Math and Percentage Calculators
From a price tag or a recipe to algebra homework and a statistics project, these calculators give the answer and the steps that lead to it. They are grouped by topic: percentages, fractions and numbers, algebra, geometry, and statistics and probability. Each follows the methods taught in open college textbooks, so you can check the work or copy the method.
Percentages
- Percentage CalculatorFind a percentage of a number, what percent one number is of another, or the whole from a part and its percent, with the equation and a worked sentence.Open calculator
- Percentage Increase CalculatorCalculate the percentage increase or decrease from one value to another, add or subtract a percent, or find the original value before a percent change.Open calculator
- Discount CalculatorFind the sale price after a percent or dollar discount, combine two stacked discounts, work out the percent off from two prices, or recover the original price.Open calculator
- Tip CalculatorCalculate the tip and total for any bill, tip before or after tax, and split the bill evenly with an option to round each share up to the dollar.Open calculator
- Percent Error CalculatorFind the percent error between a measured and an accepted value, with the signed error, the mean of several trials and the percent difference.Open calculator
Fractions, ratios and numbers
- Mixed Fraction CalculatorAdd, subtract, multiply or divide mixed numbers and fractions with whole numbers. Get the simplified mixed number, improper fraction, decimal and the steps.Open calculator
- Simplify Fractions CalculatorReduce a fraction to lowest terms using the greatest common factor, rewrite it with any denominator, and list equivalent fractions.Open calculator
- Decimal to Fraction CalculatorConvert a decimal to a fraction in lowest terms, including repeating decimals such as 0.333…, with the mixed number and the nearest 1/16 or 1/64 inch.Open calculator
- Fraction to Decimal CalculatorConvert a fraction or mixed number to a decimal by long division, find the exact repeating block, and see whether the decimal terminates and why.Open calculator
- GCF CalculatorFind the greatest common factor of two or more numbers with prime factorizations, the list of common factors and Euclid’s algorithm step by step.Open calculator
- LCM CalculatorFind the least common multiple of two or more numbers with prime factorizations, lists of multiples and the multiplier for a common denominator.Open calculator
- Factor CalculatorList every factor of a whole number with its factor pairs, prime factorization, factor count and sum, and check whether the number is prime.Open calculator
- Ratio CalculatorSimplify a ratio to whole numbers, solve a proportion for the missing value, or divide a total into shares in a ratio such as 2 : 3 : 5.Open calculator
- Aspect Ratio CalculatorFind the aspect ratio of any width and height, calculate the missing dimension at 16:9, 4:3 or a custom ratio, and fit one size inside another.Open calculator
- Rounding CalculatorRound a number to the nearest ten, hundred, tenth, hundredth or any multiple such as 0.25, using the school rule, round half to even, ceiling, floor or truncation.Open calculator
- Long Division CalculatorDivide step by step with the classic long-division layout, as a quotient and remainder or as a decimal, including repeating decimals and decimal divisors.Open calculator
- Modulo CalculatorFind a mod n and the quotient, and see how the floored, truncated and Euclidean conventions differ for negative numbers, as in Python, Excel and JavaScript.Open calculator
- Scientific Notation CalculatorConvert numbers to and from scientific, e- and engineering notation with SI prefixes, round to significant figures, and multiply or divide powers of ten.Open calculator
Algebra
- Scientific CalculatorFree online scientific calculator: type an expression with sin, cos, tan, logs, powers, roots, factorials, nPr and nCr, in degrees or radians.Open calculator
- Square Root CalculatorFind the square root, cube root or any nth root of a number, with the simplest radical form (√72 = 6√2), the whole numbers it falls between and a check.Open calculator
- Exponent CalculatorRaise any number to a power, including negative, decimal and fractional exponents such as 343^(2/3), with exact digits for large whole-number powers and the rule used.Open calculator
- Log CalculatorFind log base 10, natural log (ln), log base 2 or a logarithm in any base, or go the other way with the antilog. Shows the change-of-base step and exact answers.Open calculator
- Quadratic Formula CalculatorSolve ax² + bx + c = 0 with the quadratic formula. Get exact roots in simplest radical form, decimal values, complex roots, the discriminant, the vertex and a graph.Open calculator
- System of Equations CalculatorSolve two equations in x and y or three in x, y and z with exact fractions, and see whether the system has one solution, none or infinitely many.Open calculator
- Slope CalculatorFind the slope between two points as a fraction and decimal, with the line’s equation y = mx + b, the intercepts, angle, percent grade and distance.Open calculator
- Number Sequence CalculatorFind the nth term and the sum of an arithmetic or geometric sequence, the infinite sum when it exists, and identify a sequence from its first few terms.Open calculator
Geometry
- Pythagorean Theorem CalculatorFind the hypotenuse or a missing leg of a right triangle with a² + b² = c², with the exact square root, area, angles, and a check for right, acute or obtuse.Open calculator
- Right Triangle CalculatorSolve a right triangle from two sides or a side and an angle using sine, cosine and tangent, with all three sides, both angles, area and perimeter.Open calculator
- Triangle CalculatorSolve any triangle from three sides, two sides and an angle, or two angles and a side, with the area, perimeter and both answers in the ambiguous SSA case.Open calculator
- Area CalculatorCalculate the area of a rectangle, triangle, trapezoid, circle, ellipse or sector, with the perimeter and the result in square feet, square yards, acres and square meters.Open calculator
- Volume CalculatorFind the volume and surface area of a box, cube, cylinder, sphere, cone, pyramid or capsule, in cubic feet, cubic yards, gallons and liters.Open calculator
Statistics and probability
- Average CalculatorCalculate the mean, median, mode and range of a list of numbers, or a weighted average, from a pasted list or spreadsheet column.Open calculator
- Standard Deviation CalculatorCalculate sample or population standard deviation and variance from a list of numbers, with the mean, sum of squares, quartiles and every step.Open calculator
- Mean Absolute Deviation CalculatorFind the mean absolute deviation of a data set with a table of every distance from the mean, plus the median absolute deviation and standard deviation.Open calculator
- Z-Score CalculatorCalculate a z-score from a value, mean and standard deviation, find the percentile under the normal curve, or the value at any percentile.Open calculator
- Quartile CalculatorFind Q1, the median, Q3, the interquartile range and the 1.5 × IQR outlier fences for a data set, with the five-number summary and a box plot.Open calculator
- Percentile CalculatorFind the kth percentile of a data set or the percentile rank of a value, using the textbook (n + 1) method or Excel’s PERCENTILE.INC and .EXC, side by side.Open calculator
- Confidence Interval CalculatorBuild a confidence interval for a mean (z or t) or a proportion, including the plus-four method, with the margin of error, critical value and standard error.Open calculator
- Sample Size CalculatorWork out how many responses a survey needs for a chosen margin of error and confidence level, or the sample size to estimate a mean, with the formula shown.Open calculator
- Linear Regression CalculatorFind the least-squares line ŷ = a + bx, the correlation coefficient r and r², test whether r is significant, and predict y from x, with a scatter plot.Open calculator
- Probability CalculatorFind P(A and B), P(A or B), P(neither) and conditional probability for independent, mutually exclusive or dependent events, or the chance of at least one success in n tries.Open calculator
- Permutation and Combination CalculatorCount permutations P(n, r) and combinations C(n, r) exactly, with repetition and subset counts, or count the arrangements of the letters in a word.Open calculator
- Expected Value CalculatorFind the expected value, variance and standard deviation of a discrete random variable from outcomes and probabilities, entered as decimals, percents or fractions.Open calculator
- Random Number GeneratorGenerate one or many random whole numbers or decimals between any two values, with or without repeats, using your browser’s cryptographic random source.Open calculator
Which calculator do you need?
Percentages. Use the percentage calculator for “what is P% of a number” and “what percent is A of B,” and the percentage increase calculator when something has changed from an old value to a new one, or when you need to undo a change. The discount calculator adds stacked discounts and sales tax for shopping, the tip calculator handles the restaurant check and splitting it, and the percent error calculator compares a lab result with the accepted value.
Fractions, ratios and numbers. Convert either way with the decimal to fraction and fraction to decimal calculators; both handle repeating decimals exactly. Reduce a fraction or find a common denominator with the simplify fractions calculator, and do arithmetic with the mixed fraction calculator. The GCF and LCM calculators show the factoring behind all of these, and the factor calculator lists every factor of one number with its prime factorization. The ratio calculator simplifies ratios, solves proportions and splits totals, and the aspect ratio calculator applies the same math to screens, video and photos. For working with numbers themselves, the rounding calculator rounds to any place with the school rule or round half to even, the long division calculator shows each step of a division with a remainder or a decimal, the modulo calculator gives a mod n in the floored, truncated and Euclidean conventions, and the scientific notation calculator converts between decimal, e-notation and engineering notation and rounds to significant figures.
Algebra. The scientific calculator evaluates a typed expression with trig functions, logarithms, powers, roots, factorials and combinations, in degrees or radians, using the same order of operations the textbooks teach. The square root calculator simplifies radicals such as √72 = 6√2, the exponent and log calculators handle powers and logarithms in any base, and the quadratic formula calculator gives exact and complex roots with the vertex. The system of equations calculator solves two or three linear equations exactly, the slope calculator turns two points into a line equation, and the number sequence calculator finds any term and the sum of an arithmetic or geometric sequence, or identifies the pattern from a few terms.
Geometry. The Pythagorean theorem calculator finds the missing side of a right triangle, and the right triangle calculator solves its sides and angles with sine, cosine and tangent. The triangle calculator solves any triangle with the law of sines and the law of cosines, including the two-answer SSA case. The area and volume calculators cover common shapes and solids, with results in square and cubic feet, acres, gallons and metric units.
Statistics and probability. Start with the average calculator for the mean, median and mode, then use the standard deviation calculator for spread and the z-score calculator to see where one value sits; the mean absolute deviation calculator gives a simpler measure of spread. The quartile calculator gives the five-number summary, the IQR and outliers with a box plot, and the percentile calculator finds the value at any percentile or the percentile rank of a value. For inference, the confidence interval calculator builds z, t and proportion intervals, the sample size calculator works backward from a target margin of error, and the linear regression calculator fits a line of best fit with r and r². The probability calculator covers the and, or and conditional rules for two events and repeated tries, the permutation and combination calculator counts selections and arrangements, the expected value calculator finds the mean and standard deviation of a probability distribution, and the random number generator draws fair whole numbers or decimals in your browser, with or without repeats.
The methods follow open college textbooks from OpenStax, such as Prealgebra 2e, Algebra and Trigonometry 2e and Introductory Statistics 2e, which are linked on each page along with the worked examples the calculators reproduce.
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