Calculate percentages, percentage changes, differences, and more
A percentage is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin per centum , which means "by the hundred." Percentages make it easier to compare different quantities and understand proportions in everyday life.
For example, if you score 85 out of 100 on an exam, you scored 85%. If a shop offers "30% off," they're reducing the price by 30 parts out of every 100. Percentages are everywhere in modern life, from VAT on purchases to interest rates on savings.
Percentage = (Part ÷ Whole) × 100
Example: What percentage is 25 out of 200?
Answer: (25 ÷ 200) × 100 = 12.5%
Result = (Percentage × Number) ÷ 100
Example: What is 15% of £200?
Answer: (15 × 200) ÷ 100 = £30
% Increase = ((New - Old) ÷ Old) × 100
Example: A salary increases from £30,000 to £33,000. What's the percentage increase?
Answer: ((33,000 - 30,000) ÷ 30,000) × 100 = 10% increase
% Decrease = ((Old - New) ÷ Old) × 100
Example: A product's price drops from £80 to £64. What's the percentage decrease?
Answer: ((80 - 64) ÷ 80) × 100 = 20% decrease
Scenario: You buy a laptop for £500 + VAT
Calculation: £500 × 20% = £100 VAT
Total Price: £500 + £100 = £600
Scenario: Winter coat originally £120, now 30% off
Calculation: £120 × 30% = £36 discount
Sale Price: £120 - £36 = £84
Alternative method: £120 × 70% (100% - 30%) = £84
Scenario: Current salary £35,000, getting 5% raise
Calculation: £35,000 × 5% = £1,750 increase
New Salary: £35,000 + £1,750 = £36,750
Scenario: Scored 68 marks out of 80 possible
Calculation: (68 ÷ 80) × 100 = 85%
Result: 85% - that's a solid B grade!
Scenario: Meal bill is £45, want to leave 15% tip
Calculation: £45 × 15% = £6.75 tip
Total to Pay: £45 + £6.75 = £51.75
Quick tip: 10% = move decimal left once (£4.50), add half (£2.25) = £6.75
Scenario: Savings account with £5,000 at 4% interest for 1 year
Calculation: £5,000 × 4% = £200 interest
Balance After 1 Year: £5,200
Scenario: Taxable income of £15,000 at 20% rate
Calculation: £15,000 × 20% = £3,000 tax
Tax Due: £3,000
Scenario: Revenue grew from £100,000 to £125,000
Calculation: ((£125,000 - £100,000) ÷ £100,000) × 100 = 25%
Growth Rate: +25%
Scenario: Product sells for £50, costs £30 to make
Calculation: ((£50 - £30) ÷ £50) × 100 = 40%
Profit Margin: 40%
Scenario: Sales rep sells £25,000 worth, gets 8% commission
Calculation: £25,000 × 8% = £2,000
Commission Earned: £2,000
Scenario: 340 out of 500 people prefer Product A
Calculation: (340 ÷ 500) × 100 = 68%
Result: 68% of respondents prefer Product A
Scenario: Need 60% to pass, exam is out of 150 marks
Calculation: 150 × 60% = 90 marks needed
Pass Mark: 90 out of 150 marks
Scenario: Town population decreased from 50,000 to 47,500
Calculation: ((50,000 - 47,500) ÷ 50,000) × 100 = 5%
Population Decrease: -5%
Scenario: 1,250 visitors, 38 made a purchase
Calculation: (38 ÷ 1,250) × 100 = 3.04%
Conversion Rate: 3.04%
Note: 2-3% is typical for e-commerce sites
Scenario: Invested £8,000, now worth £9,200
Calculation: ((£9,200 - £8,000) ÷ £8,000) × 100 = 15%
Return on Investment: +15%
Profit: £1,200
Businesses rely on percentage-based metrics to track performance:
Markup Pricing: Understanding the relationship between cost, markup, and profit margin
20% off £50 = £40
Save £10 on your purchase
From 1000 to 1250 customers
= 25% increase
85 out of 100 marks
= 85% score
£100 + 20% VAT
= £120 total
£10,000 with 8% return
= £800 profit
10% of £250,000 house
= £25,000 deposit
A percentage is a way of expressing a number as a fraction of 100. The term "percent" comes from the Latin "per centum," meaning "by the hundred." Percentages are used everywhere in daily life, from calculating discounts to understanding statistics.
Percentages are one of the most useful mathematical concepts in everyday life—from calculating shop discounts and restaurant tips to understanding tax rates, investment returns, exam scores, and business profit margins. A percentage represents a part of a whole expressed as a fraction of 100 (the word "percent" literally means "per hundred"). Whether you're working out how much you'll save in a sale, comparing salary increases, or analyzing statistical data, mastering percentage calculations is an essential life skill.
This comprehensive guide explains all percentage formulas you need, provides real-world UK examples for shopping, finance, and education, reveals common percentage mistakes that trip people up (like why 20% increase followed by 20% decrease doesn't return to the original value), and gives you practical shortcuts for mental percentage calculations. By the end, you'll be able to calculate percentages confidently in any situation—no calculator needed for simple cases!
Real UK Examples:
Real UK Examples:
Real UK Examples:
Real UK Examples:
Real UK Examples:
Use when: Comparing two values with no clear "before" or "after" (unlike percentage change which needs old→new direction).
Real UK Example: Two shops sell same TV: Shop A £450, Shop B £550 → |450-550|÷((450+550)÷2) × 100 = 100÷500 × 100 = 20% price difference
X% of Y = Y% of X
16% of 25 = 25% of 16 → 25% of 16 is easier: 16 ÷ 4 =
4
12% of 50 = 50% of 12 → 50% of 12 is easier: 12 ÷ 2 =
6
To find final price after % off:
30% off = pay 70% → £50 × 0.70 = £35
15% off = pay 85% → £80 × 0.85 = £68
Use: 100% - discount% = what you pay%
In percentage problems, "of" always means multiply, and "is" means equals. So "30% of 200" translates to "0.30 × 200" which equals 60. "What % of 50 is 10?" becomes "X × 50 = 10" → X = 10÷50 = 0.20 = 20%.
Scenario: You find a laptop originally £899, now marked "40% off" in a Black Friday sale. There's also a £50 voucher code. Which should you apply first?
Result: Apply percentage discount FIRST, then fixed voucher = Save extra £20! (£489.40 vs £509.40)
Scenario: Your current salary is £32,000. You're offered two options:
Result: Option B (4% + 4%) beats Option A (5% + 3%) by £3 due to compounding! Always calculate actual amounts, not just percentage totals.
Scenario: GCSE Maths exam out of 240 marks. Grade boundaries:
You scored 178 marks: 178÷240 × 100 = 74.17% = Grade 7
To get Grade 9: Need 204 marks → You're 26 marks short → That's 26÷240 = 10.83% away → Roughly 10-11 more correct answers needed
The mistake: "£100 increased by 20% then decreased by 20% returns to £100" ❌
Reality: £100 + 20% = £120. Then £120 - 20% = £120 × 0.80 = £96 (not £100!)
Why: The 20% decrease applies to £120 (larger base) = £24 reduction, while 20% increase applied to £100 (smaller base) = £20 addition.
The mistake: Bank of England raises interest rates from 4% to 5%. That's a 1% increase. ❌
Reality: It's a 1 percentage point increase (4% → 5% = difference of 1 point)
But it's a 25% relative increase in the rate: (5-4)÷4 × 100 = 25%
Example: Unemployment drops from 5% to 4% = 1 percentage point drop, but a 20% relative decrease [(5-4)÷5 = 0.20 = 20%]
The mistake: Invest £1,000 with 10% return Year 1, 15% return Year 2. Total gain = 10% + 15% = 25% = £250. ❌
Reality (Compounding):
Year 1: £1,000 × 1.10 = £1,100 (+£100)
Year 2: £1,100 × 1.15 = £1,265 (+£165)
Total gain: £265, not £250!
(That's 26.5% total return, not 25%)
The mistake: Price drops £100 → £80. Calculate % change as (20÷80) × 100 = 25%. ❌
Reality: Always use ORIGINAL value as base: (20÷100) × 100 = 20% decrease
Rule: Percentage change = (Change ÷ ORIGINAL) × 100. The original value is always the denominator!
The mistake: Sale item £84 after 30% off. Original price = £84 + 30% = £109.20 ❌
Reality:
£84 is 70% of original (100% - 30% = 70%)
Original = £84 ÷ 0.70 =
£120
Check: £120 - 30% = £120 × 0.70 = £84 ✅
Formula: If X% off, final price = original × (1 - X/100). To reverse: original = final price ÷ (1 - X/100)
The mistake: "You can't have more than 100% of something" ❌
Reality: Percentages over 100% are common for growth:
The mistake: Test 1: 80% (40/50). Test 2: 90% (18/20). Average = (80%+90%)÷2 = 85% ❌
Reality:
Average the actual scores, not percentages:
Total: 58 marks out of 70 possible
Real average: (58÷70) × 100 =
82.86%
(not 85%!)
Rule: Only average percentages if the denominators (totals) are identical. Otherwise, combine raw values first.
Reviewed by: Dr. Peter Thompson, PhD - Mathematics Education Specialist
Credentials: PhD Mathematics Education | Chartered Mathematician (CMath) | Fellow of Institute of Mathematics and its Applications (FIMA) | 15+ years teaching mathematics at UK universities and schools
Specializations: Practical mathematics, numeracy education, financial mathematics for general public, mathematical literacy. Regular contributor to Times Educational Supplement and UK Mathematics Trust.
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✓ Expert Reviewed — This calculator is reviewed by our team of financial experts and updated regularly with the latest UK tax rates and regulations. Last verified: January 2026.
To calculate a percentage, divide the part by the whole and multiply by 100. For example, 25 out of 100 = (25÷100) × 100 = 25%.
Percentage increase = ((New Value - Original Value) / Original Value) × 100. For example, if a price increases from £50 to £60: ((60-50)/50) × 100 = 20% increase.
Percentage decrease = ((Original Value - New Value) / Original Value) × 100. For example, if a price decreases from £100 to £80: ((100-80)/100) × 100 = 20% decrease.
A percentage is a fraction out of 100, while a percentile indicates the value below which a percentage of data falls. For example, the 90th percentile means 90% of values are below that point.
To add a percentage: multiply the number by (1 + percentage/100). To subtract: multiply by (1 - percentage/100). For example, £100 + 20% = £100 × 1.20 = £120.