Percentage Calculator
Work out percentages of any number, percentage change between two values, and reverse percentages. Built for UK pay rises, VAT, sale prices, tips and ISA growth.
Related tools
How Percentages Work in Everyday Calculations
Most people in the UK do not need a percentage calculator for abstract maths homework — they need one for real money decisions. A 4.5% pay rise on the median full-time salary, the genuine saving on a "70% off" Black Friday deal, the VAT element of a contractor invoice, the service charge on a restaurant bill, the year-on-year change in their gas and electricity standing charges. These are the calculations this tool is built for.
A percentage is simply a number out of one hundred. The word comes from the Latin per centum, literally "by the hundred," and the symbol % is a typographic shorthand for /100 that emerged in Italian commercial manuscripts in the fifteenth century. Once you accept that 25% means twenty-five out of every hundred, every percentage problem reduces to one of three patterns: finding a fraction of a number, finding what fraction one number is of another, or measuring how much one number has changed compared with a starting value.
This calculator handles all three patterns and shows the working in pounds and pence where it makes sense. The longer guide below covers the calculations a UK adult is most likely to meet in any given month — pay rises and the bite that PAYE and National Insurance take out of them, the difference between the headline interest rate on a savings account and the APR on a credit card, the way the Office for National Statistics builds the Consumer Prices Index from a basket of around seven hundred goods and services, and the often-misunderstood gap between a percentage point and a percentage change. Every example is worked in sterling against current UK rules.
How to Calculate Percentage Of, Increase, and Decrease
Pick the mode that matches your question. Use "percentage of" for things like 5% of a £30,000 salary or 20% VAT on a net price. Use "what percent of" for marking a 42 out of 56 exam paper or working out what fraction of your monthly take-home goes on rent. Use "percentage change" when you have two values, such as last year's energy bill against this year's, and you want the rise or fall in percentage terms. Type the figures in plain numbers without the pound sign or % symbol — the calculator handles the formatting. Press Calculate, read the result, and use Reset to clear the form. The maths is the same whether you are working out a tip on a restaurant bill, the discount on a Black Friday TV, or the percentage point change in the Bank of England base rate.
- Pick a calculation mode: percentage of a number, what percent A is of B, or percentage change between two values.
- Enter the first value — usually the original price, salary, or starting figure.
- Enter the second value — the percentage rate, the smaller number, or the new figure depending on mode.
- Press Calculate to see the result rounded to two decimal places.
- If you are working with money, treat the answer as pounds and pence and round to the nearest penny on invoices.
- Press Reset to clear the form before starting another calculation.
Three Core Percentage Formulas
The formula used: Percentage = (Part / Whole) × 100
The first formula handles "X% of Y" questions like 20% VAT on £450 or a 4% pay rise on £35,000.
Result = Number × (Percentage / 100)
The second formula handles "what percent is A of B" questions like marking an exam, working out what share of household income goes on the mortgage, or calculating gross profit margin.
Percentage = (A / B) × 100
The third formula handles change between two values — last year's energy bill against this year's, the share price on Monday compared with Friday, or the council tax bill in 2024 versus 2025.
Change = ((New − Old) / Old) × 100
A positive result is an increase, a negative result is a decrease. The denominator is always the original figure, not the new one — getting that wrong is the single most common percentage error in UK financial reporting.
To strip 20% VAT out of a gross figure, divide by 1.20 rather than subtracting 20%. £120 gross at 20% VAT is £100 net plus £20 VAT, not £96. Subtracting 20% from a gross price is the most frequent mistake on small-business bookkeeping.
Percentage Calculations for Discounts, Grades, and Tips
5% of a £30,000 salary = £1,500. A £40 jumper at 70% off = £12. £120 gross with 20% VAT removed = £100 net plus £20 VAT.
5% pay rise on a £30,000 salary, with PAYE and National Insurance taken into account.
Gross rise = 30,000 × 0.05 = £1,500. The new salary is £31,500. Income tax at 20% on the rise takes £300, employee Class 1 NI at 8% (post-April 2024 rate) takes another £120, leaving roughly £1,080 in real take-home over the year — about £90 a month.
Headline rise: £1,500. After tax and NI: roughly £1,080 a year, or £90 per month.
A £40 jumper marked 70% off in a sale.
Discount = 40 × 0.70 = £28. Sale price = 40 − 28 = £12. To check, 30% of £40 = £12.
You pay £12 and save £28.
Stripping 20% VAT out of a £120 gross supplier invoice for a VAT return.
Net = 120 / 1.20 = £100. VAT = 120 − 100 = £20. The quick mental check is dividing the gross by six, which gives £20 — the same answer.
Net £100, VAT £20, gross £120.
Discretionary 12.5% service charge on an £85 restaurant bill.
Service = 85 × 0.125 = £10.63 (rounded to the nearest penny). Total to pay = £95.63.
Service charge £10.63, bill total £95.63. UK service charges are legally optional and you can ask for them to be removed.
Compound versus simple interest on £1,000 at 5% over 10 years (a stocks-and-shares ISA modelling exercise).
Simple interest: 1,000 × 0.05 × 10 = £500 in interest, total £1,500. Compound interest annually: 1,000 × (1.05)^10 = £1,628.89, of which £628.89 is interest. The compound figure is roughly 26% larger than the simple figure even at a modest rate.
Simple £1,500. Compound £1,628.89. The £128.89 gap is the cost of ignoring compounding.
A 9.1% CPI inflation year (the UK October 2022 print) and what it does to £1,000 in real terms.
Real value after one year = 1,000 / 1.091 = £916.59. The £1,000 has lost £83.41 of purchasing power even though the cash figure has not moved.
£1,000 in October 2022 was worth roughly £916.59 in October 2023 prices. Cash savings sat in a 1% account lost almost 8% of real value that year.
When Percentage Calculations Come Up in Daily Life
Use this calculator any time a figure is expressed as a fraction of one hundred and you need a quick, accurate answer in pounds and pence. The day-to-day UK situations are surprisingly consistent: applying 20% VAT to a quote, working out the headline value of a pay settlement, checking a Black Friday discount, splitting a restaurant service charge, comparing this year's council tax to last year's, or sense-checking a stocks-and-shares ISA projection.
Workers reach for it on payslip days. The 2024 spring round of National Insurance changes — Class 1 employee NI cut from 12% to 10% in January 2024, then again from 10% to 8% in April 2024 — left a lot of households trying to reconcile the headline tax cut with what actually landed in their bank account. ACAS and ONS pay-settlement data for 2024 put the median private-sector pay rise around 4-5%, with public-sector settlements ranging from 5% to 6.5% depending on the workforce. A percentage calculator turns those headlines into pounds.
Shoppers reach for it during sale events. The Advertising Standards Authority has issued repeated rulings against UK retailers that quote misleading "was/now" pricing, and the Pricing Practices Guide (originally 1998, regularly updated by the Chartered Trading Standards Institute) sets the framework for what counts as a genuine reference price. A quick percentage calculation against the actual everyday price — not the brief "was" price — tells you whether a deal is real.
Savers and borrowers reach for it for compound growth and APR comparisons. The headline interest rate on a savings account, the AER (Annual Equivalent Rate) which standardises compounding, and the APR on a credit card or loan are all percentages but they describe different things. The FCA requires lenders to quote a representative APR that includes most fees and assumes the worst case for variable rates, and that figure must be the rate offered to at least 51% of accepted applicants. Knowing the formula keeps you honest about what you are really being charged.
Percentage, Basis Points, and Percentage Points
Percentage Of vs Percentage Change vs Percentage Point
| Scenario | Percentage point change | Percentage (relative) change | Why it matters |
|---|---|---|---|
| NI cut 12% → 10% (Jan 2024) | −2 percentage points | −16.7% | Headline says "2p in the pound" cut, real reduction in NI bill is 16.7%. |
| NI cut 10% → 8% (Apr 2024) | −2 percentage points | −20% | Same arithmetic cut, larger relative effect because the base is smaller. |
| Base rate 4% → 5% | +1 percentage point | +25% | Mortgage interest costs rise by a quarter, not a hundredth. |
| VAT 17.5% → 20% (2011) | +2.5 percentage points | +14.3% | The VAT bill on a £100 net invoice rose from £17.50 to £20. |
| Inflation 2% → 5% | +3 percentage points | +150% | Cost-of-living headlines blur the two — the rate of inflation more than doubled. |
| Vote share 35% → 38% | +3 percentage points | +8.6% | Election night graphics often quote the 8.6% "swing" but the seat-changing number is the 3 point shift. |
Mental Maths Shortcuts for Quick Percentage Estimates
- 10% of any number is just the number with the decimal point shifted one place left. £85 → £8.50. From there, 5% is half of that (£4.25), 20% is double (£17), and 15% is 10% plus 5%.
- To strip 20% VAT mentally, divide the gross figure by six. £60 gross → £10 VAT, £50 net. It is not perfectly exact (the true divisor is 1.20, not 1.2 repeating six) but it is close enough for sense-checking a receipt.
- A 50% fall followed by a 50% rise does not get you back to where you started. £100 → £50 → £75. You need a 100% rise from the low point to recover a 50% fall.
- Add up successive percentages by multiplying factors, not by adding the rates. A 10% rise followed by a 20% rise is 1.10 × 1.20 = 1.32, a 32% total rise — not 30%.
- When a price changes by less than around 5%, the percentage rise and the percentage fall back are roughly the same number. Above that, the gap widens fast — a useful intuition when reading market commentary.
- Round percentages to one decimal place for headlines, two decimal places for invoices, and four for compound interest projections. The level of precision should match the size of the decision.
Percentage Errors That Change the Answer Completely
- Dividing by the new value instead of the original when calculating percentage change. Always divide by the starting figure — that is what "change" is measured against.
- Subtracting 20% from a gross price to find the net. £120 minus 20% is £96, but the correct net is £100. Divide by 1.20 instead, or by six for a quick check.
- Adding successive percentage rises together. Two 10% rises in a row are 21%, not 20%, because the second rise compounds on the larger base.
- Confusing percentage points with percentages. A Bank of England base rate moving from 4% to 5% is one percentage point but a 25% relative rise. Newspaper headlines routinely blur the two.
- Reading a "70% off" sticker as a guarantee of a saving without checking what the item normally sold for in the 30 days before the sale started.
- Trusting a representative APR as the rate you will personally be offered. Only 51% of accepted applicants need to receive it under FCA rules — the other 49% may be offered worse.
Percentage Calculator: Common Questions Answered
How do I work out a percentage of a number quickly in my head?
Find 10% by shifting the decimal one place left, then scale. 10% of £85 is £8.50, so 5% is £4.25, 20% is £17, and 15% is £12.75. For 1%, shift the decimal two places left.
How do I add 20% VAT to a net price?
Multiply the net figure by 1.20. £450 net × 1.20 = £540 gross. The VAT element is £90. To go the other way and strip VAT from a gross figure, divide by 1.20.
What is the difference between percentage and percentage points?
Percentage points are the arithmetic gap between two rates. Percentage change is the relative difference. National Insurance dropping from 10% to 8% is a 2 percentage point cut but a 20% relative reduction. Confusing the two is the most common error in UK political and financial reporting.
How do I work out a 12.5% service charge on a restaurant bill?
Multiply the bill by 0.125. An £85 bill × 0.125 = £10.63. Total to pay = £95.63. UK restaurant service charges are discretionary and can be removed on request — the law treats them as a tip, not a fee.
Why does Black Friday "70% off" sometimes feel like a worse deal than expected?
The percentage saving is calculated against the retailer's reference price, which under the UK Pricing Practices Guide should be the price actually charged for a meaningful period before the sale. The Advertising Standards Authority has ruled against retailers using brief, inflated "was" prices to flatter the headline discount.
How does the ONS calculate UK inflation as a percentage?
The Office for National Statistics tracks roughly 700 goods and services in a representative basket, weights each by typical household spending, and measures the year-on-year price change. The Consumer Prices Index (CPI) headline is the weighted average of those individual percentage changes — which is why a 9.1% print does not mean every item rose by 9.1%.
How do I find the original price before a discount?
Divide the sale price by (1 minus the discount as a decimal). A £12 jumper that was 70% off: £12 / 0.30 = £40 original. A £60 item with 25% off: £60 / 0.75 = £80 original. Always divide — never add the percentage back on.
What is the difference between simple and compound interest?
Simple interest pays only on the original principal. Compound interest pays on the principal plus accumulated interest. £1,000 at 5% over 10 years pays £500 simple but £628.89 compound — £128.89 more, all from interest earning interest.
What is APR and why is it different from the interest rate?
APR (Annual Percentage Rate) is a UK-regulated figure that includes most fees and assumes the worst case for variable rates. The Financial Conduct Authority requires lenders to quote a "representative APR" that 51% of accepted applicants receive. The headline interest rate is usually lower than the APR because it ignores fees.
How is a 5% pay rise affected by tax and National Insurance?
On a £30,000 salary, a 5% rise is £1,500 gross. A basic-rate taxpayer pays 20% income tax (£300) and 8% NI (£120, post-April 2024 rate), keeping roughly £1,080 — about £90 a month. The headline percentage and the take-home percentage are rarely the same.
Can a percentage be more than 100%?
Yes. A value that doubles is a 100% increase; tripling is 200%. House prices in some UK cities have risen by more than 300% over twenty years. Percentages above 100% are common in growth, investment returns, and markup calculations.
How do I calculate a percentage change between two years of bills?
Subtract the old figure from the new, divide by the old, and multiply by 100. Energy bill £1,200 last year, £1,440 this year: ((1440 − 1200) / 1200) × 100 = 20% rise. Always divide by the original — dividing by the new figure gives a different and incorrect answer.
More Maths & Conversion Calculators
Category
← Maths & Conversion CalculatorsNext up
VAT Calculator →