Percentage Calculator: How to Calculate Percentages in 3 Simple Steps

Why Percentages Matter in Everyday Life

Percentages are everywhere — sale discounts, tax rates, interest rates, exam grades, nutrition labels, salary increases, investment returns, and statistics in the news. Understanding how to calculate them accurately saves money, prevents mistakes, and helps you make better decisions.

The good news: there are only three types of percentage problems, and once you master them you can handle any percentage calculation you encounter. Our Percentage Calculator handles all three instantly.

The Three Core Percentage Calculations

Type 1: What is X% of Y?

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

Formula: Result = (X ÷ 100) × Y

Examples:

What is 20% of £350? Result = (20 ÷ 100) × 350 = 0.20 × 350 = £70

What is 7.5% of £2,400? (useful for calculating tax) Result = (7.5 ÷ 100) × 2,400 = 0.075 × 2,400 = £180

What is 15% of £65? (useful for calculating a tip) Result = (15 ÷ 100) × 65 = 0.15 × 65 = £9.75

Quick mental maths shortcuts:

• 10%: Move the decimal point one place left (10% of £340 = £34)
• 5%: Halve the 10% value (5% of £340 = £17)
• 15%: Add 10% and 5% together (15% of £340 = £34 + £17 = £51)
• 1%: Move the decimal two places left (1% of £340 = £3.40)
• 25%: Divide by 4 (25% of £340 = £85)
• 50%: Divide by 2 (50% of £340 = £170)

Type 2: X is What Percentage of Y?

This tells you what fraction one number is of another, expressed as a percentage.

Formula: Percentage = (X ÷ Y) × 100

Examples:

30 is what percentage of 150? Percentage = (30 ÷ 150) × 100 = 0.2 × 100 = 20%

A student scored 78 out of 120. What percentage did they get? Percentage = (78 ÷ 120) × 100 = 0.65 × 100 = 65%

A shop sold 47 of its 80 items. What percentage sold? Percentage = (47 ÷ 80) × 100 = 0.5875 × 100 = 58.75%

Where you use this:

• Calculating your grade as a percentage
• Finding out what percentage of budget is spent
• Calculating market share
• Determining what percentage of a journey is complete

Type 3: Percentage Change From X to Y

Percentage change tells you how much something has increased or decreased, expressed as a percentage of the original value.

Formula: % Change = ((New Value − Old Value) ÷ Old Value) × 100

A positive result is an increase. A negative result is a decrease.

Examples:

A price rises from £80 to £96. What is the percentage increase? % Change = ((96 − 80) ÷ 80) × 100 = (16 ÷ 80) × 100 = 20%

A salary drops from £45,000 to £40,500. What is the percentage decrease? % Change = ((40,500 − 45,000) ÷ 45,000) × 100 = (−4,500 ÷ 45,000) × 100 = −10%

A stock rises from 150p to 183p. What is the gain? % Change = ((183 − 150) ÷ 150) × 100 = (33 ÷ 150) × 100 = 22%

Common mistake: Percentage change is not symmetric. A 50% decrease followed by a 50% increase does not return you to the original value.

Example: £100 − 50% = £50. £50 + 50% = £75. You are still 25% below the starting point.

Practical Percentage Calculations You Will Use

Calculating a Discount

A jacket is £200 with a 30% discount. What is the sale price?

Step 1: Find the discount amount: 30% of £200 = (30 ÷ 100) × 200 = £60 Step 2: Subtract from original: £200 − £60 = £140

Or use the shortcut: Sale price = Original × (1 − discount%) = 200 × 0.70 = £140

Calculating VAT

A product costs £120 excluding 20% VAT. What is the price with VAT?

Price with VAT = £120 × 1.20 = £144

Removing VAT from a VAT-inclusive price: Net price = £144 ÷ 1.20 = £120

Calculating a Pay Rise

Your salary is £32,000 and you receive a 4.5% rise. What is your new salary?

New salary = £32,000 × 1.045 = £33,440 Rise amount = £33,440 − £32,000 = £1,440

Calculating Investment Returns

You invested £5,000 and it is now worth £6,350. What is your return?

% Return = ((6,350 − 5,000) ÷ 5,000) × 100 = (1,350 ÷ 5,000) × 100 = 27%

Calculating a Tip

Your restaurant bill is £87.50 and you want to leave an 18% tip.

Tip = (18 ÷ 100) × 87.50 = £15.75 Total = £87.50 + £15.75 = £103.25

Working Out a Grade

You scored 142 out of 180 on an exam. What percentage did you get?

Grade = (142 ÷ 180) × 100 = 78.9%

Reverse Percentage: Finding the Original Amount

Sometimes you know the final amount and the percentage change, and need to find the original.

Formula: Original = Final Amount ÷ (1 + percentage as decimal)

A price after a 25% increase is £250. What was the original price? Original = 250 ÷ 1.25 = £200

A salary after a 10% cut is £36,000. What was the original salary? Original = 36,000 ÷ 0.90 = £40,000

A product costs £96 after a 20% discount. What was the original price? Original = 96 ÷ 0.80 = £120

Percentage Points vs Percentages: An Important Distinction

A common source of confusion is the difference between a percentage change and a change in percentage points.

If the interest rate rises from 3% to 5%, it has:

• Increased by 2 percentage points
• Increased by 66.7% (because (5−3)÷3 × 100 = 66.7%)

If unemployment falls from 8% to 6%, it has:

• Decreased by 2 percentage points
• Decreased by 25% (because (6−8)÷8 × 100 = −25%)

Politicians and media often blur this distinction. When someone says an interest rate "increased by 50%," they usually mean it increased by 50 basis points (0.5 percentage points), not that it doubled.

Common Percentage Mistakes

Confusing percentage increase with the final amount A 100% increase means doubling, not tripling. Starting with £50 and increasing by 100% gives you £100, not £150.

Adding and subtracting percentages of different bases A 20% discount followed by an additional 10% discount is not 30% off. It is 20% off then 10% off the reduced price = 28% off the original.

Not accounting for the direction of change A 25% fall requires a 33.3% rise to return to the original value. A 50% fall requires a 100% rise.

Rounding errors in multi-step calculations Avoid rounding intermediate steps. Only round the final answer.

Frequently Asked Questions

• What is 20% of 500?

20% of 500 = (20 ÷ 100) × 500 = 100. Use our Percentage Calculator for any combination instantly.

• How do I calculate percentage increase?

Subtract the old value from the new value, divide by the old value, and multiply by 100. Formula: ((New − Old) ÷ Old) × 100.

• What is 15% of 200?

15% of 200 = (15 ÷ 100) × 200 = 30.

• How do I find what percentage one number is of another?

Divide the first number by the second and multiply by 100. Example: 45 is what % of 180? (45 ÷ 180) × 100 = 25%.

• What is the difference between percentage and percentile?

A percentage is a fraction expressed out of 100. A percentile is a ranking that shows what percentage of a group scored below a given value. Scoring in the 90th percentile means you scored higher than 90% of the group.

• How do I calculate a percentage of a percentage?

Multiply the two percentages together and divide by 100. For example, 20% of 15% = (20 × 15) ÷ 100 = 3%.