Percentage Calculators
Work out a percentage of a number, percentage change, and reverse a percentage back to its original value.
Everyday Maths Calculators and Guides
Free calculators for percentages, ratios, fractions, averages and commercial maths, each showing the formula behind the result, and guides that explain the methods with worked examples.
Calculators by category
Ratio Calculators
Simplify a ratio to its lowest terms and see it as a share of the whole.
Fraction Calculators
Add, subtract, multiply and divide fractions, simplify a fraction, and convert between fractions, decimals and percentages.
Statistics Calculators
Find the average of a list of numbers, or the mean, median, mode and range all at once.
Commercial Maths Calculators
Work out a sale price after a discount, a selling price after a markup, or a profit margin.
Number Tools
Find the greatest common divisor and least common multiple of two numbers, check whether a number is prime, or list all of its factors.
Where everyday maths goes wrong
Most wrong answers in everyday maths come from using the right numbers with the wrong base or the wrong method, not from arithmetic slips. Four of the most common:
- Percentage changes are not symmetrical. A rise from 80 to 100 is 25%, but a fall from 100 to 80 is 20%, because each is measured against its own starting value. See percentages explained.
- Markup is not margin. Adding 30% to a cost of 100 gives a price of 130, but the profit of 30 is only 23.08% of that price. See markup and profit margin.
- A rounded decimal is a different number. 0.333 is 333/1000, not one third, and 76.92% is not exactly 10/13. See fractions, decimals and percentages.
- The mean is not always the typical value. Four salaries of 30,000 and one of 230,000 have a mean of 70,000, which nobody earns; the median is 30,000. See mean, median and mode.
Maths guides
Each guide explains one area of everyday maths with worked examples. See all guides.
- Percentages The five everyday percentage calculations, percentage points versus percent, successive changes, and why reversing a percentage is not the same as applying it backwards.
- Markup and margin Why a 30% markup is not a 30% margin, how to convert between the two, pricing for a target margin, and how stacked discounts combine.
- Fractions, decimals and percentages Converting between the three forms, simplifying fractions, recognising terminating and recurring decimals, and avoiding rounding errors.
- Ratios and proportions What a ratio says, how to simplify one, how to share an amount in a ratio, and how to solve proportions for recipes, maps and mixtures.
- Mean, median and mode The three common averages and the range, how each is calculated, which to use when, and how outliers and ties change the answer.
- Factors, primes, GCD and LCM Finding factors and primes, prime factorisation, and how the greatest common divisor and least common multiple simplify fractions and solve scheduling problems.
About NumberUtils
Every calculator shows the formula it uses, so a result can be checked by hand or reproduced in a spreadsheet. Fractions are calculated exactly rather than as rounded decimals, and inputs that have no meaningful answer, such as a negative ratio, are rejected with an explanation rather than given a misleading result. The methodology lists the rules each calculator follows.
Calculations run in your browser rather than on a server. Read more about NumberUtils, or get in touch if a result looks wrong.