23 free math calculators — from basic percentages and fractions to scientific notation, matrices, and quadratic formulas.
These calculators cover school and university maths, everyday calculations, and the number work behind programming and science. Each links to a plain-English guide explaining the concept, not just the answer.
| What you need | Use this |
|---|---|
| Work out a percentage or percentage change | Percentage Calculator |
| Add, multiply or simplify fractions | Fraction Calculator |
| Simplify or scale a ratio | Ratio Calculator |
| Solve a quadratic equation | Quadratic Formula |
| Convert to or from scientific notation | Scientific Notation |
| Multiply or invert a matrix | Matrix Calculator |
| Convert binary, hex and decimal | Binary Calculator |
| Measure the spread of data | Standard Deviation |
| A full scientific calculator | Scientific Calculator |
Most calculator errors are not arithmetic slips — they come from a handful of concepts that are easy to misapply. Three worth fixing before you calculate anything.
Brackets, then powers and roots, then division and multiplication, then addition and subtraction. 2 + 3 × 4 is 14, not 20, because multiplication comes first. Calculators apply this automatically, so if you meant the addition first, you have to add the brackets yourself.
A rise from 40 to 50 is +25%, but the fall back from 50 to 40 is −20% — because each percentage is taken from a different starting number. This is also why a 20% discount isn't undone by adding 20% back.
Standard deviation uses a different formula depending on whether your numbers are an entire population or a sample from a larger group. Same data, different answer. Always check which your calculator is set to.
Percentages, fractions and ratios are three ways of describing a part of a whole, and they're the calculations people actually reach for — at the shops, on a payslip, splitting a bill. The traps are consistent: percentage change depends on the starting point, reverse percentages need division not subtraction, and fractions can only be added once the denominators match.
Calculators: Percentage · Fraction · Ratio · Rounding · Percent Error
Guide: Percentages, fractions & ratios explained
The quadratic formula solves any equation of the form ax² + bx + c = 0, and its discriminant tells you how many real solutions exist before you finish. Scientific notation tames very large and very small numbers, matrices handle many equations at once, and binary is simply base 2 — the same numbers written differently.
Calculators: Quadratic Formula · Scientific Notation · Matrix · Binary · Hexadecimal · Exponent · Logarithm · Root
Guide: Algebra & notation explained
Probability measures how likely something is on a scale of 0 to 1; standard deviation measures how spread out data is around its average. The mean alone hides that spread, which is why the two go together — and the population-versus-sample distinction quietly changes the standard deviation you calculate.
Calculators: Standard Deviation · Probability · Statistics · Factor · GCF · LCM
Guide: Probability & standard deviation explained
What's the order of operations?
Brackets first, then orders (powers and roots), then division and multiplication worked left to right, then addition and subtraction. It's often remembered as BODMAS or BIDMAS. So 2 + 3 × 4 equals 14, because the multiplication is done before the addition.
Why isn't a percentage increase cancelled by the same percentage decrease?
Because each percentage is calculated from a different starting number. A 25 per cent rise from 100 gives 125, but a 25 per cent fall is then taken from 125, landing at 93.75. The changing base means they don't cancel out.
How do I add two fractions?
Give them a common denominator, then add the numerators. To add 1/2 and 1/3, rewrite both over 6 as 3/6 and 2/6, which add to 5/6. The bottoms must match before you can add the tops.
How many solutions does a quadratic equation have?
It depends on the discriminant, b² − 4ac. If it's positive there are two real solutions, if zero there's one repeated solution, and if negative there are no real solutions, because you can't take the square root of a negative number in the real numbers.
What does standard deviation tell me?
It measures how spread out data is around the mean. A small standard deviation means values cluster tightly around the average; a large one means they're widely spread. Two datasets can share a mean but have very different spreads.
What's the difference between population and sample standard deviation?
If your data is the entire population you divide by the number of values (n); if it's a sample from a larger group you divide by n − 1. This gives different answers for the same data, so choose the formula that matches what your data represents.
Why do computers use binary?
Because a circuit is either off or on, which maps to 0 and 1. Binary is base 2, where each place is a power of two. It doesn't change the numbers, only how they're written — 1011 in binary is 11 in ordinary base 10.
These tools are built to show the working, not just the answer, so they're most useful when you use the result to check your own steps rather than replace them. For assignments and exams, always confirm the method your course expects — conventions differ, particularly between population and sample statistics, and between notations taught at different levels.
Read more about how we build and check our calculators, or about who writes this site.
Note: MegaCalcOnline provides free educational calculators and explanations for general learning. Worked examples are illustrative. Always check the specific method, formula convention, or rounding rule required by your course, exam board, or field before relying on a result for assessment or professional work.
From basic percentage calculations to matrix operations and number base conversions, this page gathers general-purpose math tools that come up in study, trades, computing, and everyday problem solving. Each calculator handles one specific type of calculation reliably and instantly, without needing to remember formulas or reach for a scientific calculator.
Percentage, fraction, and ratio calculators cover the most common everyday math — working out discounts, splitting bills proportionally, or converting between fraction and decimal forms. Algebra tools like the quadratic formula calculator solve equations that would otherwise require manual factoring or the quadratic formula worked out by hand.
Binary, hexadecimal, and scientific notation calculators are especially useful for programming, computer science study, and electronics work, where numbers are frequently represented in bases other than the familiar base-10 decimal system. Converting between these accurately by hand is time-consuming and error-prone — these tools handle the conversion instantly.
Tools like the standard deviation, log, and matrix calculators support more advanced coursework and professional use, where manual calculation is both slow and prone to arithmetic mistakes. These are built to show working steps where relevant, so the calculator supports learning the underlying method rather than only producing a final answer.
Are these calculators suitable for high school and university coursework?
Yes, they're built to match standard formulas taught in Australian high school and first-year university math courses. However, always check with your teacher or lecturer whether calculator use is permitted for a specific assessment.
What's the difference between a ratio and a fraction calculator?
A ratio calculator compares two or more quantities relative to each other (like 2:3), while a fraction calculator performs arithmetic on fraction values (like adding 1/2 + 1/3). They solve related but distinct types of problems.
Why would I need a binary or hex calculator in everyday life?
These come up most often in computer science study, programming, networking (like understanding IP subnets), and some electronics work, where data is represented in binary or hexadecimal rather than decimal.
These tools are for general calculation and study support. Always verify results against your course requirements and check with your instructor for assessment-specific rules on calculator use.
Get an occasional email when we add new calculators or publish a new guide. No spam, unsubscribe anytime.