Fraction arithmetic
Add, subtract, multiply or divide fractions and mixed numbers. See exact simplified results, common denominators and each calculation step.
Math calculators with steps and worked examples
Calculate fractions, percentages, ratios, statistics and algebra. Check formulas, exact fraction steps and independently checked examples.
Each page includes an interactive tool, a complete worked example, its method and limits, and links to the relevant reference material. Calculations and text conversion run in your browser. You do not need an Ithy account.
Math and statistics
Compare and order fractions
Compare two or more fractions, decimals and mixed numbers. Order them exactly and see the common-denominator explanation.
Decimal to fraction
Convert a finite decimal or scientific notation into a simplified fraction, with place-value and greatest-common-divisor steps.
Percentage calculator
Calculate a percent of a number, express one number as a percent of another, or find the whole from a known part and percentage.
Percentage change
Calculate relative percentage change, absolute change, multiplier and the reverse change. Distinguish percentage points from relative percent.
Ratio calculator
Simplify two positive decimal quantities to an exact whole-number ratio, then scale that ratio to a new first quantity.
Mean, median and mode
Find mean, median, all repeated modes, range, sum and a sorted list. See how an outlier changes the average compared with the middle value.
Standard deviation
Calculate sample and population variance and standard deviation together. See the mean, squared-deviation sum and the n versus n−1 denominator.
Weighted average
Calculate a weighted mean from value–weight pairs. See total weight, each weighted contribution and how percentage weights are normalized.
MAE, MSE, RMSE and R²
Compare actual and predicted values with per-row errors, MAE, MSE, RMSE and R². Handle constant targets and negative R² explicitly.
Binary, decimal and hex
Convert signed integers among binary, decimal, octal and hexadecimal without losing large integer digits. Check unsigned and two’s-complement 8-bit values.
Scientific notation
Convert a finite decimal or e notation into normalized scientific notation and an exact decimal expansion without rounding the entered digits.
Quadratic equation solver
Solve ax² + bx + c = 0, inspect the discriminant and vertex, and handle repeated, complex and linear cases explicitly.
Slope between two points
Calculate slope, rise, run, intercept, line equation and distance from two points. Handle vertical lines and identical points explicitly.
GCD and LCM
Find the greatest common divisor and least common multiple of signed whole numbers using exact integer arithmetic and Euclidean steps.
Pythagorean theorem
Find a hypotenuse or missing leg of a right triangle. See the squared-side equation, area and perimeter with explicit geometry assumptions.
Choose a tool by the question
Use fraction comparison to establish order, fraction arithmetic to calculate a result, and decimal conversion to express a finite decimal exactly. For percentages, identify whether you need a share of a total or a change from an earlier baseline. These questions use different denominators.
Statistics tools describe the values you supply. A small data set, a convenient average or a good fit does not by itself establish a cause or a reliable prediction. Keep the units, sampling process and evaluation split with your result.
Developer tools operate on text or bytes, depending on the format. UTF-8 byte counts differ from visible character counts, Base64 is reversible encoding, and a SHA-256 digest is a one-way checksum. For time conversion, select seconds or milliseconds explicitly and include a time zone in a date-time input.
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