how to calculate percentages

Percentage Calculator

Use any section below to quickly solve common percentage problems.

1) Find What is X% of Y?

2) Find X is what percent of Y?

3) Find percentage increase or decrease

What is a percentage?

A percentage is simply a way of expressing a number as a fraction of 100. The word comes from the Latin phrase per centum, meaning “by the hundred.” So if something is 35%, it means 35 out of every 100.

Percentages are everywhere: discounts in stores, test scores, tax rates, inflation, savings growth, conversion rates, and nutrition labels. Once you understand a few core formulas, percentage problems become easy and fast.

Master idea: Percentage = (Part ÷ Whole) × 100

The 3 most common percentage calculations

1) How to find X% of Y

This is the classic “discount/tip/tax” style question.

Formula: X% of Y = (X ÷ 100) × Y

Example: What is 15% of 240?

  • Convert 15% to decimal: 15 ÷ 100 = 0.15
  • Multiply: 0.15 × 240 = 36

Answer: 15% of 240 is 36.

2) How to find what percent one number is of another

Use this when comparing two values, like “50 is what percent of 200?”

Formula: Percentage = (Part ÷ Whole) × 100

Example: 50 is what percent of 200?

  • Divide: 50 ÷ 200 = 0.25
  • Convert to percent: 0.25 × 100 = 25%

Answer: 50 is 25% of 200.

3) How to calculate percentage increase or decrease

Use this for prices, population changes, salary adjustments, and performance metrics.

Formula: Percentage change = ((New − Old) ÷ Old) × 100

Example: Price rises from $80 to $100.

  • Difference: 100 − 80 = 20
  • Divide by old value: 20 ÷ 80 = 0.25
  • Convert to percent: 0.25 × 100 = 25%

Answer: 25% increase.

How to reverse percentages (find the original value)

Reverse percentages are useful when you know the final number after a discount or increase and need the starting number.

After a discount

If a shirt costs $68 after a 15% discount, then $68 is 85% of the original price (because 100% − 15% = 85%).

Original value = Final value ÷ (Remaining percent as decimal)

Original price = 68 ÷ 0.85 = 80.

After an increase

If revenue is $126 after a 5% increase, then $126 is 105% of the original.

Original value = 126 ÷ 1.05 = 120.

Real-life percentage examples

Discounts while shopping

For a 30% sale on a $90 item:

  • Discount amount = 0.30 × 90 = $27
  • Sale price = 90 − 27 = $63

Tips at restaurants

For an 18% tip on a $55 bill:

  • Tip = 0.18 × 55 = $9.90
  • Total = 55 + 9.90 = $64.90

Grade percentages

If you got 42 correct out of 50 questions:

  • 42 ÷ 50 = 0.84
  • 0.84 × 100 = 84%

Simple interest understanding

If you earn 4% annually on $2,000 (simple one-year example):

  • Interest = 0.04 × 2000 = $80
  • New total = $2,080

Quick mental math tricks for percentages

  • 10%: Move decimal one place left (10% of 350 is 35).
  • 1%: Move decimal two places left (1% of 350 is 3.5).
  • 5%: Half of 10% (5% of 350 is 17.5).
  • 25%: One quarter of the number.
  • 50%: Half of the number.
  • 75%: Half plus a quarter.

Common mistakes to avoid

  • Forgetting to divide by 100 when turning percent into decimal.
  • Using the wrong base value in percentage change (always divide by old/original value).
  • Confusing percentage points with percent change. Example: from 10% to 12% is +2 percentage points, but a 20% relative increase.
  • Rounding too early. Keep extra decimals until the final step for better accuracy.

Practice problems (with answers)

  1. What is 12% of 250? Answer: 30
  2. 45 is what percent of 60? Answer: 75%
  3. A value drops from 500 to 425. What is the percentage decrease? Answer: 15%
  4. A jacket after a 20% discount costs $96. What was the original price? Answer: $120
  5. Your score rises from 72 to 81. What is the percent increase? Answer: 12.5%

Final takeaway

To calculate percentages confidently, remember one core concept: percentages are ratios out of 100. Learn the three key formulas, practice with everyday examples, and use the calculator above whenever you need a quick check. With repetition, percentage math becomes automatic.

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