Math & Statistics
These tools show the steps, not just the answer, because the reason to use a percentage calculator is usually to check your own arithmetic rather than to avoid doing it. Nothing here depends on where you are, so the answer is the same in every region.
Percentage
Percentage CalculatorWhat one number is as a percentage of another, and what that percentage of a number comes to. The plainest arithmetic on the site, done with the working shown.Percentage Increase CalculatorIncrease a number by a percentage. Note that reversing this needs division, not subtraction. The reverse-percentage calculator handles that.Percentage Decrease CalculatorDecrease a number by a percentage, with the amount removed shown separately.Percentage Change CalculatorPercentage change between two values, in either direction, with the absolute change shown alongside. Handles a negative starting value, which most calculators get wrong.Percentage Difference CalculatorPercentage difference and percentage change, which are different measures constantly used interchangeably. Difference is symmetric; change depends on which value you started from.Percent of a Number CalculatorA percentage of a number, with the increase and decrease shown alongside. Finding a percentage and adding one are different questions and the page answers both.What Percent of X is Y CalculatorWhat percentage one number is of another. The most common percentage question and the one phrased most awkwardly.Reverse Percentage CalculatorWork backwards from a value that has already had a percentage applied. Division, not subtraction. Taking 12% off 1120 gives 985.60, but the original was 1000.
Fractions
Fraction CalculatorAdd, subtract, multiply or divide two fractions, with the result simplified. Division inverts the second fraction, which is the step that turns a hard operation into an easy one.Fraction to Decimal CalculatorA fraction as a decimal and a percentage, with whether the decimal terminates. Once reduced, only denominators built from twos and fives terminate in base ten.Decimal to Fraction CalculatorA decimal as its simplest fraction. Terminating decimals convert exactly; anything else gets the best rational approximation within the denominator you allow.Mixed Number CalculatorA mixed number as an improper fraction and a decimal. The conversion is one multiplication and one addition, and getting the sign right on a negative whole part is where it goes wrong.Simplify Fraction CalculatorA fraction reduced to lowest terms, with the mixed number, the decimal and the percentage, and an optional second fraction to add. Dividing by the greatest common divisor reaches the answer in one step, where cancelling common factors by eye usually takes several and often stops early.
Ratio
Ratio CalculatorSimplify a ratio, express it as a decimal and as percentages of the whole, and scale it to any figure. Whole-number inputs simplify exactly; decimals are handled by scaling first.Ratio SimplifierA ratio reduced to its simplest whole-number form, with the option to scale it or to divide a total in its proportions. Works on any number of parts, since a three-way split is where reducing by eye starts to go wrong.Proportion SolverSolve a proportion for its missing fourth term by cross-multiplication. The check is built in: both cross products must be equal, and they are shown.
Statistics
Average / Mean CalculatorMean, median and mode together with the spread, because which average is right depends on the shape of the data. One extreme value moves the mean and leaves the median where it was.Weighted Average CalculatorWeighted average with each item's contribution, and what a remaining item needs to score to hit a target. The gap against the simple average shows how much the weighting is doing.Median CalculatorThe median with the full summary alongside. The median resists outliers where the mean does not, which is why incomes and house prices are reported as medians and averages of them mislead.Mode CalculatorThe mode alongside the mean and median. Comparing all three is the fastest read on whether a distribution is skewed, and the mode is the only one that works on categories.Range and IQR CalculatorRange, quartiles and the interquartile range, with outliers flagged by the standard 1.5 rule. The IQR ignores the extremes entirely, which is exactly why it is more useful than the range.Standard Deviation CalculatorStandard deviation on both conventions, with the coefficient of variation that makes it comparable across datasets. A deviation of 5 means nothing until you know whether the mean is 10 or 10,000.Variance CalculatorVariance and standard deviation on both conventions. Dividing by n-1 rather than n is Bessel correction, and on small samples the two answers differ substantially.Z-Score CalculatorZ-score with the percentile and two-tailed p-value it implies, using the normal CDF.Confidence Interval CalculatorA confidence interval for a mean or a proportion. A 95 percent interval does not mean there is a 95 percent chance the true value sits inside this one: it means intervals built this way contain the true value 95 percent of the time.Sample Size CalculatorSample size for a survey, with the finite population correction. Precision costs quadratically: halving the margin of error needs four times the sample, which is why national polls stop at around a thousand.Correlation Coefficient CalculatorPearson correlation between two variables, with R squared and a caution about sample size. Correlation measures straight-line association only, and a strong curved relationship can show r near zero.Linear Regression CalculatorLeast-squares line of best fit, with R squared and a prediction. The line always passes through the mean of both variables, which is a useful check on any regression.
Probability
Permutation CalculatorPermutations, with the matching combination count shown so the difference between "order matters" and "order does not" is visible rather than assumed.Combination CalculatorCombinations, the binomial coefficient. Computed through log-gamma rather than raw factorials, so it stays exact well past where n! overflows.Factorial CalculatorFactorials up to 170, which is where a double-precision float stops being able to hold the answer.
Algebra
Exponent CalculatorA base raised to any power, including negative and fractional exponents, with the result in scientific notation when it runs long. A negative exponent is a reciprocal, not a negative number.Square Root CalculatorThe square root of a number, with the negative root shown alongside because both satisfy the equation. A negative input has no real square root and this says so rather than returning nothing.Cube Root and Nth Root CalculatorAny root of a number, computed as a fractional power. Odd roots of negative numbers are real and are handled; even roots of negatives are not.Logarithm CalculatorA logarithm in any base, computed through the change-of-base identity. A logarithm answers "what power do I raise this base to", which is the sentence that makes the whole idea click.Antilog CalculatorThe inverse of a logarithm: given the log, recover the number. Useful for reading log-scale data such as pH, decibels or seismic magnitudes back into ordinary units.Quadratic Equation SolverA quadratic solved with the discriminant, the vertex and both roots, including complex ones. A negative discriminant is a conjugate pair rather than an error, and reporting it as no solution is simply wrong.Linear Equation SolverA linear equation of the form ax plus b equals c, solved with the substitution shown as a check. The two degenerate cases, no solution and infinitely many, are named rather than hidden behind a division by zero.Polynomial CalculatorEvaluate a polynomial and its derivative at a point, with any integer roots found by search. Evaluation uses Horner, which needs far fewer multiplications and loses less precision than raising powers.
Number Theory
GCD / HCF CalculatorGreatest common divisor and lowest common multiple of any list of integers, by the Euclidean algorithm.LCM CalculatorLowest common multiple of a list of integers, computed through the GCD rather than by enumerating multiples.Prime Number CheckerWhether a number is prime, and if not, its smallest factor. Trial division only up to the square root, which is all that is ever needed.Prime Factorization CalculatorThe prime factorization of a number, with the divisor count computed from the exponents rather than by trial division. Comparing two factorizations shows their common factors, which is where the GCD and LCM both come from.Number Base ConverterWhole numbers converted between binary, octal, decimal, hexadecimal and base 36, with the bit width and an optional zero padding. Hexadecimal exists because one hex digit is exactly four bits, which is why memory addresses are written in it and not in decimal.Modulo CalculatorThe modulo of two integers under both conventions, because they disagree on negative numbers and the disagreement causes real bugs. Minus seventeen mod five is three in Python and minus two in C, and both are defensible.
Geometry
Area CalculatorArea and perimeter for the common plane figures. A triangle given three sides is checked against the triangle inequality first, because three lengths that cannot close have no area.Perimeter CalculatorPerimeter and the area it encloses. For a fixed perimeter a circle encloses the most area of any shape, which is why the ratio is shown.Circle CalculatorEvery circle property from any one of four measurements, including sector, arc and segment. The circumference is exactly the derivative of the area with respect to radius, which is why growing a circle by a thin ring adds area equal to the circumference times the thickness.Triangle CalculatorEvery property of a triangle from its three sides. Three sides fix a triangle completely, so the angles, heights and both circle radii follow without further measurement, and any two sides must exceed the third or no triangle exists.Pythagorean Theorem CalculatorThe missing side of a right triangle, whichever one it is, with the angles and area that follow. The 3-4-5 form is how a corner gets squared on site without a set square, and the page checks whether a measured corner is true.Rectangle and Square CalculatorEvery measurement of a rectangle from its two sides, including the diagonal and the simplified aspect ratio. The diagonal is Pythagoras, which is why a 16:9 screen is measured across the corner.Trapezoid CalculatorTrapezoid area from the two parallel sides and the height. The area is the median times the height, which is the same rule as a rectangle with the average width.Polygon CalculatorRegular polygon area, angles and radii. As the side count rises the shape approaches a circle, which the apothem and circumradius converging makes visible.Ellipse CalculatorEllipse area, perimeter and eccentricity. The area is exact and simple; the perimeter has no closed form at all, which is a genuinely surprising fact about a shape this ordinary.Volume CalculatorVolume of the common solids, in cubic metres, litres, cubic feet and gallons. All volumes scale with the cube of a linear dimension, so doubling any one measurement of a box doubles the volume but doubling all three multiplies it by eight.Surface Area CalculatorSurface area of the common solids, with paint quantity. Area scales with the square of a dimension while volume scales with the cube, which is why a larger container needs proportionally less material.Sphere CalculatorSphere properties from any one of five measurements. The surface area is the derivative of the volume with respect to radius, which is why growing a sphere by a thin shell adds volume equal to the area times the thickness.Cylinder CalculatorCylinder volume and area, with partial fill. A vertical cylinder is the one common shape that fills linearly, so half the height really is half the volume, which is not true of a horizontal tank or a cone.Cone CalculatorCone volume and surface, including truncated cones. The curved surface uses the slant height rather than the vertical height, which is the mistake that makes a paper cone come out too small.Pyramid CalculatorPyramid volume and surface for a rectangular base. A pyramid holds exactly one third of the prism enclosing it, and the face slant and edge slant are different lengths that are easy to confuse.Angle ConverterAngles across degrees, radians, gradians and arcseconds. Radians are the natural unit because they make the trigonometric derivatives come out clean, which is why every programming language expects them.Arc Length and Sector Area CalculatorArc length, sector area, chord and segment from a radius and an angle. The formulas are trivial in radians and awkward in degrees, which is the whole argument for radians.Golden Ratio CalculatorGolden ratio divisions from any one known dimension. Phi is the only number whose reciprocal is itself minus one, which is what makes the proportion self-similar.Scale Factor CalculatorScale factor with its area and volume consequences. Doubling a length quadruples the area and multiplies volume by eight, which is why scaling a recipe or a structure is never proportional.
More
Scientific Notation ConverterA number in scientific and engineering notation. Engineering notation keeps the exponent a multiple of three so it lines up with the metric prefixes, which is why instruments use it.Rounding CalculatorRounding under all four common rules at once, because they disagree on exactly the values people check. The difference only shows up on a tie, and a column of ties is where a total drifts.Significant Figures CalculatorHow many significant figures a number carries, and rounding to a chosen count. Trailing zeros are the whole difficulty: 1200 has two, and 1200.0 has five.Arithmetic & Geometric Progression CalculatorArithmetic and geometric progressions: the nth term and the running sum. The difference between adding and multiplying each step is the difference between linear and exponential, which is most of what the topic is for.Summation (Sigma) CalculatorSummation over a range for the standard expressions, with the closed form shown where one exists. Gauss got the first of these at seven years old and it still saves the loop.Long Division CalculatorWhole-number division with the remainder and the identity that checks it. The division algorithm guarantees exactly one quotient and remainder for any pair, and this shows both.Number to Words ConverterA number written out in words, in either the Indian lakh and crore system or the international million and billion one. The two group digits differently, three-two-two against three-three-three, which is why a number that is one crore twenty-three lakh is also twelve point three million.Roman Numeral ConverterRoman numerals in both directions, using the six standard subtractive pairs and the conventional 1–3999 range.