How to Calculate Percentage: Simple Formulas with Examples

A percentage expresses how large one number is compared to another, scaled to a base of 100. The word itself comes from per centum — Latin for “by the hundred” — and the symbol % means “out of 100.” Whether you are figuring out a test score, a store discount, a tip at dinner, or month-over-month sales growth, the same handful of formulas covers almost every everyday percentage problem. This guide walks through those formulas with clear examples, shows how to convert between fractions and decimals, and points you to free ShoutingNow calculators when you want instant answers.

What is a percentage?

Think of a percentage as a standardized fraction. Instead of saying “15 out of 60,” you can say “25 out of 100,” written as 25%. That makes comparisons easier: 25% on a quiz, 25% battery remaining, and a 25% discount all share the same scale even though the underlying units differ.

Every percentage has three related forms:

• Percent: 25%
• Decimal: 0.25 (divide the percent by 100)
• Fraction: 25/100, which simplifies to 1/4

Converting between them is the first skill to lock in. Once you can move freely among percent, decimal, and fraction, the rest of percentage math becomes mechanical.

The core percentage formula

Almost every percentage question boils down to a part–whole relationship:

Percentage (%) = (Part ÷ Whole) × 100

Here, the part is the slice you are measuring and the whole is the total reference amount. If 45 students passed an exam out of 300 who took it, the pass rate is (45 ÷ 300) × 100 = 15%.

Rearrange the same formula when you know two of the three values:

Our Percentage Calculator implements all three rearrangements — enter any two values in the “percent of a number” panel and leave the third blank.

Three essential percentage calculations

Most homework, shopping, and spreadsheet tasks fit one of three phrasing patterns. Learn to recognize the words and map them to the right formula.

1. What is X% of Y? (find the part)

Formula: Result = (X ÷ 100) × Y

Example: What is 25% of 80?

1. Convert 25% to a decimal: 25 ÷ 100 = 0.25
2. Multiply: 0.25 × 80 = 20

So 25% of 80 is 20. On a $80 jacket with 25% off, you save $20 and pay $60.

2. X is what percent of Y? (find the percentage)

Formula: Percentage = (X ÷ Y) × 100

Example: What percent is 45 of 300?

1. Divide part by whole: 45 ÷ 300 = 0.15
2. Multiply by 100: 0.15 × 100 = 15%

Forty-five is 15% of 300. Use this pattern for test scores (42 correct out of 50 → 84%), survey response rates, and market share.

3. Increase or decrease Y by X% (percentage change)

Increase: New value = Original + (X ÷ 100) × Original

Decrease: New value = Original − (X ÷ 100) × Original

Both simplify to: New = Original × (1 ± X/100)

Example: Increase 120 by 10%.

1. Find 10% of 120: (10 ÷ 100) × 120 = 12
2. Add to the original: 120 + 12 = 132

Or in one step: 120 × 1.10 = 132. For a 10% decrease, multiply by 0.90 instead.

Salary raises, inflation adjustments, and year-over-year revenue all use this pattern. The Percentage Calculator has a dedicated percentage change panel for increase, decrease, and reverse calculations.

Converting between fractions, decimals, and percentages

Quick conversions save time on exams and in spreadsheets:

Fraction → percent

Divide numerator by denominator, then multiply by 100. Example: 3/8 → 3 ÷ 8 = 0.375 → 37.5%

Percent → decimal

Divide by 100. Example: 6.5% → 0.065

Decimal → percent

Multiply by 100. Example: 0.42 → 42%

Percent → fraction

Write over 100 and simplify. Example: 40% → 40/100 → 2/5

Memorizing common equivalents — 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/10 = 10% — speeds up mental math at the store or in a meeting.

Percentage change vs. percentage difference

These sound similar but answer different questions.

Percentage change

Measures growth or decline from a specific starting value (the “old” number):

Change % = ((New − Old) ÷ Old) × 100

Example: Revenue rose from $80,000 to $100,000.

((100,000 − 80,000) ÷ 80,000) × 100 = 25% increase

Use percentage change for stock returns, population growth, and KPI dashboards where the baseline matters.

Percentage difference

Compares two values symmetrically, without treating either as the original:

Difference % = (|V₁ − V₂| ÷ ((V₁ + V₂) / 2)) × 100

Example: Compare lab readings of 48 and 52.

|48 − 52| ÷ 50 × 100 = 8% difference relative to their average.

Scientists and quality teams use percentage difference when neither measurement is clearly the “before” value. The Percentage Calculator includes both modes so you do not mix them up.

Real-life percentage applications

Once you recognize the pattern, percentages appear everywhere:

Stacked and successive discounts

Retailers sometimes advertise “20% off, plus an extra 15% off clearance.” The discounts multiply — they do not add to 35% off.

Final price = Original × (1 − d₁/100) × (1 − d₂/100)

Example: $279 item with 20% off, then 15% off the sale price:

$279 × 0.80 × 0.85 = $189.72 (about 32% off the original, not 35%).

The Percent Off Calculator handles stackable coupons so you can verify register totals before checkout.

Worked practice problems

Try these by hand, then check with our Percentage Calculator:

1. What is 15% of 240? → (15 ÷ 100) × 240 = 36
2. 72 is what % of 90? → (72 ÷ 90) × 100 = 80%
3. Increase 85 by 12%. → 85 × 1.12 = 95.2
4. Decrease 200 by 30%. → 200 × 0.70 = 140
5. A price rose from $50 to $62.50. What is the % increase? → ((62.50 − 50) ÷ 50) × 100 = 25%
6. Convert 5/8 to a percent. → 5 ÷ 8 × 100 = 62.5%

Common percentage mistakes

• Adding discounts instead of multiplying. 20% + 15% is not 35% off — multiply the remaining factors (0.80 × 0.85).
• Using the wrong whole. “What % is 30 of 120?” divides by 120, not 30.
• Confusing percentage points with percent change. A rate moving from 10% to 15% is a 5 percentage point rise but a 50% relative increase.
• Forgetting to convert before multiplying. Always turn 25% into 0.25 (or 25/100) before arithmetic.
• Mixing up change and difference. Revenue vs. last year uses percentage change; comparing two lab readings may need percentage difference.

Quick mental-math shortcuts

• 10%: move the decimal one place left ($84 → $8.40).
• 5%: half of 10% ($8.40 ÷ 2 = $4.20).
• 15%: 10% + 5% ($8.40 + $4.20 = $12.60 tip on $84).
• 1%: move the decimal two places left — useful for fine-grained estimates.

Putting it together

Percentage math is not a pile of unrelated tricks — it is one idea repeated in different costumes: part compared to whole, scaled to 100. Identify whether you need a part, a percent, a whole, or a change from a baseline; plug into the matching formula; convert to decimal when multiplying.

When numbers get messy or you are double-checking homework, open the Percentage Calculator for instant results across all three core patterns plus change and difference modes. For shopping, tax, and finance-specific layouts, use the specialized tools linked below.

Percentage calculators on ShoutingNow

• Percentage Calculator — percent of a number, “is what % of,” percentage change, and percentage difference
• Percent Off Calculator — sale price, amount saved, and stackable coupon discounts
• Sales Tax Calculator — add or remove tax from a price using a percentage rate
• ROI Calculator — return on investment as a percentage of cost
• Commission Calculator — earnings from a sale amount and commission rate
• Simple Interest Calculator — interest earned when a rate is quoted as a percent per year
• Compound Interest Calculator — growth when interest compounds at a percentage rate
• How to Calculate Percentage: Simple Formulas with Examples — this guide with worked problems and reference tables