷ 5).

What's the difference between percentage and percentage points?

A percentage is a ratio (60% approval rating). A percentage point is the arithmetic difference between two percentages. If approval rises from 60% to 65%, it increased by 5 percentage points — but by 8.3% (because 5 is 8.3% of 60). Politicians and marketers often use "percentage" when they mean "percentage points" — the distinction matters when evaluating claims.

How do I calculate a percentage increase to reach a target?

Formula: Required increase % = [(Target − Current) ÷ Current] × 100. Example: you earn $60,000 and want $75,000 — that's [(75,000 − 60,000) ÷ 60,000] × 100 = 25% increase.

Why does adding and removing the same percentage not return to the original?

Because the base changes. Increase $100 by 10% = $110. Remove 10% from $110 = $99 — not $100. The second calculation uses $110 as the base, not $100. To reverse a 10% increase, you need to decrease by 9.09% (1/1.1 − 1 = −0.0909).

How do you calculate compound percentages?

For compound growth, apply each percentage sequentially to the running total. Two 10% increases = 1.10 × 1.10 = 1.21, so 21% total growth (not 20%). This is why compound interest and compound annual growth rate (CAGR) formulas use exponents rather than simple addition.