Free online calculators and a unit converter

How to, step by step

• 6÷2(1+2): is it 9 or 1? Why calculators disagree

  Why some calculators give 9 for 6 ÷ 2(1 + 2) and others give 1, which rule each follows, and how to write a sum nobody can misread.

• Why does 0.1 + 0.2 = 0.30000000000000004?

  Why computers write 0.1 + 0.2 as 0.30000000000000004, why it matters for money and percentages, and how a calculator can keep decimals exact.

• How to use a scientific calculator online

  Degrees or radians, sin and its inverse, logs of any base, powers and roots, factorials and nCr on a scientific calculator, with exact answers where they exist.

• How to calculate a percentage of a number

  How to work out 20% of 85, what percent 17 is of 85, and the other everyday percentage sums, with the formula and the steps on your own numbers.

• Percentage change vs percentage points, explained

  How to work out a percentage increase or decrease, why a rate going from 4% to 5% is a rise of 25%, and how percentage difference differs again.

• How to calculate percent off a price

  How to take 20% off a price, what you save, and why 20% off and then 10% off comes to 28% off, not 30%. With the steps on your own numbers.

• Reverse percentage: how to find the original price

  How to work back to a price before tax was added or a discount taken off, and why taking the percentage off again gives the wrong answer.

• How to calculate percentage of marks in exams

  How to turn marks into a percentage for one subject or all of them, and why an average of subject percentages can give a different answer.

• Mixed numbers to improper fractions, and back

  What a mixed number such as 2 ¾ means, how to turn it into an improper fraction and back again, and how to type one into a fraction calculator.

• How to add, subtract, multiply and divide fractions

  The steps for adding fractions with a common bottom, multiplying across, dividing by turning over, and writing the answer as a mixed number.

• How to convert a repeating decimal to a fraction

  How to turn 0.375 into 3/8, and a repeating decimal such as 0.1666… into 1/6, step by step, plus the nearest fraction of an inch to a decimal.

• Why do some fractions repeat as decimals?

  Why 1/8 ends but 1/3 and 1/7 repeat for ever, how to tell from the bottom alone, and how long the repeating part can be.

• How to simplify a ratio, with steps

  How to simplify a ratio such as 12 : 18 to 2 : 3, clear decimals from 1.5 : 2.25 : 3, and turn a ratio into each part's share of the whole.

• How to solve a proportion for x by cross-multiplying

  How to find the missing number in a : b = c : x by cross-multiplying, with any box missing, and how to share an amount out in a ratio.

• How to calculate aspect ratio from pixels

  How to find the aspect ratio of a picture or screen from its pixels, why 1366 × 768 is not quite 16:9, and how to work out a new size that keeps the shape.

• Exact unit conversions: where the factors come from

  Why an inch is exactly 2.54 cm, why a kilogram in pounds never ends, and how a converter can be exact without rounding factors from a table.

• How to convert kg to lbs, with pounds and ounces

  How many pounds are in a kilogram, how to turn kg into pounds and ounces or stone, and why pounds to kg is exact but kg to pounds is not.

• How to convert cm to inches, and inches to cm

  An inch is exactly 2.54 cm. How to turn centimetres into inches as a decimal and as a ruler fraction, and inches back into centimetres.

• mm to inches as a fraction: a conversion chart method

  How to turn millimetres into inches and then into the nearest eighth, sixteenth or sixty-fourth of an inch, with how far off each fraction is.

• Celsius to Fahrenheit formula, with examples

  The formula for °C to °F and back, why −40 is the same on both scales, and why a change of 10 °C is 18 °F, not 50 °F.

• How to convert km to miles, and miles to km

  A mile is exactly 1.609344 kilometres. How to turn kilometres into miles, with the 5K, 10K and marathon distances worked out.

• How to convert meters to feet and inches

  A foot is exactly 0.3048 metres. How to turn metres into feet, then into feet and inches, and feet back into metres, with examples.

• Height converter: feet and inches to cm, and cm to feet

  How to turn a height such as 5 ft 11 in into centimetres exactly, and a height in centimetres into feet and inches, with a quick check.

• How to convert ml to oz, US and UK fluid ounces

  A US fluid ounce is 29.5735 mL and a UK one 28.4131 mL. How to convert ml to fl oz and back, and why labels say 30 mL.

• How many grams in a cup of flour, sugar or butter?

  How many grams are in a cup of flour, sugar or butter, why the answers differ, and how to halve or double a recipe without losing track.

• How to convert grams to ounces and ounces to grams

  An ounce is exactly 28.349523125 grams. How to convert grams to ounces and back, and how weight ounces, fluid ounces and troy ounces differ.

• How many liters in a gallon, US and UK

  A US gallon is exactly 3.785411784 litres and a UK gallon 4.54609 litres. How to convert litres to gallons, and why the two differ.

• How to convert square feet to acres and hectares

  An acre is exactly 43,560 square feet. How to convert square feet to acres and hectares, and land in gaj, cent and guntha, and why bigha varies.

• How to convert mph to km/h and km/h to mph

  A mile an hour is exactly 1.609344 km/h. How to convert speed limits and speeds between mph and km/h, with metres a second and knots.

• MB to GB: 1,000 or 1,024? Why drives look smaller

  Why a 1 TB drive shows as about 931 GB, how MB and GB are counted by 1,000 and by 1,024, and how to convert between them.

• How to convert psi to bar, for tyres and pumps

  A bar is 100,000 pascals and a psi about 6,894.76. How to convert tyre and pump pressures between psi, bar, kPa and kg/cm².