Percentages are everywhere in daily UK life: the 20% VAT on your shopping, the 40% higher-rate income tax band, a 15% sale discount, or your mortgage interest rate. Once you understand the basic formula, working out any percentage becomes straightforward — no advanced maths required.
This guide explains how to work out a percentage using step-by-step examples, covers every type of percentage calculation you are likely to encounter, and answers the most common questions people ask.
The Core Percentage Formula
Every percentage calculation starts from the same fundamental relationship:
Rearranging this formula gives you three tools:
- Find the percentage: (Part ÷ Whole) × 100
- Find the part: (Percentage ÷ 100) × Whole
- Find the whole: Part ÷ (Percentage ÷ 100)
These three rearrangements cover virtually every percentage problem you will encounter.
Type 1: What Percentage Is One Number of Another?
Use this when you want to express one value as a percentage of another — for example, converting an exam score to a percentage.
You scored 45 out of 60 in a test. What percentage did you get?
Step 1: Divide the part by the whole: 45 ÷ 60 = 0.75
Step 2: Multiply by 100: 0.75 × 100 = 75%
You had a monthly budget of £2,000 and spent £1,450. What percentage did you spend?
(1,450 ÷ 2,000) × 100 = 72.5%
Type 2: Find a Percentage of a Number
This is the most common type. You know the whole and you want to find a specific percentage of it — for example, calculating VAT, a tip at a restaurant, or a commission payment.
A quicker method: convert the percentage to a decimal by dividing by 100, then multiply.
- 10% = 0.10 • 20% = 0.20 • 25% = 0.25 • 50% = 0.50
UK standard VAT rate is 20%. How much VAT is charged on a £50 item?
Method 1 (formula): (20 ÷ 100) × 50 = 0.20 × 50 = £10
Method 2 (decimal shortcut): 50 × 0.20 = £10
Total price including VAT: £50 + £10 = £60 (or simply 50 × 1.20 = £60)
A jacket priced at £80 has a 25% off sale. What is the sale price?
Step 1: Find 25% of £80: 80 × 0.25 = £20 (the discount)
Step 2: Subtract: £80 − £20 = £60
Shortcut: multiply by (1 − 0.25) = 0.75: 80 × 0.75 = £60
Type 3: Percentage of Income Tax
One of the most important applications in the UK is working out how much income tax you owe. The UK uses a progressive tax system — meaning different portions of your income are taxed at different rates.
2025/26 tax rates (England, Wales, Northern Ireland):
| Band | Taxable Income | Rate |
|---|---|---|
| Personal Allowance | Up to £12,570 | 0% |
| Basic rate | £12,571 to £50,270 | 20% |
| Higher rate | £50,271 to £125,140 | 40% |
| Additional rate | Over £125,140 | 45% |
Salary: £30,000 | Personal Allowance: £12,570
Step 1: Taxable income = £30,000 − £12,570 = £17,430
Step 2: Tax at 20% basic rate: £17,430 × 0.20 = £3,486
Step 3: Effective tax rate: (£3,486 ÷ £30,000) × 100 = 11.62%
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Use our free percentage calculator to check any percentage in seconds.
Open Percentage Calculator →Type 4: Percentage Change (Increase or Decrease)
Percentage change tells you how much something has grown or shrunk relative to its original value. This applies to salary increases, price rises, inflation, and investment returns.
- A positive result = percentage increase
- A negative result = percentage decrease
Your salary rose from £25,000 to £27,500. What is the percentage increase?
((27,500 − 25,000) ÷ 25,000) × 100 = (2,500 ÷ 25,000) × 100 = 10%
A house worth £320,000 drops in value to £304,000. What is the percentage decrease?
((304,000 − 320,000) ÷ 320,000) × 100 = (−16,000 ÷ 320,000) × 100 = −5%
Type 5: Percentage Difference Between Two Numbers
Percentage difference is used when neither of the two numbers is clearly the "starting point". It measures the relative difference between two values symmetrically.
Item A costs £40. Item B costs £50. What is the percentage difference?
|40 − 50| = 10 | (40 + 50) ÷ 2 = 45
(10 ÷ 45) × 100 = 22.2%
How to Work Out a Percentage on a Calculator
Most smartphones and physical calculators have a % key that makes this even faster.
On a Standard Calculator with a % Key
- To find 20% of 150: press 150 × 20 % = 30
- To add 20% VAT to £80: press 80 + 20 % = 96
- To take 15% off £200: press 200 − 15 % = 170
On a Basic Calculator (No % Key)
- Convert the percentage to a decimal: 20% = 0.20, 7.5% = 0.075
- Multiply: £150 × 0.20 = £30
On a Smartphone (iOS/Android)
Turn your phone to landscape mode to reveal the scientific calculator. The % button divides a number by 100 instantly. Type 20 % to get 0.20, then multiply by your number.
- 10% of any number: move the decimal one place left (10% of £350 = £35)
- 5%: halve the 10% figure (5% of £350 = £17.50)
- 20%: double the 10% figure (20% of £350 = £70)
- 25%: divide by 4 (25% of £80 = £20)
- 50%: divide by 2 (50% of £90 = £45)
- 1%: move decimal two places left, then scale up
Reverse Percentages: Working Backwards
Sometimes you know the final amount (after a percentage has been applied) and need to find the original. This is called a reverse percentage and is common when removing VAT from a VAT-inclusive price.
A laptop costs £1,200 including 20% VAT. What is the pre-VAT price?
£1,200 ÷ 1.20 = £1,000 (pre-VAT)
VAT amount: £1,200 − £1,000 = £200
Real-World UK Percentage Examples at a Glance
| Scenario | Calculation | Answer |
|---|---|---|
| 20% VAT on £50 | 50 × 0.20 | £10 VAT (£60 total) |
| 25% off £80 | 80 × 0.75 | £60 |
| Exam: 45/60 | (45 ÷ 60) × 100 | 75% |
| Salary rise £25k to £27.5k | ((2500 ÷ 25000) × 100) | 10% increase |
| Income tax on £30k salary | (17,430 × 0.20) | £3,486 |
| 5% mortgage interest on £200k | 200,000 × 0.05 | £10,000/yr interest |
| 10% service charge on £45 bill | 45 × 0.10 | £4.50 tip |
| Remove 20% VAT from £120 | 120 ÷ 1.20 | £100 pre-VAT |
Common Mistakes to Avoid
"20% of £100" = £20. But "a 20% increase from £100" = £120. These are different operations.
Adding 20% and then removing 20% does NOT return to the original. Example: £100 + 20% = £120. £120 − 20% = £96, not £100. Removing 20% from £120 requires dividing by 1.20.
If interest rates rise from 2% to 3%, that is an increase of 1 percentage point, but a 50% increase in the rate itself. These two statements are both correct but mean different things.
50 × 20 = 1,000. That is wrong. You must divide by 100 first: 50 × (20 ÷ 100) = 50 × 0.20 = 10.
Percentage Formula Summary
| What You Want | Formula | Example |
|---|---|---|
| % of a number | Number × (% ÷ 100) | 20% of £50 = £10 |
| What % is A of B | (A ÷ B) × 100 | 45 of 60 = 75% |
| % increase | ((New−Old)÷Old)×100 | 25k to 27.5k = 10% |
| % decrease | ((Old−New)÷Old)×100 | 320k to 304k = 5% |
| Reverse % (find original) | Final ÷ (1 + %/100) | £120 incl VAT ÷ 1.20 = £100 |
| Add a % to a number | Number × (1 + %/100) | £50 + 20% VAT = £60 |
| Subtract a % from a number | Number × (1 − %/100) | £80 − 25% = £60 |
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Use the Percentage Calculator →Frequently Asked Questions
How How to Work Out a Percentage: Step-by-Step Guide Works
This calculator helps you work out VAT amounts using current UK rates. Value Added Tax (VAT) is charged on most goods and services sold by VAT-registered businesses in the UK. Understanding how VAT is calculated is essential for businesses approaching the registration threshold and for consumers wanting to know the pre-VAT price of purchases.
VAT is calculated as a percentage of the net price. To add VAT, multiply by 1.2 (for standard rate). To find the VAT-exclusive price from a VAT-inclusive amount, divide by 1.2. This tool handles both calculations automatically.
Key Information for 2025/26
The UK VAT rates are: standard rate 20% (most goods and services), reduced rate 5% (home energy, children's car seats, sanitary products), and zero rate 0% (most food, children's clothing, books, newspapers). The VAT registration threshold is £90,000 (from April 2024). Businesses with taxable turnover below this can register voluntarily. VAT returns are typically submitted quarterly via Making Tax Digital (MTD).
Example Calculation
A product priced at £500 excluding VAT: VAT at 20% = £100, giving a VAT-inclusive price of £600. Conversely, if an item costs £600 including VAT, the net price is £500 (£600 / 1.2) and the VAT element is £100. For reduced-rate items at 5%, a £1,200 energy bill includes £57.14 VAT (£1,200 / 1.05 x 0.05).
Source: Based on official HMRC 2025/26 VAT rates. Last updated March 2026.
How do you work out a percentage of a number?
Multiply the number by the percentage and divide by 100. Or convert the percentage to a decimal (divide by 100) and multiply. Example: 20% of £50 = 50 × 0.20 = £10.
How do we find percentage from two numbers?
Divide the first number (part) by the second (whole) and multiply by 100. Example: 45 out of 60 = (45 ÷ 60) × 100 = 75%.
How can I work out a percentage increase?
Percentage increase = ((New Value − Old Value) ÷ Old Value) × 100. A salary rising from £25,000 to £27,500 is a 10% increase.
How do I work out a percentage on a calculator?
Press the number, the multiply key, the percentage figure, then the % key. For example: 150 × 20% = 30. Without a % key, type: 150 × 0.20 = 30.
How to workout the percentage of a discount?
Multiply the original price by (1 − discount rate). For 25% off £80: 80 × 0.75 = £60. Or calculate the discount amount first: 80 × 0.25 = £20, then subtract: £80 − £20 = £60.
How do I calculate VAT on a price?
Multiply the pre-VAT price by 1.20 (for 20% VAT) to get the total. Or multiply by 0.20 to find the VAT amount only. To remove VAT from a VAT-inclusive price, divide by 1.20.
What is the percentage difference between two numbers?
Use: |A − B| ÷ ((A + B) ÷ 2) × 100. This gives a symmetric percentage difference, useful when neither number is the clear "original".
How to work out percentage of income tax in the UK?
Subtract your Personal Allowance (£12,570 in 2025/26) from your gross salary. Apply 20% to income up to £50,270, 40% to income between £50,271 and £125,140. Divide total tax by gross salary and multiply by 100 for your effective tax rate.
How do I work out a reverse percentage?
A reverse (back) percentage finds the original value before a percentage was applied. Formula: Original = Final Value ÷ (1 ± percentage rate). For example, a sale price of £72 after a 20% reduction: £72 ÷ 0.80 = £90 original price. For a VAT-inclusive price of £60 at 20% VAT: £60 ÷ 1.20 = £50 pre-VAT price.
What is the percentage change formula?
Percentage change = ((New Value − Old Value) ÷ Old Value) × 100. A positive result is an increase; negative is a decrease. Example: house price rose from £200,000 to £230,000: ((230,000 − 200,000) ÷ 200,000) × 100 = 15% increase. If it fell to £190,000: ((190,000 − 200,000) ÷ 200,000) × 100 = −5% decrease.
What is the difference between percentage and percentage points?
A percentage point is an absolute arithmetic difference between two percentages, while a percentage change is a relative change. Example: if the Bank of England raises interest rates from 4% to 5%, that is a rise of 1 percentage point — but a 25% relative increase (1 ÷ 4 × 100). Confusing the two is one of the most common errors in financial reporting and exam questions.
What are useful mental math shortcuts for common percentages?
Quick shortcuts: 10% — divide by 10 (£85 → £8.50). 5% — halve the 10% figure (£8.50 ÷ 2 = £4.25). 25% — divide by 4 (£80 → £20). 50% — divide by 2 (£80 → £40). 75% — find 25% then multiply by 3 (£80 → £20 → £60). 1% — divide by 100 (£350 → £3.50). For any percentage: find 1% first then scale up. For 17.5% VAT (old UK rate): find 10% + 5% + 2.5%.