Solve percentages, fractions, averages, grades and geometry problems with free calculators that show every step.
Our math calculators help students, parents and teachers check homework and understand how an answer is reached. Work with percentages, fractions, ratios, averages, standard deviation, square roots, circles and the Pythagorean theorem, or convert grades between systems.
How do I calculate a percentage of a number?
To calculate a percentage of a number, multiply the number by the percentage and divide by 100. For example, 15 percent of 200 is 200 times 15 divided by 100, which equals 30. Our math calculators handle this and related percentage questions instantly.
Many tools show worked steps instead of a bare number, which makes them useful for revision in the UK, Ireland and the EU as well as the United States. Grade tools cover GPA and percentage conversions, and geometry tools use metric units such as centimeters and meters by default.
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Percent, ratio, fraction and decimal tools
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Roots, LCM, GCF and number formats
Statistics and Geometry
Spread, z scores, circles and right triangles
Algebra, Division and Statistics
Step by step answers for homework and lab reports
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Algebra, geometry, statistics, grading and random pickers
How Can Math Calculators Help You Check Homework?
Math calculators are most useful when you solve the problem yourself first and then compare your answer, because a mismatch shows exactly which step to revisit. Tools that display working, such as fraction simplification or standard deviation steps, turn a wrong answer into a lesson rather than a dead end.
The fraction calculator is a good example. Adding 1/3 and 1/4 needs a common denominator of 12, giving 4/12 + 3/12 = 7/12, and seeing that step written out helps students who keep adding the denominators by mistake. The percentage calculator works the same way for discounts, marks and test scores.
Teachers and parents can also use math calculators to create answer keys quickly. Rounding is worth agreeing in advance: exam boards often ask for answers to 3 significant figures or 2 decimal places, and a calculator set to a different rule will appear to disagree.
For grades, the GPA calculator weights each course by its credits, so a 4 credit module counts twice as much as a 2 credit one. Students moving between UK, EU and US systems should check how their own university converts marks, since there is no single official conversion table.
What Is the Difference Between Sample and Population Standard Deviation?
Population standard deviation divides the sum of squared deviations by N, while sample standard deviation divides by N − 1, which gives a slightly larger result. The N − 1 version, known as Bessel’s correction, is used when your data is a sample from a bigger group, and the NIST Engineering Statistics Handbook defines the sample variance this way.
Take the values 2, 4, 4, 4, 5, 5, 7 and 9. The mean is 5, the population standard deviation is exactly 2 and the sample standard deviation is about 2.14. If those eight numbers are every test score in a class, use 2; if they are eight pupils picked from a whole year group, use 2.14.
For data that follows a bell curve, about 68 percent of values fall within one standard deviation of the mean, 95 percent within two and 99.7 percent within three. The standard deviation calculator lets you choose sample or population and writes out each step.
A common slip is mixing the two formulas within one piece of work. Exam questions usually say whether the data is a sample or a whole population, and spreadsheets mark the difference too, with STDEV.S for samples and STDEV.P for populations.
How Do You Work Out a Percentage Change Correctly?
Percentage change equals (new value − old value) ÷ old value × 100, so a rise from 80 to 100 is a 25 percent increase. The base is always the starting value, which is why the same gap gives different percentages depending on direction.
Going back down from 100 to 80 is a 20 percent decrease, not 25 percent, because the starting value is now 100. This is also why a 50 percent loss needs a 100 percent gain to recover.
Percentage points are different again. If an interest rate moves from 2 percent to 3 percent, it has risen by 1 percentage point, but by 50 percent in relative terms. News reports mix these up often, so it is worth checking which one a figure describes.
Reverse percentages need the same care. If a price after a 20 percent discount is 80, the original price is 80 ÷ 0.8 = 100, not 80 + 16 = 96. Dividing by the remaining fraction is the reliable method for any discount, tax or markup question.
| Calculation | Formula | Example |
|---|---|---|
| Percentage of a number | value × percent ÷ 100 | 15% of 240 = 36 |
| Percentage change | (new − old) ÷ old × 100 | 80 to 100 = 25% increase |
| Mean | sum of values ÷ number of values | 2, 4, 9 gives 5 |
| Population standard deviation | √(Σ(x − mean)² ÷ N) | 2, 4, 4, 4, 5, 5, 7, 9 gives 2 |
| Sample standard deviation | √(Σ(x − mean)² ÷ (N − 1)) | Same data gives about 2.14 |
| Pythagorean theorem | c = √(a² + b²) | a = 3, b = 4 gives c = 5 |
| Area of a circle | π × r² | r = 5 gives about 78.54 |
Frequently Asked Questions
Do math calculators show the steps?
Many do. Where a method matters, such as fractions, LCM or standard deviation, the calculator lays out the working so you can follow the logic, check your own answer and learn the method rather than only copy a result.
Are these calculators suitable for homework?
Yes, as a checking tool. Work the problem yourself first, then compare your answer with the calculator and study any difference. Always follow your school or exam board rules on calculator use.
Can I convert grades between UK, EU and US systems?
Grade tools convert GPA and CGPA to percentages and back using common formulas. Universities set their own scales, so confirm the official conversion with your institution before using a result in an application.
What is the difference between mean, median and mode?
The mean is the sum of values divided by their count, the median is the middle value when sorted and the mode is the value that appears most often. Each describes the center of a data set differently.
Do the calculators work on phones?
Yes. Every math calculator is responsive, works in any modern browser on phones, tablets and computers, and needs no download or sign up, so you can check a result in class or on the move.
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Last reviewed: October 2026