Percentage, Fraction & Ratio Calculators
Six calculators for the arithmetic that actually comes up day to day — parts of a whole, and how to move between the ways of writing them.
Percentages, fractions and ratios are one idea in three notations
A half, 50% and 1:1 are the same relationship written three ways, and most confusion comes from switching notation mid-problem. The Percentage Calculator handles the three questions percentages actually answer — what is X% of Y, X is what percent of Y, and the percentage change between two numbers. The Fraction Calculator adds, subtracts and simplifies without decimal rounding, which matters in recipes and measurements. The Ratio Calculator scales a ratio up or down while keeping the proportion, the form mixing and dilution problems come in.
Which average did you mean?
"Average" is three different statistics. The mean is the total divided by the count, the median is the middle value once sorted, and the mode is the most common one. On skewed data they can be far apart — one very high salary drags a mean upward while leaving the median where it was, which is why income is usually reported as a median. The Average Calculator gives all three at once, and reading them together tells you whether the mean is safe to quote.
Percentage change is not symmetric
This is the trap worth internalising: a 20% fall followed by a 20% rise does not get you back. £100 down 20% is £80, and £80 up 20% is £96. The multipliers are 0.8 and 1.2, and they do not cancel. The same asymmetry is why a 50% markup is only a 33% margin — percentages made simple works through it, and the Markup Calculator handles the pricing case.
The two odd ones out
The Basic Calculator is exactly what it sounds like — a keyboard-friendly four-function calculator for when you do not want a tool with a formula behind it. The Roman Numerals goes both ways between Arabic and Roman numerals, which is a genuine need for dates on buildings, book front matter, film credits and monarch numbering. For anything with an unknown in it, move up to the algebra and advanced tools linked above.
Frequently asked questions
Are percentages, fractions and ratios really the same thing?＋
They are three notations for one idea: a part measured against a whole. A half is 0.5, 50% and 1:1 depending on which notation suits. The choice is about communication, not maths — percentages read well in prose, fractions in exact arithmetic, ratios when comparing two quantities directly.
Why is a 50% fall not undone by a 50% rise?＋
Because each percentage is taken from a different base. Falling 50% from 100 leaves 50; rising 50% from 50 returns 75, not 100. Recovering a 50% fall takes a 100% rise. This asymmetry catches people out constantly, and it grows more severe as the percentages get larger.
Which average should I be using?＋
The mean when values are evenly spread and you want the arithmetic centre. The median when a few extreme values would drag the mean somewhere unrepresentative — incomes and house prices are the classic cases. The mode when you want the most common value rather than a central one. The average calculator shows all three so you can see how far apart they are.
What is a percentage point, and why does it matter?＋
A percentage point is an absolute difference between two percentages; a percentage is a relative one. A rate moving from 2% to 3% has risen one percentage point but fifty per cent. Both statements are true and they describe the same change, which is why the distinction is worth being precise about.