Percentage Calculator: How to Calculate Percentages, Percentage Increase, Reverse VAT and Every Formula You Need for Tax, Shopping and Exams

Last month I was shopping for a sofa during the DFS sale. The tag said "Was £1,299, now £849 — save 35%!" I stood there doing the maths in my head. £1,299 minus £849 is £450. Is £450 really 35% of £1,299? I pulled out my phone, divided 450 by 1,299, multiplied by 100, and got 34.6%. Close enough for a furniture shop, but technically they'd rounded up.

The thing is, I do this constantly. Checking restaurant tips, working out tax, figuring out how much I'm actually saving in a sale, calculating exam grades, splitting bills. Percentages are everywhere, and most of us get them slightly wrong more often than we'd like to admit.

That's why we built our free percentage calculator. It handles every type of percentage calculation instantly — percentage of a number, percentage increase or decrease, percentage difference, and reverse percentages. No formulas to remember, no mental arithmetic mistakes.

The Five Percentage Calculations Everyone Needs

1. What Is X% of Y?

The most basic and most common. "What is 20% of £350?" or "What is 15% of 80?"

Formula: (X / 100) × Y

Example: What is 17.5% of £240?

(17.5 / 100) × 240 = £42

Real-world uses:

• Calculating tips in restaurants — "What's 15% of this £67 bill?"
• Working out VAT — "What's 20% of £500?" (Answer: £100, making the total £600)
• Sale discounts — "What's 30% off £89.99?"
• Tax calculations — "What's 40% of my £50,000 salary?" (for the higher rate band)

For restaurant tips specifically, our tip calculator handles this even faster, including bill splitting.

2. What Percentage Is X of Y?

"I scored 67 out of 80 on my exam. What percentage is that?"

Formula: (X / Y) × 100

Example: What percentage is 67 of 80?

(67 / 80) × 100 = 83.75%

Real-world uses:

• Exam and test scores — essential for students tracking grades
• Sales targets — "We hit £340,000 of our £400,000 target. What percentage is that?"
• Body fat percentage — "I weigh 80kg and have 14kg of body fat. What's my body fat percentage?" (Answer: 17.5%). Also check our BMI calculator
• Savings rate — "I earn £2,500 and save £400. What percentage am I saving?" (Answer: 16%)

3. Percentage Increase

"My rent went from £950 to £1,100. What's the percentage increase?"

Formula: ((New Value - Old Value) / Old Value) × 100

Example: Rent increase from £950 to £1,100

((1,100 - 950) / 950) × 100 = (150 / 950) × 100 = 15.8% increase

Real-world uses:

• Rent increases — UK landlords must give proper notice, and knowing the percentage helps you negotiate or challenge unreasonable rises
• Salary increases — "My salary went from £35,000 to £37,500. Is that a good raise?" (Answer: 7.1% — above the 2024 UK average of about 5-6%)
• Price inflation — "Petrol was £1.45 last year, now it's £1.52. What's the increase?" (Answer: 4.8%)
• Investment returns — check our compound interest calculator for long-term growth
• Weight gain/loss — "I went from 85kg to 79kg. What percentage did I lose?" (Answer: 7.1%)

4. Percentage Decrease

"This laptop was £899, now it's £679. What's the percentage discount?"

Formula: ((Old Value - New Value) / Old Value) × 100

Example: Laptop price drop from £899 to £679

((899 - 679) / 899) × 100 = (220 / 899) × 100 = 24.5% decrease

For shopping discounts specifically, our discount calculator is even faster and shows you the final price after multiple discounts.

5. Reverse Percentage (Finding the Original)

This is the one that trips everyone up. "A jacket costs £72 after a 20% discount. What was the original price?"

Most people instinctively calculate 20% of £72 (£14.40) and add it back to get £86.40. But that's wrong. £72 is 80% of the original price, not 100%.

Formula: Current Value / (1 - Discount/100)

Example: £72 after 20% off

72 / (1 - 0.20) = 72 / 0.80 = £90

Check: 20% of £90 = £18. £90 - £18 = £72. ✓

The same principle applies to VAT. If something costs £120 including 20% VAT, the pre-VAT price isn't £96 (£120 - 20%). It's £120 / 1.20 = £100.

Our percentage calculator handles reverse percentages automatically — just select the calculation type and enter your numbers.

Percentage Calculations for UK Tax

Understanding percentages is essential for UK tax. Here's how the 2024/25 tax bands work:

Common mistake: People think earning £51,000 means paying 40% on everything. It doesn't. You only pay 40% on the amount above £50,270. On a £51,000 salary:

• First £12,570: 0% = £0
• £12,571 to £50,270 (£37,700): 20% = £7,540
• £50,271 to £51,000 (£730): 40% = £292
• Total tax: £7,832 — an effective rate of about 15.4%, not 40%

National Insurance adds another layer. For 2024/25, employees pay 8% on earnings between £12,570 and £50,270, and 2% above that.

Percentage Calculations for Shopping

Stacking Discounts

Here's something that catches people out: two 20% discounts don't equal 40% off.

If a £100 item has 20% off, it becomes £80. If you then apply another 20% off (like a loyalty code), it's 20% of £80 = £16 off. Final price: £64.

That's 36% off the original price, not 40%. The more discounts you stack, the bigger the gap between what you expect and what you get.

Our discount calculator handles stacked discounts correctly.

The "Per Unit" Trap

Supermarkets love percentage-based offers that aren't actually good deals:

• "50% extra free" on a 500ml bottle means you get 750ml. But the 1-litre bottle next to it might be cheaper per ml
• "Buy 2 get 1 free" is a 33% discount, not 50%
• "3 for £10" when each item is £3.50 saves you only 50p total — just 4.8% off

Always calculate the per-unit price. Our percentage calculator helps you compare deals quickly.

Percentage Calculations for Health

Body Fat Percentage

Body fat percentage is a better health indicator than weight alone. Healthy ranges:

For a comprehensive health check, use our BMI calculator, BMR calculator, and calorie calculator together.

Calorie Percentages

Nutritionists often recommend macronutrient splits as percentages of total calories:

• Balanced diet: 50% carbs, 30% fat, 20% protein
• Low carb: 25% carbs, 45% fat, 30% protein
• High protein: 40% carbs, 25% fat, 35% protein

If you eat 2,000 calories per day on a balanced diet, that's 1,000 calories from carbs (250g), 600 from fat (67g), and 400 from protein (100g).

Percentage Calculations for Education

Exam Grades

Converting raw marks to percentages is essential for tracking academic progress:

Note: These are approximate — actual grade boundaries vary by subject and exam board each year.

For university grades, our GPA calculator converts between UK degree classifications and GPA scores.

Weighted Averages

Most university courses weight assessments differently. If coursework is worth 40% and the exam is worth 60%:

• Coursework mark: 72%
• Exam mark: 58%
• Weighted average: (72 × 0.40) + (58 × 0.60) = 28.8 + 34.8 = 63.6%

That's a 2:1 — even though the exam mark alone would be a 2:2. Weighting matters enormously.

Percentage Calculations for Finance

Interest Rates

Understanding percentage-based interest is crucial for borrowing and saving:

• Savings accounts — a 4.5% AER on £10,000 earns you £450 per year. Use our savings calculator for exact figures
• Mortgages — a 0.5% difference in mortgage rate on a £250,000 loan over 25 years means roughly £18,000 more or less in total interest. Check our mortgage calculator
• Credit cards — a typical UK credit card charges 22-25% APR. On a £3,000 balance paying minimum payments, you'd pay over £2,000 in interest before clearing the debt
• Loans — compare rates with our loan calculator

Compound Interest

The most powerful percentage concept in finance. Compound interest means earning interest on your interest. At 5% annual return:

After 30 years, compound interest gives you 73% more than simple interest. That's why starting to save early matters so much. Explore this further with our compound interest calculator.

Inflation

UK inflation (CPI) has been volatile recently:

• 2021: 5.4%
• 2022: 10.5% (40-year high)
• 2023: 4.0%
• 2024: approximately 2.5-3%

If inflation is 3% and your savings earn 2%, your money is losing 1% of its purchasing power every year. After 10 years, £10,000 in purchasing power becomes roughly £9,044. Understanding these percentages helps you make better financial decisions.

Percentage Tricks for Mental Maths

You don't always need a calculator. These shortcuts work in your head:

• 10% — move the decimal point one place left. 10% of £67 = £6.70
• 5% — find 10% and halve it. 5% of £67 = £3.35
• 1% — move the decimal point two places left. 1% of £67 = £0.67
• 20% — find 10% and double it. 20% of £67 = £13.40
• 15% — find 10% + 5%. 15% of £67 = £6.70 + £3.35 = £10.05
• 25% — divide by 4. 25% of £67 = £16.75
• 33% — divide by 3. 33% of £67 ≈ £22.33
• 50% — halve it. 50% of £67 = £33.50
• 75% — find 50% + 25%. 75% of £67 = £33.50 + £16.75 = £50.25

The secret: break any percentage into combinations of 10%, 5%, and 1%. Want 17%? That's 10% + 5% + 1% + 1%.

Common Percentage Mistakes

1. Percentage Points vs Percentages

If interest rates go from 4% to 5%, that's a 1 percentage point increase but a 25% percentage increase. News headlines often confuse these, which can be misleading.

2. The Base Rate Fallacy

"Crime increased by 100%!" sounds terrifying. But if crime went from 2 incidents to 4 incidents in a small village, the absolute numbers are tiny. Always ask: 100% of what?

3. Asymmetric Percentages

A 50% loss requires a 100% gain to recover. If your £10,000 investment drops 50% to £5,000, you need a 100% gain (doubling) to get back to £10,000. This is why protecting against losses matters more than chasing gains.

4. The Reverse Percentage Error

As mentioned above, adding a percentage back doesn't reverse a discount. 20% off £100 = £80. But 20% added to £80 = £96, not £100. The base changes.

Percentages in Everyday UK Life

• VAT — 20% standard rate, 5% reduced rate (energy bills, child car seats), 0% zero rate (most food, children's clothes, books)
• Council Tax — increases capped at referendum threshold (usually 3-5% per year)
• Stamp Duty — 0% up to £250,000, then 5%, 10%, 12% on higher bands
• Student Loan repayment — Plan 2: 9% of everything earned above £27,295
• Pension contributions — minimum auto-enrolment is 8% (5% employee, 3% employer)
• Tipping — 10-15% is standard in UK restaurants. Use our tip calculator

Other Useful Calculation Tools

• Discount Calculator — calculate sale prices and stacked discounts
• Tip Calculator — work out tips and split bills
• Compound Interest Calculator — see how percentages compound over time
• Savings Calculator — calculate interest earned on savings
• Mortgage Calculator — work out monthly repayments
• Loan Calculator — compare loan costs at different rates
• BMI Calculator — health percentage calculations
• GPA Calculator — convert exam percentages to GPA
• Scientific Calculator — for complex percentage formulas

Try Our Free Percentage Calculator

Whether you're calculating a tip, checking a discount, working out your tax, tracking exam grades, or comparing investment returns, our free percentage calculator handles every type of percentage calculation instantly. Percentage of a number, percentage increase, percentage decrease, percentage difference, and reverse percentages — all completely free with no sign-up required.

Frequently Asked Questions

How do I calculate a percentage of a number?

Divide the percentage by 100 and multiply by the number. For example, 15% of 200 = (15/100) × 200 = 30. Or use our percentage calculator for instant results.

How do I calculate percentage increase?

Subtract the old value from the new value, divide by the old value, and multiply by 100. Example: from 80 to 100 = ((100-80)/80) × 100 = 25% increase.

What is the difference between percentage and percentage points?

If something goes from 10% to 15%, that's a 5 percentage point increase but a 50% percentage increase. Percentage points measure the absolute difference between two percentages. Percentage measures the relative change.

How do I reverse a percentage?

To find the original price before a discount, divide the current price by (1 - discount/100). For example, if something costs £80 after 20% off: £80 / 0.80 = £100 original price.

How do I calculate VAT?

To add 20% VAT: multiply by 1.20. To find the pre-VAT price from a VAT-inclusive price: divide by 1.20. Example: £120 including VAT = £120 / 1.20 = £100 before VAT.