Percentage Calculator 2025/26
Last updated: February 2026
Calculate percentages, percentage changes, differences, and more
Basic Percentage
Percentage Of
Percentage Change
Percentage Difference
Percentage Increase
Percentage Decrease
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 , 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.
Why Percentages Matter
- Universal Standard: Percentages provide a common way to compare different quantities
- Easy to Understand: "50%" is immediately clear - it means half
- Practical Applications: Used in finance, business, education, health, and statistics
- Decision Making: Help evaluate discounts, returns, growth rates, and probabilities
How to Calculate Percentages
The Basic Formula
Percentage = (Part ÷ Whole) × 100
Example: What percentage is 25 out of 200?
Answer: (25 ÷ 200) × 100 = 12.5%
Finding a Percentage OF a Number
Result = (Percentage × Number) ÷ 100
Example: What is 15% of £200?
Answer: (15 × 200) ÷ 100 = £30
Calculating Percentage Increase
% 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
Calculating Percentage Decrease
% 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
Common Mistakes to Avoid
- Percentage points vs percentages: Going from 20% to 30% is a 10 percentage point increase, but a 50% relative increase
- Reversibility myth: A 50% increase followed by a 50% decrease doesn't return to the original value!
- Dividing by zero: You can't calculate percentage change when the original value is zero
- Order matters: 20% of 50 equals 50% of 20, but percentage increase from 20 to 50 differs from 50 to 20
15 Real-World Percentage Examples
1. VAT Calculations (20% UK Standard Rate)
Scenario: You buy a laptop for £500 + VAT
Calculation: £500 × 20% = £100 VAT
Total Price: £500 + £100 = £600
2. Sale Discount (30% Off)
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
3. Salary Increase (5% Annual Raise)
Scenario: Current salary £35,000, getting 5% raise
Calculation: £35,000 × 5% = £1,750 increase
New Salary: £35,000 + £1,750 = £36,750
4. Exam Score Percentage
Scenario: Scored 68 marks out of 80 possible
Calculation: (68 ÷ 80) × 100 = 85%
Result: 85% - that's a solid B grade!
5. Restaurant Tip (15% Service)
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
6. Simple Interest (4% Annual)
Scenario: Savings account with £5,000 at 4% interest for 1 year
Calculation: £5,000 × 4% = £200 interest
Balance After 1 Year: £5,200
7. Income Tax (Basic Rate 20%)
Scenario: Taxable income of £15,000 at 20% rate
Calculation: £15,000 × 20% = £3,000 tax
Tax Due: £3,000
8. Business Revenue Growth
Scenario: Revenue grew from £100,000 to £125,000
Calculation: ((£125,000 - £100,000) ÷ £100,000) × 100 = 25%
Growth Rate: +25%
9. Profit Margin Calculation
Scenario: Product sells for £50, costs £30 to make
Calculation: ((£50 - £30) ÷ £50) × 100 = 40%
Profit Margin: 40%
10. Sales Commission (8%)
Scenario: Sales rep sells £25,000 worth, gets 8% commission
Calculation: £25,000 × 8% = £2,000
Commission Earned: £2,000
11. Survey Results
Scenario: 340 out of 500 people prefer Product A
Calculation: (340 ÷ 500) × 100 = 68%
Result: 68% of respondents prefer Product A
12. Grade Boundaries (Pass Mark 60%)
Scenario: Need 60% to pass, exam is out of 150 marks
Calculation: 150 × 60% = 90 marks needed
Pass Mark: 90 out of 150 marks
13. Population Change
Scenario: Town population decreased from 50,000 to 47,500
Calculation: ((50,000 - 47,500) ÷ 50,000) × 100 = 5%
Population Decrease: -5%
14. Conversion Rate (Website)
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
15. Investment Return (Portfolio)
Scenario: Invested £8,000, now worth £9,200
Calculation: ((£9,200 - £8,000) ÷ £8,000) × 100 = 15%
Return on Investment: +15%
Profit: £1,200
Business Applications of Percentages
Key Performance Indicators (KPIs)
Businesses rely on percentage-based metrics to track performance:
- Gross Profit Margin: (Revenue - Cost) ÷ Revenue × 100
- Net Profit Margin: Net Profit ÷ Revenue × 100
- Customer Retention Rate: (Customers at End - New) ÷ Start × 100
- Market Share: Company Sales ÷ Total Market Sales × 100
Pricing Strategies
Markup Pricing: Understanding the relationship between cost, markup, and profit margin
- Cost-Plus Pricing: Cost + (Cost × Markup %) = Selling Price
- Example: Product costs £60, apply 40% markup = £60 + £24 = £84 selling price
- Profit Margin vs Markup: A 40% markup gives a 28.6% profit margin (not 40%!)
Financial Analysis
- Year-over-Year Growth: ((This Year - Last Year) ÷ Last Year) × 100
- Return on Investment (ROI): (Gain - Cost) ÷ Cost × 100
- Break-Even Analysis: Fixed Costs ÷ (Price - Variable Cost) = Units needed
Related Financial Calculators
Common Percentage Calculations
Sales & Discounts
20% off £50 = £40
Save £10 on your purchase
Business Growth
From 1000 to 1250 customers
= 25% increase
Exam Scores
85 out of 100 marks
= 85% score
VAT Calculation
£100 + 20% VAT
= £120 total
Investment Returns
£10,000 with 8% return
= £800 profit
Mortgage Deposit
10% of £250,000 house
= £25,000 deposit
Understanding Percentages
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.
Common Uses:
- Retail & Shopping: Calculate discounts, sales tax, and markups
- Finance: Interest rates, investment returns, loan calculations
- Business: Profit margins, growth rates, market share
- Education: Test scores, grade calculations, attendance rates
- Statistics: Survey results, probability, data analysis
- Health: Body fat percentage, medication dosages, health metrics
Quick Tips:
- To find 10% of any number, simply move the decimal point one place to the left
- To find 5%, calculate 10% and divide by 2
- To find 1%, move the decimal point two places to the left
- Remember: "of" means multiply, "is" means equals in percentage problems
- Percentage increase and decrease are not inverses (20% increase followed by 20% decrease doesn't return to original)
Complete Percentage Calculator Guide 2026
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!
6 Essential Percentage Formulas Explained
1⃣ What is X% of Y? (Finding a Percentage of a Number)
Real UK Examples:
- Shop discount: 25% off £80 jacket → (25÷100) × 80 = £20 discount → Pay £60
- Restaurant tip: 15% tip on £45 meal → (15÷100) × 45 = £6.75 tip → Total £51.75
- VAT calculation: 20% VAT on £150 → (20÷100) × 150 = £30 VAT → Total £180
- Savings goal: Save 10% of £2,500 monthly salary → (10÷100) × 2,500 = £250/month savings
2⃣ X is What % of Y? (Converting to Percentage)
Real UK Examples:
- Exam score: Got 68 out of 80 marks → (68÷80) × 100 = 85% score
- Savings rate: Saved £400 from £2,000 income → (400÷2,000) × 100 = 20% savings rate
- Market share: 45,000 customers out of 150,000 total → (45,000÷150,000) × 100 = 30% market share
- Attendance: Attended 18 out of 20 lectures → (18÷20) × 100 = 90% attendance
3⃣ Percentage Increase (Growth)
Real UK Examples:
- Salary rise: £28,000 → £30,000 → ((30,000-28,000)÷28,000) × 100 = 7.14% pay rise
- House price: £250,000 → £275,000 → ((275,000-250,000)÷250,000) × 100 = 10% increase
- Investment return: £5,000 → £5,750 → ((5,750-5,000)÷5,000) × 100 = 15% gain
- Customer growth: 800 → 1,040 customers → ((1,040-800)÷800) × 100 = 30% growth
4⃣ Percentage Decrease (Decline)
Real UK Examples:
- Sale reduction: £150 → £105 → ((150-105)÷150) × 100 = 30% off
- Weight loss: 85kg → 78kg → ((85-78)÷85) × 100 = 8.24% weight loss
- Energy bill: £180/mo → £144/mo → ((180-144)÷180) × 100 = 20% reduction
- Car value: £20,000 → £14,000 → ((20,000-14,000)÷20,000) × 100 = 30% depreciation
5⃣ Increase/Decrease a Number by X%
Real UK Examples:
- Add VAT: £200 + 20% VAT → 200 × (1+0.20) = 200 × 1.20 = £240
- Salary rise: £35,000 + 3% rise → 35,000 × 1.03 = £36,050
- Remove discount: £80 - 15% off → 80 × (1-0.15) = 80 × 0.85 = £68
- Investment growth: £10,000 + 8% return → 10,000 × 1.08 = £10,800
6⃣ Percentage Difference (Between Two Numbers)
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
Mental Percentage Shortcuts - Calculate Without Calculator!
Finding 10%, 5%, 1%
- 10%: Move decimal one left → 10% of £47 = £4.70
- 5%: Find 10% ÷ 2 → 5% of £60 = £6 ÷ 2 = £3
- 1%: Move decimal two left → 1% of £350 = £3.50
Building Complex %
- 15%: 10% + 5% → 15% of £80 = £8 + £4 = £12
- 25%: Divide by 4 → 25% of £200 = £200 ÷ 4 = £50
- 20%: 10% × 2 → 20% of £45 = £4.50 × 2 = £9
Reverse Trick
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
Quick Doubling
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%
Pro Tip: The "Of" Rule
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%.
Real-World UK Percentage Scenarios
Shopping & Retail: Black Friday Sale
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?
£899 - 40% = £899 × 0.60 = £539.40
£539.40 - £50 = £489.40 final price
£899 - £50 = £849
£849 × 0.60 = £509.40 final price
Result: Apply percentage discount FIRST, then fixed voucher = Save extra £20! (£489.40 vs £509.40)
Finance: Salary Negotiations
Scenario: Your current salary is £32,000. You're offered two options:
Year 1: £32,000 × 1.05 = £33,600
Year 2: £33,600 × 1.03 = £34,608
Total gain over 2 years: £2,608
Year 1: £32,000 × 1.04 = £33,280
Year 2: £33,280 × 1.04 = £34,611
Total gain over 2 years: £2,611
Result: Option B (4% + 4%) beats Option A (5% + 3%) by £3 due to compounding! Always calculate actual amounts, not just percentage totals.
Education: Understanding Exam Grade Boundaries
Scenario: GCSE Maths exam out of 240 marks. Grade boundaries:
- Grade 9: 85% = 204+ marks
- Grade 7: 70% = 168+ marks
- Grade 5 (pass): 50% = 120+ marks
- Grade 4 (standard pass): 40% = 96+ marks
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
7 Common Percentage Mistakes (And How to Avoid Them!)
1. Thinking % Increase + Same % Decrease = Original Value
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.
2. Confusing Percentage Points vs Percentages
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%]
3. Adding Percentages Directly (Instead of Compounding)
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%)
4. Using Wrong Base for Percentage Change
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!
5. Reverse Percentage Errors (Finding Original Price)
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)
6. Percentages Over 100% Confusion
The mistake: "You can't have more than 100% of something"
Reality: Percentages over 100% are common for growth:
- Sales doubled: 100% increase (200% of original = 2× original)
- Tripled: 200% increase (300% of original = 3× original)
- Stock went £50 → £200: ((200-50)÷50) × 100 = 300% increase (or 4× original)
7. Averaging Percentages Instead of Underlying Values
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.
Written by UKCalculator.com
Reviewed by: UK Calculator, Founder & Developer - UKCalculator.com
Credentials: Founder & Developer of UKCalculator.com
Specializations: Free, accurate UK calculators for tax, finance, health, and education
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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: February 2026.
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