Arithmetic & Percentages Calculators

The arithmetic everything else is built on

Every calculator on this site, from mortgages to molar masses, ultimately rests on the operations covered by this shelf: adding, dividing, taking a percentage, simplifying a fraction, rounding a result sensibly. These nine tools handle that layer directly, and each one shows its working rather than just printing an answer. That matters more here than anywhere else on the site, because arithmetic is the subject where people most often know the answer is wrong but cannot see why.

The tools split into three rough groups. The Percentage Calculator and Percent Error Calculator deal with proportional comparisons. The Fraction Calculator, Ratio Calculator and Long Division Calculator deal with exact division and its many notations. And the Basic Calculator, Scientific Calculator, Big Number Calculator and Rounding Calculator are general workhorses for computing and presenting numbers. Everything here is free to use, with no limits on how many sums you run.

Percentages: three questions, one idea

Almost every percentage problem you will ever meet is one of three questions. What is X% of a number? What percentage is one number of another? And by what percentage did a value change? The Percentage Calculator answers all three in one tool, and it is worth being clear about which one you are actually asking, because mixing them up is the single most common percentage mistake.

The first question is a multiplication: 15% of 240 is 0.15 × 240 = 36. The second is a division: 36 as a share of 240 is 36 ÷ 240 = 0.15, which is 15%. The third compares two values over time or between scenarios: the change from an old value to a new one, divided by the old value, times 100. The divisor is always the starting value. A rise from 40 to 50 is a 25% increase, but the fall from 50 back to 40 is only a 20% decrease, because the base has changed. Percentage changes are not symmetric, and treating them as if they were is how people convince themselves a price that rose 50% then fell 50% is back where it started. It is not; it is 25% lower.

Measuring how wrong a measurement is

The Percent Error Calculator applies the same proportional thinking to experiments and estimates. It compares a measured value against the accepted or true one and reports the absolute error, the percent error and the direction of the miss. The standard formula divides the size of the error by the size of the true value, then multiplies by 100. It is the tool to reach for in chemistry and physics practicals, but it is just as useful for checking a forecast against what actually happened.

Fractions, ratios and division that shows its remainder

Fractions, ratios and long division are three notations for the same underlying act of splitting. The Fraction Calculator adds, subtracts, multiplies and divides two fractions, simplifies a fraction to lowest terms, and converts a decimal into a fraction, with every step written out. The rules are few but easy to misremember. Adding and subtracting need a common denominator first. Multiplying works straight across: numerator times numerator, denominator times denominator. Dividing means multiplying by the reciprocal of the second fraction, which is why dividing by a half doubles a number rather than halving it.

The Ratio Calculator covers the jobs fractions are awkward for: simplifying a ratio such as 18:24 to 3:4, finding the missing number in a proportion like A:B = C:D, and scaling a ratio up to a target total. Scaling is the version people meet most in real life, whether that is adjusting a recipe for six instead of four or splitting a bill in agreed shares. The key habit is to find the value of one part first, then multiply out.

The Long Division Calculator works through the classic paper method digit by digit and reports the answer three ways: quotient with remainder, mixed number, and decimal, including spotting when the decimal repeats. The three forms always agree, and the tool checks them against each other using the relationship that ties division together: dividend = divisor × quotient + remainder. If you are helping a child with homework, this is the tool that shows the method schools actually teach rather than skipping straight to the answer.

Rounding, precision and numbers too big for a normal calculator

Rounding looks trivial until two people round the same number differently and both insist they are right. The Rounding Calculator rounds by decimal places, by significant figures, or to the nearest amount you choose, and it compares the main conventions side by side: half up, half down, banker's rounding (half to even), truncation and away from zero. The differences only appear on exact halves, but exact halves come up constantly in money, which is precisely why accountants and programming languages often prefer banker's rounding: over many transactions it does not drift systematically upwards the way half-up rounding does.

Significant figures and decimal places are not the same thing, and confusing them is a reliable source of lost marks. 0.00456 has three significant figures but five decimal places, and a value reported as 12,300 to three significant figures could have started anywhere from 12,250 to just under 12,350. The calculator makes the distinction explicit rather than leaving you to guess which rule was applied.

When ordinary calculators run out of digits

Standard calculators and spreadsheets store numbers in floating point, which keeps roughly 15 to 17 significant digits and quietly discards the rest. For everyday sums that is fine; for factorials, cryptographic-sized integers or exact accounting on huge figures it is not. The Big Number Calculator works on whole numbers running to thousands of digits and computes exactly, with no rounding at all. It adds, subtracts, multiplies, divides, takes powers, remainders and greatest common divisors, includes a factorial tool, and even demonstrates live where ordinary float arithmetic starts to lie to you. If you have ever seen a spreadsheet insist that a 20-digit number ends in several zeros it should not, this tool shows you why.

The two general-purpose calculators

Sometimes you do not want a specialist tool, just a calculator. The Basic Calculator is a pocket-style keypad that evaluates as you press each key, with memory keys, a running tape of your session and an honest, documented percent convention. That last point is worth a sentence: pocket calculators disagree with each other about what the % key does in the middle of a sum, so this one states its rule plainly instead of leaving you to reverse-engineer it.

The Scientific Calculator is the step up. You can type a whole expression or build it on the keypad, and a genuine expression parser evaluates it with the order of operations shown, so you can see exactly why 2 + 3 × 4 is 14 and not 20. It handles trigonometry in degrees or radians, factorials, and chaining with the previous answer, and it echoes back exactly how it read your input, which settles the ambiguous-expression arguments that fill maths forums. If your sums drift into powers and logarithms proper, the Exponent Calculator and Log Calculator on the Powers, Roots & Logs shelf go deeper on those specific operations.

Common mistakes worth unlearning

A few errors account for most wrong answers in this territory. Percentage changes get computed against the wrong base, usually the new value instead of the old one. Fractions get added by adding tops and bottoms separately, which fails the moment the denominators differ. Ratios get scaled by adding the same amount to each side rather than multiplying both sides. Rounding gets applied at every intermediate step instead of once at the end, which stacks small errors into a visible one. And people trust a calculator display showing 16 digits of a number that was only ever accurate to three. Every tool on this shelf is built to surface these traps in its working rather than paper over them.

Frequently asked questions

What is the difference between a percentage and a percentage point?

A percentage point is the simple arithmetic gap between two percentages. If a rate moves from 4% to 6%, it has risen by 2 percentage points, but by 50% in relative terms, because 2 is half of 4. News reports mix these up constantly. The Percentage Calculator reports relative change, so if you want points, subtract the percentages directly.

How do I turn a repeating decimal back into a fraction?

The Fraction Calculator converts decimals to fractions, and the Long Division Calculator shows the reverse direction, revealing where a division starts repeating. A decimal repeats exactly when the simplified denominator has a prime factor other than 2 or 5.

Which rounding method should I use for money?

For a one-off sum, half-up rounding matches most people's expectations. For long runs of transactions, banker's rounding avoids a systematic upward drift, which is why financial systems often use it. The Rounding Calculator shows both on your own number so you can see when they differ.

Do these tools cost anything?

No. Every calculator on this shelf is free, and each one shows the full method alongside the answer, so you can check the working rather than take it on trust.