How do I work out reverse percentage to find the original price?

To find the original price before a percentage increase, divide by (1 + rate). A product costs £60 after 20% increase: £60 ÷ 1.20 = £50 original. To remove VAT: £120 inc VAT ÷ 1.20 = £100 ex VAT.

Percentage Calculator UK 2025/26 | X% of Y, Change & Increase

Calculator

Use this free percentage calculator to quickly work out percentages. Choose a mode below — find a percentage of a number, calculate what percentage one number is of another, or work out the percentage change between two values.

What is X% of Y?

X is what % of Y?

Percentage Change

Percentage (%)

of Number

Formula: Result = (Number × Percentage) ÷ 100

Number (part)

of Total (whole)

Formula: Percentage = (Part ÷ Whole) × 100

From (original value)

To (new value)

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

How Percentages Work

A percentage is a number expressed as a fraction of 100. The word comes from the Latin per centum, meaning "by the hundred." Percentages are used everywhere in daily life — from VAT on shopping (20% in the UK) to interest rates on savings, exam scores, discounts, and nutritional labels.

Quick examples: 50% means half. 25% means a quarter. 10% of any number is simply that number divided by 10. To find 1% of any number, move the decimal point two places to the left.

Tip: "X% of Y" always equals "Y% of X." So 8% of 50 = 50% of 8 = 4. Use whichever is easier to calculate mentally.

Common Percentage Reference Table

Percentage	As a Decimal	As a Fraction	Example (of 200)
5%	0.05	1/20	10
10%	0.10	1/10	20
20% (UK VAT)	0.20	1/5	40
25%	0.25	1/4	50
33.33%	0.333	1/3	66.67
50%	0.50	1/2	100
75%	0.75	3/4	150
100%	1.00	1/1	200

How to Calculate Percentage of a Percentage

To find a percentage of a percentage, convert both to decimals and multiply. For example, 20% of 50% = 0.20 × 0.50 = 0.10 = 10%. This is common in UK scenarios like calculating the effective tax rate on a portion of income.

Real-world example: A shop offers 30% off, then an extra 10% off the sale price. The total discount is not 40%. It is: 100% − (70% × 90%) = 100% − 63% = 37% total discount.

How to Calculate Percentage Difference Between Two Numbers

Percentage difference compares two values without defining one as the "original." The formula is: |Value 1 − Value 2| ÷ ((Value 1 + Value 2) ÷ 2) × 100.

This is different from percentage change, which has a clear "before" and "after." Use percentage difference when comparing two independent values, such as prices at two different shops.

Value A	Value B	% Difference
£50	£60	18.18%
£100	£120	18.18%
£250	£300	18.18%
£1,000	£1,500	40.00%

How to Convert Fractions to Percentages

To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100. For example: 3/8 = 3 ÷ 8 = 0.375 = 37.5%.

Fraction	Decimal	Percentage
1/8	0.125	12.5%
1/6	0.1667	16.67%
2/5	0.40	40%
3/8	0.375	37.5%
5/6	0.8333	83.33%
7/8	0.875	87.5%

Worked Percentage Examples for UK Everyday Situations

These worked examples show how percentages apply to real UK financial scenarios.

Scenario	Calculation	Answer
VAT (20%) on £85 purchase	£85 × 0.20	£17.00 VAT
25% discount on £120 jacket	£120 × 0.25	Pay £90.00
Basic tax (20%) on £17,430	£17,430 × 0.20	£3,486.00
3% pay rise on £32,000	£32,000 × 0.03	£960.00 rise
4.5% mortgage rate on £200,000	£200,000 × 0.045	£9,000/year interest
5% pension on £35,000 salary	£35,000 × 0.05	£1,750.00/year
15% tip on £48 meal	£48 × 0.15	£7.20 tip

UK Percentage Quick Reference Table

Common percentages you encounter in UK daily life, from tax bands to tipping.

UK Context	Percentage	Details
Standard VAT rate	20%	Most goods and services
Reduced VAT rate	5%	Home energy, children's car seats
Basic rate income tax	20%	£12,571 to £50,270
Higher rate income tax	40%	£50,271 to £125,140
Employee NI rate	8%	£12,570 to £50,270
Auto-enrolment pension (employee)	5%	Minimum contribution
Auto-enrolment pension (employer)	3%	Minimum employer contribution
Student loan Plan 2 rate	9%	Above £27,295 threshold
Stamp duty (first band)	5%	£250,001 to £925,000

Source: GOV.UK — rates for 2025/26 tax year.

Related Calculators

Frequently Asked Questions

How do I calculate a percentage?

To calculate a percentage of a number, multiply the number by the percentage and divide by 100. For example, 15% of 200 = (200 × 15) ÷ 100 = 30. You can also convert the percentage to a decimal first: 15% = 0.15, then 0.15 × 200 = 30.

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

Divide the part by the whole and multiply by 100. For example, to find what percentage 30 is of 200: (30 ÷ 200) × 100 = 15%. This formula works for any two numbers — just remember: part divided by whole, times 100.

How do I calculate percentage increase or decrease?

Subtract the old value from the new value, divide by the old value, and multiply by 100. For example, from 100 to 150: ((150 − 100) ÷ 100) × 100 = +50% increase. From 200 to 150: ((150 − 200) ÷ 200) × 100 = −25% decrease. A positive result means increase; negative means decrease.

What is 20% of 100?

20% of 100 is 20. The calculation is (100 × 20) ÷ 100 = 20. This is one of the simplest percentage calculations — whenever the base number is 100, the percentage equals the answer directly. This is also the UK standard VAT rate, so 20% VAT on a £100 item = £20 VAT.

How do I work out VAT (20%)?

To add VAT at 20%, multiply the net amount by 1.20. For example, £100 + 20% VAT = £100 × 1.20 = £120. To find the VAT amount alone, multiply by 0.20 (e.g. £100 × 0.20 = £20 VAT). To remove VAT from a gross price, divide by 1.20 (e.g. £120 ÷ 1.20 = £100 net). The reduced VAT rate is 5% for home energy and children’s car seats.

How do I calculate a percentage of a percentage?

Multiply the two percentages together as decimals. For example, 25% of 60% = 0.25 × 0.60 = 0.15 = 15%. This is useful for stacking discounts: a 20% discount then an extra 10% off is 0.80 × 0.90 = 0.72, meaning the total discount is 28%, not 30%.

How do I convert a fraction to a percentage?

Divide the top number by the bottom number and multiply by 100. For example, 3/8 = 3 ÷ 8 = 0.375, then 0.375 × 100 = 37.5%. Common conversions: 1/4 = 25%, 1/3 = 33.33%, 1/5 = 20%, 2/3 = 66.67%, 3/4 = 75%.

What is the difference between percentage change and percentage difference?

Percentage change measures change from an original value: ((New − Old) ÷ Old) × 100. Percentage difference compares two values without defining one as original: |A − B| ÷ ((A + B) ÷ 2) × 100. Use percentage change when there is a clear "before" and "after." Use percentage difference when comparing two independent values, such as prices at two shops.

How do I work out reverse percentage (find the original price)?

To find the original price before a percentage increase, divide by (1 + rate). For example, a product costs £60 after a 20% increase: £60 ÷ 1.20 = £50 original price. To find the price before a discount, divide by (1 − rate). A sale price of £80 after 20% off: £80 ÷ 0.80 = £100 original. This is how you remove VAT: £120 inc. VAT ÷ 1.20 = £100 ex. VAT.

How do I calculate percentage on a calculator?

On a standard calculator, to find X% of Y: type Y, press ×, type X, press %. On a phone calculator, enter Y × X ÷ 100 =. For percentage increase, multiply by (1 + rate). For example, £80 + 15% = 80 × 1.15 = £92. Our online calculator above handles all these modes automatically.