Why isn't a 20% rise followed by a 20% fall back to the start?

Because each percentage is measured against a different number. 100 rises by 20 to 120, then falls by 20% of 120 — which is 24 — leaving 96.

Which fractions give exact decimals?

Only those whose denominator has no prime factors other than 2 and 5: halves, quarters, fifths, eighths, tenths. Thirds, sixths and sevenths repeat forever.

Why does programming use hexadecimal?

One hexadecimal digit is exactly four binary digits, so a byte is two neat characters instead of eight — which is why colours are written #FF8800.

21 free tools

Maths Calculators

Percentages, fractions, decimals, number bases and weighted grades. Every tool shows its working, so you take away the method and not just the answer.

NewNumber ConverterQuickly and accurately convert numbers between different formats, including binary, decimal, hexadecimal, and octal, making calculations and data conversions seamless for students, developers, and professionals.Open NewGrade CalculatorGrade Calculator in progressOpen NewPercentage CalculatorWork out X% of a number, what percent one number is of another, percentage change, increases, discounts and percentage difference.Open

Number Converter — quick conversions

In short

Free maths converters for number bases (binary, octal, decimal, hexadecimal), fractions, decimals and percentages, with worked methods on every page.

Overview

The everyday maths that is easy to get slightly wrong: percentage change measured from the wrong number, a fraction rounded too early, a hexadecimal digit misread. Each tool here shows its working so the method sticks.

Which one do you need?

Discounts, tips and change — percentage of, percentage change and difference
Fractions and decimals — exact and repeating decimals, both directions
Programming and colour codes — binary, octal, decimal and hexadecimal with the steps

All 20 tools in this section are free, work on a phone, and keep what you type on your own device. Nothing is stored and there is no sign-up.

Maths Calculators: frequently asked questions

Why isn't a 20% rise followed by a 20% fall back to the start?: Because each percentage is measured against a different number. 100 rises by 20 to 120, then falls by 20% of 120 — which is 24 — leaving 96.
Which fractions give exact decimals?: Only those whose denominator has no prime factors other than 2 and 5: halves, quarters, fifths, eighths, tenths. Thirds, sixths and sevenths repeat forever.
Why does programming use hexadecimal?: One hexadecimal digit is exactly four binary digits, so a byte is two neat characters instead of eight — which is why colours are written #FF8800.