Percentage Calculator

How to Calculate Percentages

A percentage is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin per centum, meaning "by the hundred." Percentages are used everywhere in daily life — from calculating discounts and tips to understanding tax rates, interest rates, exam scores, and statistical data.

The basic percentage formula is straightforward: to find X% of a number Y, you multiply Y by X and divide by 100. Alternatively, you can convert the percentage to a decimal by dividing by 100 first, and then multiply. Both methods give the same result. For example, 25% of 80 can be calculated as (80 x 25) / 100 = 20, or equivalently 80 x 0.25 = 20.

Our percentage calculator supports four common percentage operations: finding a percentage of a number, calculating the percentage change between two values, determining what percentage one number is of another, and increasing or decreasing a value by a given percentage. Each mode is explained in detail below.

Percentage Formula Explained

There are several core percentage formulas you should know. Each serves a different purpose, and understanding when to use which formula is the key to getting accurate results.

Formula 1: Finding X% of Y

This is the most basic percentage calculation. The formula is:

Result = Y x (X / 100)

For example, to find 15% of 300: Result = 300 x (15 / 100) = 300 x 0.15 = 45. This formula is used when you need to calculate a tip, work out a discount amount, find the tax on a purchase, or determine your share of a bill.

Formula 2: What Percentage is X of Y?

This formula determines how one number relates to another as a percentage:

Percentage = (Part / Whole) x 100

For example, if you scored 72 out of 90 on an exam: Percentage = (72 / 90) x 100 = 80%. This tells you that 72 is 80% of 90. This formula is commonly used for exam scores, completion rates, market share calculations, and budget analysis.

Formula 3: Finding the Original Number

Sometimes you know the percentage and the result, but you need to find the original number. The formula is:

Original = Result / (Percentage / 100)

For example, if 30% of a number is 45, then the original number is 45 / 0.30 = 150. This is useful when working backwards from a discount or tax amount to find the original price.

How to Calculate Percentage Change

Percentage change measures how much a value has increased or decreased relative to its original amount. It is one of the most useful percentage calculations in finance, business, and everyday life.

The formula for percentage change is:

Percentage Change = ((New Value - Original Value) / Original Value) x 100

If the result is positive, the value has increased. If it is negative, the value has decreased. The absolute value gives you the magnitude of the change.

For example, if your electricity bill went from £85 last month to £102 this month, the percentage change is ((102 - 85) / 85) x 100 = (17 / 85) x 100 = 20%. Your bill increased by 20%.

Conversely, if a share price drops from £150 to £120, the percentage change is ((120 - 150) / 150) x 100 = (-30 / 150) x 100 = -20%. The share price decreased by 20%.

It is important to note that percentage changes are not symmetrical. A 50% increase followed by a 50% decrease does not return you to the original value. If £100 increases by 50%, it becomes £150. If £150 then decreases by 50%, it becomes £75 — not £100. This asymmetry catches many people out and is important to understand when analysing financial data or investment returns.

How to Calculate Percentage Increase and Decrease

Increasing or decreasing a number by a percentage is a common operation used in pricing, salary adjustments, and financial calculations.

Percentage Increase

To increase a value by a given percentage, use this formula:

New Value = Original Value x (1 + Percentage / 100)

For example, to increase £500 by 12%: New Value = 500 x (1 + 12/100) = 500 x 1.12 = £560. The increase amount is £60.

Percentage Decrease

To decrease a value by a given percentage, use this formula:

New Value = Original Value x (1 - Percentage / 100)

For example, to decrease £800 by 30%: New Value = 800 x (1 - 30/100) = 800 x 0.70 = £560. The decrease amount is £240.

These formulas are essential for applying discounts, calculating salary raises, adjusting prices for inflation, and working with tax rates. In the UK, the standard VAT rate of 20% means that adding VAT to a net price is a percentage increase of 20% (multiply by 1.20), while removing VAT from a gross price requires dividing by 1.20 — not subtracting 20%.

Common Percentage Calculations

Here are some of the most common real-world percentage calculations you might encounter in the UK:

VAT at 20%

The standard UK VAT rate is 20%. To add VAT to a price, multiply by 1.20. To remove VAT from a VAT-inclusive price, divide by 1.20. For example, an item costing £50 before VAT costs £60 including VAT. The VAT amount is £10.

Restaurant Tips (10%, 12.5%, 15%)

Tipping in the UK typically ranges from 10% to 15% of the bill. Common tip amounts: 10% of £80 = £8, 12.5% of £80 = £10, and 15% of £80 = £12. Many restaurants add an optional 12.5% service charge automatically.

Shop Discounts (10% off, 25% off, 50% off)

Sale discounts are percentage decreases. A £120 item with 25% off costs £120 x 0.75 = £90. A £50 item with 10% off costs £50 x 0.90 = £45. During a 50% off sale, you simply halve the price.

Income Tax Rates

UK income tax rates for 2025/26 are: 20% basic rate (on income £12,571 to £50,270), 40% higher rate (£50,271 to £125,140), and 45% additional rate (above £125,140). In Scotland, there are six income tax bands ranging from 19% to 48%.

Mortgage Interest

Mortgage interest is typically quoted as an annual percentage rate. For example, a 4.5% interest rate on a £200,000 mortgage means roughly £9,000 in interest per year (though the actual amount depends on the repayment method and remaining balance). Understanding how percentage rates affect your monthly payments is crucial when choosing a mortgage deal.

Worked Examples

Example 1: Calculating a Discount

A jacket is priced at £85 and has a 30% discount. What is the sale price?

• Discount amount: £85 x 30 / 100 = £25.50
• Sale price: £85 - £25.50 = £59.50
• Or directly: £85 x 0.70 = £59.50

Example 2: Salary Increase

Your annual salary is £35,000 and you receive a 4.5% pay rise. What is your new salary?

• Increase amount: £35,000 x 4.5 / 100 = £1,575
• New salary: £35,000 + £1,575 = £36,575
• Or directly: £35,000 x 1.045 = £36,575

Example 3: Percentage Change in House Prices

A house was bought for £250,000 and is now worth £290,000. What is the percentage increase?

• Difference: £290,000 - £250,000 = £40,000
• Percentage change: (£40,000 / £250,000) x 100 = 16%
• Result: The house has increased in value by 16%

Example 4: Exam Score

A student scores 68 marks out of a possible 85. What percentage is this?

• Percentage: (68 / 85) x 100 = 80%
• Result: The student scored 80%

Example 5: Adding VAT to a Business Invoice

A consultant charges £2,500 for a project and needs to add 20% VAT:

• VAT amount: £2,500 x 20 / 100 = £500
• Total invoice: £2,500 + £500 = £3,000
• Or directly: £2,500 x 1.20 = £3,000

Example 6: Splitting a Restaurant Bill with Tip

Three friends share a £96 restaurant bill and want to leave a 12.5% tip:

• Tip amount: £96 x 12.5 / 100 = £12
• Total with tip: £96 + £12 = £108
• Per person: £108 / 3 = £36 each

Quick Reference Table

Use this table to quickly look up common percentages of round numbers. These are the most frequently needed percentage calculations:

Mental Maths Tricks for Percentages

You do not always need a calculator to work out percentages. Here are some useful mental arithmetic shortcuts:

• 10%: Simply divide by 10. To find 10% of £350, move the decimal point one place left: £35.
• 5%: Find 10% and halve it. 5% of £350 = £35 / 2 = £17.50.
• 1%: Divide by 100. To find 1% of £350, move the decimal point two places left: £3.50.
• 20%: Find 10% and double it. 20% of £350 = £35 x 2 = £70.
• 25%: Divide by 4. To find 25% of £350 = £350 / 4 = £87.50.
• 50%: Simply halve the number. 50% of £350 = £175.
• 15%: Find 10% and add half of it. 15% of £200 = £20 + £10 = £30.
• Any percentage: Break it into parts. For 35% of 200: 30% is 60, 5% is 10, so 35% is 70.

Another useful trick: percentages are commutative, meaning X% of Y equals Y% of X. So 8% of 50 is the same as 50% of 8 = 4. This can make tricky calculations much simpler. For example, 4% of 75 is the same as 75% of 4 = 3.

Common Mistakes When Calculating Percentages

1. Confusing Percentage Change with Percentage Points

If an interest rate moves from 3% to 5%, many people say it has "increased by 2%." Strictly speaking, it has increased by 2 percentage points. The percentage increase is actually (2/3) x 100 = 66.7%. This distinction matters in finance and economics.

2. Assuming Percentage Changes Are Reversible

A 25% increase followed by a 25% decrease does not return to the original number. If £100 increases by 25%, it becomes £125. If £125 decreases by 25%, it becomes £93.75 — a net loss of £6.25. To return to the original after a 25% increase, you need a decrease of 20% (not 25%).

3. Removing VAT by Subtracting the Percentage

To remove 20% VAT from £120, you must divide by 1.20 (giving £100), not subtract 20% (which gives £96). VAT is calculated on the net price, so removing it requires dividing, not subtracting.

4. Applying Successive Percentages Incorrectly

If an item is discounted by 20% and then by a further 10%, the total discount is not 30%. A £100 item discounted by 20% becomes £80. A further 10% discount on £80 gives £72. The total discount is £28, or 28% — not 30%.