How do I calculate a percentage of a number?

Multiply the number by the percentage and divide by 100. For example, 20% of 150 = (150 × 20) ÷ 100 = 30.

How do I calculate percentage increase?

Use the formula: ((New Value - Old Value) ÷ Old Value) × 100. For example, if a price goes from £50 to £60, the increase is ((60-50) ÷ 50) × 100 = 20%.

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

Divide the first number by the second and multiply by 100. For example, 30 is what % of 150? (30 ÷ 150) × 100 = 20%.

Percentage Calculator Guide: How to Calculate Percentages

Last updated: February 2026 | 9 min read

Percentages are everywhere in daily life - from shopping discounts to exam scores, tax calculations to fitness goals. This comprehensive guide teaches you how to calculate any percentage problem with simple formulas and real-world examples.

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What is a Percentage?

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."

50% means 50 out of 100, or 50/100 = 0.5

Understanding this fundamental concept makes all percentage calculations much easier.

The Three Main Types of Percentage Calculations

Most percentage problems fall into one of these three categories:

Question Type	Example	Formula
What is X% of Y?	What is 20% of 150?	(Y × X) ÷ 100
X is what % of Y?	30 is what % of 150?	(X ÷ Y) × 100
X is Y% of what?	30 is 20% of what?	X ÷ (Y ÷ 100)

Type 1: Finding a Percentage of a Number

The most common percentage question: "What is X% of Y?"

Answer = (Number × Percentage) ÷ 100
Or: Number × (Percentage / 100)

Example 1: What is 20% of 150?

(150 × 20) ÷ 100 = 3000 ÷ 100 = 30

Example 2: What is 15% of £80 (discount)?

(80 × 15) ÷ 100 = 1200 ÷ 100 = £12 discount

Final price: £80 - £12 = £68

Mental Math Shortcuts

10%: Move the decimal point one place left (10% of 250 = 25)
5%: Find 10%, then halve it (5% of 250 = 12.5)
1%: Move the decimal two places left (1% of 250 = 2.5)
15%: Find 10% + 5% (15% of 250 = 25 + 12.5 = 37.5)
20%: Find 10% × 2 (20% of 250 = 50)
25%: Divide by 4 (25% of 250 = 62.5)
50%: Divide by 2 (50% of 250 = 125)

Type 2: Finding What Percentage One Number is of Another

Question: "X is what percent of Y?"

Percentage = (X ÷ Y) × 100

Example: 45 is what percent of 180?

(45 ÷ 180) × 100 = 0.25 × 100 = 25%

Example: You scored 72 out of 90 on a test. What's your percentage?

(72 ÷ 90) × 100 = 0.8 × 100 = 80%

Type 3: Finding the Original Number

Question: "X is Y% of what number?"

Original Number = X ÷ (Y ÷ 100)
Or: X × (100 ÷ Y)

Example: 30 is 20% of what number?

30 ÷ (20 ÷ 100) = 30 ÷ 0.2 = 150

Calculating Percentage Increase

When a value goes up, you can calculate the percentage increase:

% Increase = ((New Value - Old Value) ÷ Old Value) × 100

Example: Your salary increased from £30,000 to £33,000

((33,000 - 30,000) ÷ 30,000) × 100

= (3,000 ÷ 30,000) × 100

= 0.1 × 100 = 10% increase

Calculating Percentage Decrease

For decreasing values, the formula is similar:

% Decrease = ((Old Value - New Value) ÷ Old Value) × 100

Example: A TV's price dropped from £500 to £400

((500 - 400) ÷ 500) × 100

= (100 ÷ 500) × 100

= 0.2 × 100 = 20% decrease

Percentage Change (General Formula)

A single formula works for both increases and decreases:

% Change = ((New - Old) ÷ Old) × 100
Positive result = increase, Negative result = decrease

Common Real-World Percentage Problems

Sale Discounts

A coat costs £120 with 25% off. What's the sale price?

Method 1: Find discount, then subtract

Discount = (120 × 25) ÷ 100 = £30

Sale price = £120 - £30 = £90

Method 2: Multiply by remaining percentage

£120 × (100 - 25)% = £120 × 0.75 = £90

Tips at Restaurants

Your bill is £64. How much is a 15% tip?

10% of £64 = £6.40

5% of £64 = £3.20

15% tip = £6.40 + £3.20 = £9.60

Tax Calculations

A product costs £50 before 20% VAT. What's the total?

£50 × 1.20 = £60

Or: VAT = (50 × 20) ÷ 100 = £10, Total = £50 + £10 = £60

Finding Original Price Before Discount

After 30% off, an item costs £70. What was the original price?

The £70 represents 70% (100% - 30%) of the original

Original = £70 ÷ 0.70 = £100

Percentages and Fractions

Understanding the relationship between percentages and fractions helps with mental math:

Percentage	Fraction	Decimal
10%	1/10	0.1
12.5%	1/8	0.125
20%	1/5	0.2
25%	1/4	0.25
33.33%	1/3	0.333
50%	1/2	0.5
66.67%	2/3	0.667
75%	3/4	0.75

Compound Percentage Changes

When multiple percentage changes occur, you cannot simply add them:

Important: Percentages Don't Simply Add!

A 10% increase followed by a 10% decrease does NOT equal the original:

£100 + 10% = £110

£110 - 10% = £99 (not £100!)

The formula for compound changes:

Final = Original × (1 + r₁) × (1 + r₂) × ...
where r is the decimal form of each change (positive for increase, negative for decrease)

Using Our Percentage Calculator

Our free percentage calculator solves all these problems instantly. It handles:

Finding a percentage of any number
Calculating what percentage one number is of another
Percentage increase and decrease
Finding original values before percentage changes

Calculate Any Percentage

Try our free Percentage Calculator now!

Summary: Key Percentage Formulas

Calculation	Formula
X% of Y	(Y × X) ÷ 100
X is what % of Y?	(X ÷ Y) × 100
X is Y% of what?	X ÷ (Y ÷ 100)
% Increase	((New - Old) ÷ Old) × 100
% Decrease	((Old - New) ÷ Old) × 100
Increase by X%	Number × (1 + X/100)
Decrease by X%	Number × (1 - X/100)

Conclusion

Mastering percentage calculations is a valuable life skill. From understanding discounts while shopping to analysing data at work, percentages appear everywhere. With the formulas in this guide and our free calculator, you'll never struggle with a percentage problem again.

UK Calculator Financial Team

Our team of financial experts creates accurate, easy-to-use calculators and guides to help you make informed decisions about your money.

James Mitchell, ACCA

Chartered Accountant & Former HMRC Advisor

James is a Chartered Certified Accountant (ACCA) specialising in UK personal taxation and financial planning. With over 12 years in practice and a background as a former HMRC compliance officer, he brings authoritative insight to complex tax topics.

Percentages in UK Everyday Life

Percentages are woven into almost every aspect of financial life in the United Kingdom. The Bank of England base rate, which influences mortgage rates, savings interest, and the broader economy, is expressed as a percentage and reviewed eight times a year by the Monetary Policy Committee. As of early 2026, understanding how changes in the base rate translate into actual pounds-and-pence differences on monthly mortgage payments is a vital skill for UK homeowners. A 0.25 percentage point change on a 200,000-pound mortgage can mean a difference of over 25 pounds per month on a variable-rate deal.

UK taxation relies heavily on percentage calculations. Income tax operates on a tiered system with a personal allowance (0%), basic rate (20%), higher rate (40%), and additional rate (45%). National Insurance contributions add further percentage-based deductions. Council Tax increases, announced annually by local authorities and typically expressed as a percentage rise, directly affect household budgets. The UK government also uses percentages extensively when reporting economic indicators such as inflation (measured by the Consumer Prices Index), GDP growth, unemployment rates, and public sector borrowing as a percentage of GDP.

In education, GCSE and A-level results are often discussed in terms of percentage pass rates and grade distributions. Universities set entry requirements using UCAS tariff points, but many employers and institutions also refer to degree classifications: a First requires 70 percent or above, an Upper Second (2:1) requires 60 to 69 percent, and a Lower Second (2:2) requires 50 to 59 percent. Understanding these percentage thresholds helps students set realistic targets and track their academic progress throughout their studies.

Practical Tips for Percentage Calculations

Use the 1% method for mental maths: Find 1% by dividing by 100, then multiply by the percentage you need. For example, 1% of 340 pounds is 3.40 pounds, so 15% is 3.40 times 15 equals 51 pounds.
Remember that percentages are reversible: 8% of 50 is the same as 50% of 8 (both equal 4). Choose whichever calculation is easier to perform mentally.
Convert between fractions and percentages: Knowing common equivalents such as 25% equals one-quarter, 33.3% equals one-third, and 12.5% equals one-eighth can speed up everyday calculations significantly.

Percentage Calculations in UK Everyday Life

Percentages are woven into nearly every aspect of financial and consumer life in the United Kingdom. From the 20% standard rate of Value Added Tax (VAT) applied to most goods and services, to the annual percentage rate (APR) on credit cards and loans, understanding how to calculate percentages is an essential life skill for UK residents. The Money and Pensions Service (MaPS), the UK government's financial guidance body, identifies basic numeracy including percentage calculations as one of the fundamental building blocks of financial capability.

UK retailers frequently use percentage-based promotions, and being able to quickly calculate discounts can help consumers make better purchasing decisions. For example, during the January sales or Black Friday events, understanding that a 30% discount on a 120-pound item saves 36 pounds, or that an additional 10% off an already-reduced price is not the same as a total 40% discount, protects shoppers from misleading marketing. The Advertising Standards Authority (ASA) and Competition and Markets Authority (CMA) both regulate how UK businesses present percentage-based offers, requiring that reference prices are genuine and that savings claims are accurate.

In the UK education system, percentage calculations are taught as part of the national curriculum for mathematics in Key Stages 2 and 3. Students are expected to be fluent in converting between fractions, decimals, and percentages by the end of primary school. Despite this, the National Numeracy charity estimates that approximately 49% of UK working-age adults have the numeracy level expected of primary school children, highlighting the importance of accessible percentage calculation tools for the general public.

Percentage Calculator Guide: How to Calculate Percentages Easily