Quick math, shown step by step
Every calculator on this page shows its formula. That's deliberate. A bare answer helps once. Seeing how the answer came together helps you do it yourself next time, whether you're a student checking homework or an adult halving a recipe.
There's no sign-up, no ads in the way of the result and no data leaving your browser. Type a number and the answer appears.
Percentages in three flavors
Percent questions come in three shapes. What is 15 percent of 80? 12 is what percent of 60? And how much did a price change from $40 to $52? The percentage calculator handles all three and prints the formula under each result.
A few handy anchors. Ten percent is just a decimal shift: move the point one place. Five percent is half of that. Twenty percent is double. Tips, sales tax and discounts all fall out of those three.
Percentage change trips people up because it depends on the starting point. A price that rises 50 percent and then falls 50 percent doesn't return to where it began. Start at 100, go up to 150, then fall to 75. The calculator makes that obvious.
Factors, multiples and averages
The GCF and LCM calculator takes two whole numbers and returns the greatest common factor and the least common multiple. It also shows prime factorization and the steps of the Euclidean algorithm. GCF is what you use to simplify fractions. LCM is what you need to add fractions with different denominators, or to find when two repeating events line up.
The mean, median and mode calculator accepts a list and returns the average, the middle value, the most common value, the range, the sum and the count, with a step-by-step breakdown.
Which average should you quote? It depends. Mean is sensitive to outliers. If nine people earn $40,000 and one earns $1,000,000, the mean is $136,000, and nobody in the group earns anything like that. The median, $40,000, tells the truer story. Use median for incomes and house prices.
- Mean: add everything, divide by how many
- Median: the middle value after sorting
- Mode: the value that appears most
- Range: highest minus lowest
Scientific notation
Scientists write 0.000000052 as 5.2 × 10⁻⁸ because it's shorter and harder to miscount. The scientific notation calculator converts both ways and lets you multiply and divide numbers in that form.
When you multiply, multiply the front numbers and add the exponents. When you divide, divide the front numbers and subtract the exponents. If the front number ends up above 10 or below 1, adjust it and shift the exponent to match.
Unit converters
Four converters cover everyday needs: length, volume, weight and temperature. Each updates live and displays the formula.
Length runs from millimeters to miles. Volume includes milliliters, liters, cubic meters, fluid ounces, cups, pints, quarts and both US and UK gallons. That last pair matters. A UK gallon is about 20 percent larger than a US one, and mixing them up ruins recipes and fuel math.
Weight covers milligrams through tonnes, plus ounces, pounds and stone. Temperature converts between Celsius, Fahrenheit and Kelvin, and all three update at once.
Quick mental tricks help. An inch is 2.54 centimeters. A kilogram is a bit over 2.2 pounds. To turn Celsius into Fahrenheit, double it, subtract ten percent of that, and add 32. It's close enough for the weather.
Common slip-ups
Rounding too early. If you round at each step, the errors add up. Keep full precision until the final answer.
Mixing units. Don't add feet to meters. Convert first.
Forgetting order of operations. Multiplication and division come before addition and subtraction, and brackets go first of all.
Trusting the calculator when the answer looks silly. If a 15 percent tip on a $40 bill comes out at $60, a digit went wrong somewhere.
Using these for learning
Teachers and parents can use the formula display as a check. Ask a student to work a problem on paper, then compare. If the answers disagree, the steps show where the paper version went off.
The tools work on phones too, which makes them handy in the kitchen, the garage and the classroom.
Checking your own work
Calculators are great, and bad habits creep in when we trust them blindly. Estimate first. If you're taking 18 percent of 250, you know the answer should be a bit under a fifth of 250, so near 45. If the result says 450 or 4.5, a decimal slipped.
The same trick works for conversions. A mile is about 1.6 kilometers, so 10 miles should land around 16. A kilogram is about 2.2 pounds, so 70 kilograms is roughly 154. Round numbers in your head catch typos that a tool can't see.
Do it every time for a week and it becomes automatic.
Choosing between mean, median and mode
Take five salaries: 30, 32, 35, 38 and 400 thousand. The mean is 107 thousand, which describes nobody. The median is 35, which describes the typical person. The mode, here missing, tells you the most common value.
Skewed data, like pay, house prices or response times, is where the median shines. Symmetrical data, like heights in a group, is where the mean works. When in doubt, look at both.
The calculator here shows all three, so you can see how far apart they are.
Units are where errors hide
Mixing up units is one of the oldest mistakes in practical math. A recipe in cups, a bolt in millimeters, a dose in milligrams. Write the unit next to every number as you go, and convert once, at the start. Everything runs in your browser, so feel free to try odd values.