Maths

Maths Calculators

Instant tools for percentages, VAT, averages, and everyday maths — with step-by-step workings shown. Free, no sign-up, no ads.

4Calculators
FreeAlways

These free maths calculators handle the everyday arithmetic that’s quick to get wrong by hand: working out a percentage discount, adding or removing UK VAT at 20%, averaging a set of numbers, or making sense of large figures like millions and billions. Each tool shows its full working, not just an answer, so you can check the method and learn it — useful whether you’re a student revising, a shopper comparing deals, or a small-business owner reconciling invoices. Everything runs instantly in your browser with no sign-up, no adverts and nothing stored.

All Maths Calculators
÷ Percentage Calculator All 5 types: X% of Y, what % is it, % change, reverse %, and % difference › ∑ Average Calculator — Mean, Median & Mode Mean, median, mode, range, std dev and more — with step-by-step workings › ⇄ Unit Converter Dashboard 300+ units across 30 categories — length, mass, pressure, viscosity, flow rate, fuel efficiency and more › × Million to Billion Converter Instantly convert millions to billions and back — with real-world UK comparisons and chart ›

How to use these maths calculators

Every tool works the same way: type your numbers in, read the result and the step-by-step working underneath. Nothing needs to be installed and no answer is rounded away behind a paywall — the intermediate steps are always shown so you can follow the logic and reproduce it on paper.

Percentages and VAT

The percentage calculator covers all five common questions in one place: X% of Y (a discount or tip), what percent is X of Y, percentage change between two values, reverse percentage (finding the original price before a discount), and the percentage difference between two numbers. For UK shopping and invoicing, the same tool handles adding 20% VAT to a net figure or stripping VAT back out of a gross total — the two most-searched money calculations in Britain.

Averages and statistics

The average calculator returns the mean, median, mode and range from any list of numbers, plus standard deviation, and explains the difference between them — handy when an outlier makes the “average” misleading and the median tells the truer story.

Big numbers and conversions

The million-to-billion converter makes very large figures intuitive (a billion is a thousand million), and the unit converter covers 300+ units across 30 categories for everything from length and mass to fuel efficiency.

Frequently asked questions

How do I add or remove 20% VAT?

To add VAT, multiply the net amount by 1.2. To remove VAT from a gross (VAT-inclusive) price, divide by 1.2 — not by 0.8, a common mistake. The percentage calculator does both and shows the working.

Are these calculators free?

Yes. Every maths tool here is free to use, needs no account, and runs entirely in your browser — your numbers are never sent to a server or stored.

Maths

Four percentage mistakes that catch almost everyone

By CalculatorDashboard Editorial Team·Updated ·Reviewed ·3 min read

Percentages are the most common piece of maths in everyday life, from discounts and pay rises to interest rates and statistics in the news. They're also easy to get wrong in ways that feel right. Here are four mistakes that catch almost everyone, each with a worked example you can check in the calculators on this page.

1. A percentage rise and fall don't cancel out

If a price rises by 20% and then falls by 20%, it doesn't end up where it started. Take a £100 item. A 20% rise makes it £120. A 20% fall from £120 takes off £24, leaving £96. The fall is applied to a bigger number, so it removes more. The same thing happens with investments: a portfolio that falls 50% needs to rise 100%, not 50%, to get back to where it was.

2. Percent and percentage points are different

When an interest rate rises from 4% to 5%, it has gone up by one percentage point. But as a percentage of the old rate, it has risen by 25%, because one is a quarter of four. Both statements are true, and news headlines often choose whichever sounds more dramatic. When you compare rates, mortgage deals or survey results, check which one is being used.

3. You can't simply average percentages

Suppose you scored 90% on a 10-question quiz and 60% on a 40-question quiz. The average of the two percentages is 75%, but your overall score is lower. You got 9 of the first 10 and 24 of the second 40, so 33 out of 50 overall, which is 66%. The bigger quiz carries more weight. Whenever groups are different sizes, combine the underlying numbers before you work out a percentage. The average calculator can help with weighted averages.

4. Removing VAT isn't the same as taking off 20%

UK VAT is usually charged at 20%, so a £120 price including VAT has a net price of £100. But 20% of £120 is £24, and £120 minus £24 is £96, which is wrong. The correct method is to divide by 1.2, because the VAT was added to the net price, not the gross one. The same rule applies to reversing any percentage increase: divide by one plus the rate, rather than subtracting the rate. The percentage calculator does this for you and shows the working.

Why these matter

Each of these mistakes can lead to a real decision going wrong: overestimating a recovery, misreading a rate change, misjudging a result, or setting the wrong price on an invoice. The fix in every case is the same. Ask what the percentage is a percentage of, and do the calculation on the underlying numbers when in doubt. The calculators on this page show their working, so you can see each step rather than trusting a single answer.