Mathematics Calculators
Mathematical calculators for algebra, geometry, and calculus
Geometry
Volume CalculatorGeometryFind the volume of a sphere, cube, box, cylinder, cone, pyramid, capsule, spherical cap, frustum, ellipsoid, or tube. Pick a solid, enter its measurements, and get the volume and surface area in any unit.
Triangle Perimeter CalculatorGeometryFind the perimeter of a triangle three ways: from one side of an equilateral triangle, from the equal sides and base of an isosceles triangle, or from the three sides of a scalene triangle. Also gives the area, semi-perimeter, angles, heights, medians, and circles, and estimates a fencing cost.
Triangle Area CalculatorGeometryFind the area of a triangle five ways: from the base and height, from three sides with Heron's formula, from two sides and the angle between them, from one side of an equilateral triangle, or from the base and equal sides of an isosceles one. Also gives the perimeter, angles, heights, medians, and circles.Triangle Area Calculator (3 Sides)GeometryFind the area of a triangle from its three side lengths with Heron's formula, or enter the area with two sides to solve for the third. Also gives the angles, heights, medians, and inscribed and circumscribed circles.
Trapezoid Area CalculatorGeometryFind the area of a trapezoid from its two bases and height, or enter the area to solve for a missing base or the height. Also gives the median, perimeter, legs, base angles, and diagonal.
Trapezoid Perimeter CalculatorGeometryFind the perimeter of a trapezoid from its four sides, from the two bases and one leg of an isosceles trapezoid, or from the two bases and the height of a right trapezoid. Also gives the median, height, area, and base angles, solves for a missing side, and estimates a fencing cost.
Tetrahedron Volume CalculatorGeometryEnter any one of a regular tetrahedron's edge, height, surface area, or volume and get the other three instantly, plus angles, sphere radii, a general-tetrahedron mode, and material weight.
Surface Area CalculatorGeometryFind the surface area of a sphere, cube, box, cylinder, cone, pyramid, capsule, spherical cap, frustum, or ellipsoid. Pick a solid, enter its measurements, and get the surface area and volume in any unit.
Square Perimeter CalculatorGeometryFind the perimeter of a square from the side, area, diagonal, or perimeter, with every other measurement alongside, in any unit.
Square Area CalculatorGeometryEnter any one of a square's side, diagonal, perimeter, or area and get the other three instantly, plus optional border and tiling-cost layers.
Sphere Surface Area CalculatorGeometryEnter any one of a sphere's radius, diameter, surface area, or volume and get the other three instantly, plus optional hollow-shell and coating-cost layers.
Sector Perimeter CalculatorGeometryFind the perimeter of a circular sector from any two of its radius, central angle, arc length, or perimeter, plus the sector's area, chord, and share of the circle.
Sector Area CalculatorGeometryEnter any two of a circular sector's radius, central angle, or area and get the third instantly, plus the arc length, perimeter, chord, segment, and the share of the full circle.
Rhombus Perimeter CalculatorGeometryFind the perimeter of a rhombus from one side, the perimeter, or both diagonals, with the area, angles, and height alongside, in any unit.
Rhombus Area CalculatorGeometryFind the area of a rhombus from its diagonals, from a side and height, or from a side and angle, and get the perimeter, side, height, diagonals, and angles too, with full unit conversion.
Rectangle Perimeter CalculatorGeometryEnter any two of a rectangle's length, width, perimeter, area, or diagonal and get the rest instantly, with the area and corner-to-corner diagonal.
Rectangle Area CalculatorGeometryEnter any two of a rectangle's length, width, area, diagonal, or perimeter and get all the others instantly, with full unit conversion and an optional cost estimate.
Pyramid Surface Area CalculatorGeometryFind the lateral, base, and total surface area of a regular pyramid with a triangle, square, pentagon, hexagon, or octagon base, from any two of its base edge, height, or slant height, plus volume and angles.
Prism Surface Area CalculatorGeometryFind the lateral and total surface area of a triangular, rectangular, square, pentagonal, hexagonal, or octagonal prism, or any prism from its base area and perimeter. Solve in reverse and get the volume too.
Pentagon Perimeter CalculatorGeometryEnter any one of a regular pentagon's side, perimeter, apothem, circumradius, or area and get the other four instantly, plus its golden-ratio diagonal.
Pentagon Area CalculatorGeometryEnter any one of a regular pentagon's side, perimeter, diagonal, height, circumradius, apothem, or area and get all the others instantly, with full unit conversion.
Octagon Perimeter CalculatorGeometryEnter any one of a regular octagon's side, perimeter, apothem, circumradius, or area and get the other four instantly, plus its widths and diagonals.
Octagon Area CalculatorGeometryEnter any one of a regular octagon's side, perimeter, short, medium, or long diagonal, circumradius, apothem, or area and get all the others instantly, with full unit conversion.
Nonagon Perimeter CalculatorGeometryEnter any one of a regular nonagon's side, perimeter, apothem, circumradius, or area and get the other four instantly, plus its three diagonals.
Nonagon Area CalculatorGeometryEnter any one of a regular nonagon's side, perimeter, apothem, circumradius, or area and get all the others instantly, with full unit conversion.
Hexagon Perimeter CalculatorGeometryEnter any one of a regular hexagon's side, perimeter, apothem, circumradius, or area and get the other four instantly, plus the optional diagonals and triangle area.
Hexagon Area CalculatorGeometryEnter any one of a regular hexagon's side, perimeter, long or short diagonal, circumradius, apothem, or area and get all the others instantly, with full unit conversion.
Heptagon Perimeter CalculatorGeometryEnter any one of a regular heptagon's side, perimeter, apothem, circumradius, or area and get the other four instantly, plus its two diagonals.
Heptagon Area CalculatorGeometryEnter any one of a regular heptagon's side, perimeter, apothem, circumradius, or area and get all the others instantly, with full unit conversion.
Hemisphere Surface Area CalculatorGeometryEnter any one of a hemisphere's radius, diameter, total or curved surface area, or volume and get all the others instantly, with full unit conversion.
Ellipse Area CalculatorGeometryFind the area of an ellipse from its semi-major and semi-minor axes with A = pi a b, or solve for a missing axis. Includes the perimeter, eccentricity, focus distance, an equal-area circle, and unit conversion.
Ellipse Perimeter CalculatorGeometryFind the perimeter (circumference) of an ellipse from its semi-major and semi-minor axes using Ramanujan's approximation, and compare five methods against the exact value. Includes area, eccentricity, foci, and unit conversion.
Decagon Perimeter CalculatorGeometryEnter any one of a regular decagon's side, perimeter, apothem, circumradius, or area and get the other four instantly, plus an optional height and width.
Decagon Area CalculatorGeometryEnter any one of a regular decagon's side, perimeter, apothem, circumradius, or area and get all the others instantly, with full unit conversion.
Cylinder Surface Area CalculatorGeometryEnter any two of a cylinder's radius, height, volume, or lateral surface area and get the total and lateral surface area, volume, and more instantly, with full unit conversion.
Cuboid Surface Area CalculatorGeometryFind the surface area of a cuboid (rectangular box) from its length, width, and height, or solve for a missing edge. Also returns the volume, the space diagonal, and a face-by-face breakdown.
Cube Surface Area CalculatorGeometryEnter any one of a cube's edge, total or lateral surface area, volume, or space diagonal and get all the others instantly, with full unit conversion.
Cone Surface Area CalculatorGeometryFind the lateral, base, and total surface area of a cone from any two of its radius, height, or slant height, plus its volume and apex angles.
Circle Perimeter CalculatorGeometryEnter any one of a circle's radius, diameter, perimeter, or area and get the other three instantly, plus an optional sector arc length and sector perimeter.
Circle Area CalculatorGeometryEnter any one of a circle's radius, diameter, circumference, or area and get the other three instantly, plus an optional sector area and arc length.
Bolt Circle CalculatorGeometryWork out a bolt circle diameter from a measured hole spacing, or lay out the X and Y coordinate of every hole from a known PCD. Handles edge to edge measurements, skipped hole chords, start angle, direction and centre offsets.
Board Foot CalculatorGeometryCalculate board feet from thickness, width, length, and quantity, estimate the cost and weight, or scale a log with the Doyle and International rules.
Base of a Triangle CalculatorGeometryFind the base of a triangle from its area and height, or from two equal sides, a right-angle hypotenuse, the perimeter, or a side and two angles. Solve for the area or height too.
Area of a Triangle (SAS) CalculatorGeometryFind the area of a triangle from two sides and the included angle (SAS) with A = 1/2 a b sin(C). Also finds the missing third side, all three angles, the perimeter, heights, medians, and circles.
Area of a Triangle With Coordinates CalculatorGeometryFind the area of a triangle from the coordinates of its three vertices using the shoelace formula. Also returns the perimeter, side lengths, interior angles, and centroid, and checks whether the points are collinear.
Area of an Obtuse Triangle CalculatorGeometryFind the area of an obtuse triangle four ways - from the base and height, three sides, two sides and the angle between them, or two angles and the side between them - and check that the triangle really is obtuse.
Area of an Oblique Triangle CalculatorGeometryFind the area of an oblique (non-right) triangle from two sides and the included angle, two angles and a side, or three sides. Solves the whole triangle with the Law of Sines and the Law of Cosines and reports the perimeter, angles, heights, medians, and circles.
Area CalculatorGeometryFind the area of a square, rectangle, triangle, circle, sector, ellipse, trapezoid, parallelogram, or rhombus. Pick a shape, enter its measurements, and get the area and perimeter in any unit.
Arc Length CalculatorGeometryFind arc length from any two of the central angle, radius, arc length, or sector area, plus the chord, diameter, and major arc.
Angle of a Right Triangle CalculatorGeometryFind the two acute angles of a right triangle from any two parts, or solve the whole triangle, with sides, area, perimeter, altitude, and special-triangle recognition.
Angle of Incidence CalculatorGeometryFind the angle of incidence from the angle of refraction and two refractive indices, and solve Snell's law for any of the four quantities. Adds the law of reflection and grazing angle, the ray deviation, the critical angle and total internal reflection, the speed of light and wavelength in each medium, and Brewster's angle.
Angle Cut CalculatorGeometryFind the angle to cut for a miter joint, a regular polygon frame, or a diagonal knee brace. Enter the corner angle and board widths, the number of sides, or the brace measurements, and get the miter angle and the miter-saw setting for every piece.
Acute Triangle CalculatorGeometryEnter three side lengths to tell whether a triangle is acute, right, or obtuse, and solve it fully: angles, area, perimeter, heights, medians, inradius, and circumradius, in your choice of length and angle units.
Acreage CalculatorGeometryFind the acreage of a plot from its shape, and convert between acres, hectares, square feet, square metres, and more. Rectangle, triangle, trapezoid, four-sided, and circular plots, plus a direct area converter.
ABC Triangle CalculatorGeometryRight-triangle solver: enter any two measurements - two sides, a side and an acute angle, or the area with one side - and it finds the missing sides, both acute angles, the area, perimeter, height to the hypotenuse, circumradius, and inradius, with a built-in Pythagorean-triple check.
AAS Triangle CalculatorGeometrySolve any AAS (angle-angle-side) triangle: enter two angles and one side and get the third angle, all three sides, the area, perimeter, semi-perimeter, heights, circumradius, and inradius - plus a full triangle classification.
AAA Triangle CalculatorGeometryAngle-Angle-Angle triangle calculator: enter two angles to find the third, classify the triangle, and get the exact side ratios. Add one known side and it scales the whole triangle - sides, area, perimeter, heights, and circle radii - in degrees, radians, or gradians.
3D Distance CalculatorGeometryFind the straight-line distance between two points in 3D (or 2D) space, plus the per-axis differences, the distance squared, and the midpoint.Arithmetic
Square Root CalculatorArithmeticFind the principal and negative square roots of any number, check whether it is a perfect square, and simplify the radical with a step-by-step prime-factor breakdown.
Significant Figures CalculatorArithmeticRound a number to significant figures, count the significant figures it carries, round to decimal places, and calculate while keeping the correct significant figures.
Rounding CalculatorArithmeticRound a number to decimal places, significant figures, a place value, a fraction, or a multiple, using any of six rounding methods.
Radical CalculatorArithmeticTake any nth root — square, cube, fourth, and higher — of any number, check whether it is a perfect power, and simplify the radical with a step-by-step prime-factor breakdown.
Proportion CalculatorArithmeticSolve a proportion A / B = C / D for any missing term by cross-multiplication, with step-by-step working, direct and inverse modes, ratio simplification, and scaling.
Perfect Square CalculatorArithmeticCheck whether a number is a perfect square, see its square root and the two nearest perfect squares, or list the first N perfect squares with their sum.
Percentage CalculatorArithmeticCalculate the percentage of a number, percentage change, percentage difference, and percentage of a percentage, and solve for any value you leave blank.
Natural Logarithm CalculatorArithmeticCompute the natural logarithm ln(x) of any positive number, or run it in reverse to find e raised to a power. Shows the common and binary logs, the ln-to-log10 conversion, and a continuous-growth doubling-time layer.
Modulo CalculatorArithmeticCalculate a mod n: the remainder when a is divided by n, with the quotient, the a = n x q + r breakdown, negative-number and remainder conventions, and a modular congruence check.
Logarithm CalculatorArithmeticCalculate logarithms in any base: common (10), natural (e), binary (2), or a custom base. Solve forward or backward from any two values, see the natural, common, and binary logs at once, and explore the logarithm laws.
Log Base 2 CalculatorArithmeticCompute the binary logarithm log base 2 of any number, run it in reverse to find the number, or change the base for a general logarithm. Shows cross-base equivalents, bit width, and the logarithm rules.
Golden Ratio CalculatorArithmeticSplit any length into its golden sections, or check whether two lengths are in the golden ratio phi, about 1.618.
Fraction CalculatorArithmeticAdd, subtract, multiply, or divide two fractions or mixed numbers. See the answer in lowest terms, as a mixed number, as a decimal, and as a percent, with a full step-by-step breakdown.
Fibonacci CalculatorArithmeticFind the nth Fibonacci number, list the Fibonacci sequence with its running sum and golden-ratio drift, or check whether a number is a Fibonacci number and where it sits.
Distance CalculatorArithmeticFind the distance between two points: a 2D or 3D coordinate distance, or the great-circle distance between two places by latitude and longitude.
Digital Root CalculatorArithmeticFind the digital root of any whole number, with the digit sum, additive and multiplicative persistence, digit product, other bases, and step-by-step reduction.
Decimal to Percent CalculatorArithmeticConvert a decimal to a percent and back, with the reduced fraction, per mille and basis-point forms, a part-of-100 chart, and worked steps.
Binary Fraction CalculatorArithmeticConvert binary fractions to decimal and decimals to binary fractions, with a step-by-step place-value expansion, a multiply-by-two ladder, and a precision control for values that never end in binary.
Billion to Trillion CalculatorArithmeticConvert billions to trillions and between every common number scale, with the full number, scientific notation, and a scale-by-scale breakdown.
Baker's Percentage CalculatorArithmeticTurn baker's percentages into ingredient weights and back. Build a full recipe from flour weight and percentages, see dough weight and hydration, and scale to any batch.
Antilog CalculatorArithmeticCalculate the antilog (inverse logarithm) for any base: common (10), natural (e), binary (2), or a custom base. Solve b to the x, recover the exponent, and see the characteristic and mantissa breakdown.
Age Difference CalculatorArithmeticFind the age gap between two people in years, months and days — from their ages, their birth dates, or just their birth years — and see which one is older.
Addition CalculatorArithmeticAdd a list of numbers and get the sum, count and average. Enter whole numbers, decimals or negatives, see the smallest, largest and range, and check the total against a target.
Adding Fractions CalculatorArithmeticAdd and subtract two or three fractions or mixed numbers using the least common denominator. See the answer in lowest terms, as a mixed number, a decimal, and a percent, with a full step-by-step breakdown.
Absence Percentage CalculatorArithmeticWork out absence percentage and attendance percentage from a single total or from a team of people times workdays. See days present and how many days you can miss to hit a target.Statistics
Z-Score CalculatorStatisticsFind the z-score of a value, or solve for the value, mean, or standard deviation from a z-score, and convert any z-score to a percentile and tail probabilities.
Weighted Average CalculatorStatisticsFind the weighted average (weighted mean) of up to eight values and weights, compare it with a plain average, and plan the value you need next to reach a target.
Standard Deviation CalculatorStatisticsFind the sample and population standard deviation of your data set, along with the variance, mean, and a step-by-step breakdown. Enter your values and read the full summary.
Sample Variance CalculatorStatisticsFind the sample and population variance of your data set, along with the standard deviation, mean, and sum of squares. Enter your values and read the full breakdown.
Percentile CalculatorStatisticsFind the value at any percentile of your data set, or the percentile rank of a score, plus the quartiles, median, and interquartile range. Enter your values and read the full summary.
Mean CalculatorStatisticsFind the mean (average) of your data set, along with the median, mode, range, standard deviation, and more. Enter your values and read the full summary.
Expected Value CalculatorStatisticsFind the expected value of a discrete random variable from its outcomes and probabilities, with the variance, standard deviation, and a step-by-step breakdown. Enter probabilities or weights and read the full summary.
Critical Value CalculatorStatisticsFind the critical value for Z, t, chi-square, and F tests at any significance level, for left-tailed, right-tailed, and two-tailed hypothesis tests.
Conditional Probability CalculatorStatisticsFind conditional probability P(A | B) from the joint probability and P(B), solve for any value, check independence, and apply Bayes' theorem with a contingency table and worked examples.
Binomial Expansion CalculatorStatisticsExpand (a + b) to the power n with the binomial theorem: full expansion, a term-by-term table, the evaluated value, the general term, Pascal's triangle, and the coefficient chart.
Binomial Distribution CalculatorStatisticsCompute binomial probabilities (individual and cumulative), the critical value for a target probability, and summary measures such as the mean, variance, standard deviation, mode, median, skewness, and kurtosis, with mass and cumulative plots.
Binomial Coefficient CalculatorStatisticsCompute the binomial coefficient n choose k, C(n, k), with a factorial breakdown, permutations, Pascal's triangle, combinations with repetition, and binomial probability.
Beta Distribution CalculatorStatisticsEvaluate the beta distribution: probabilities, the density and cumulative functions, quantiles, and summary measures such as the mean, variance, mode, median, skewness, and kurtosis, with density and CDF plots.
Benford's Law CalculatorStatisticsLook up the Benford probability of any leading digit, or test a dataset's first-digit counts against Benford's law with a chi-square goodness-of-fit test and the mean absolute deviation.
Bayes' Theorem CalculatorStatisticsUpdate a probability with Bayes' theorem. Enter a prior, a likelihood, and a false-positive rate to get the posterior, or solve for any term of the four-term Bayes' rule.
Average Percentage CalculatorStatisticsFind the average of several percentages, weighted correctly by sample size. Combine up to six values and compare the simple and weighted averages.
Average Deviation CalculatorStatisticsFind the average deviation (mean absolute deviation) of your data set about the mean or the median, with the mean, median, range, a step-by-step breakdown, and related measures.
Altman Z-Score CalculatorStatisticsCalculate the Altman Z-Score for public, private, or non-manufacturing companies to gauge bankruptcy risk, with a full ratio-by-ratio breakdown.
Accuracy CalculatorStatisticsCalculate accuracy three ways: from a confusion matrix, from sensitivity and specificity adjusted for prevalence, or as percent accuracy from percent error.
A/B Test CalculatorStatisticsCheck A/B test significance and plan sample size and duration. Get conversion rates, relative uplift, p-value, confidence intervals, and the visitors each variant needs.
6-Sided Dice Probability CalculatorStatisticsFind the probability of any dice roll: the chance of a sum across several dice, or of a chosen value appearing exactly, at least, or at most a number of times, with the full distribution, odds, and expected value.
Five Number Summary CalculatorStatisticsFind the five-number summary (minimum, Q1, median, Q3, maximum) of your data, plus the IQR, range, and outlier fences. Choose the exclusive or inclusive quartile method.Algebra
Point-Slope Form CalculatorAlgebraBuild the equation of a line from a point and a slope, or from two points. Get point-slope, slope-intercept, and standard form, plus the slope, intercepts, angle, and a graph.
Geometric Sequence CalculatorAlgebraFind the n-th term, the sum of the first n terms, and the infinite sum of a geometric sequence. Enter the first term and common ratio, a ratio and one term, or two terms, with a terms table, a chart, and convergence detection.
Exponential Growth CalculatorAlgebraModel exponential growth or decay: solve for the initial value, rate, time, or final value, and see the growth factor, doubling time or half-life, and a growth curve.
Exponential Equation CalculatorAlgebraSolve an exponential equation for x, the unknown in the exponent. Handles a single exponential term equal to a number and exponentials on both sides, with logarithm steps, a substitute-back check, a graph, and no-solution detection.
Cube Root CalculatorAlgebraFind the cube root of any number, check for perfect cubes, simplify to radical form, and cube or take nth roots.
Cross Product CalculatorAlgebraFind the cross product a x b of two vectors in 2D or 3D, with the magnitude, parallelogram and triangle areas, the angle between the vectors, and the unit normal.
Ceiling Function CalculatorAlgebraTake the ceiling of any number and see it beside the floor, the nearest whole number and the truncation, work out how many whole units cover an amount, evaluate a ceiling step function, and work backwards from a target count.
Arithmetic Sequence CalculatorAlgebraFind the nth term, first term, common difference, number of terms, or sum of an arithmetic sequence. Enter any three values and solve for the rest, with a term chart and a step-by-step table.
Absolute Value CalculatorAlgebraFind the absolute value of a number or an expression, measure the distance between two values, and solve absolute-value equations with the bars on one side or both, with every solution shown.Trigonometry
Trigonometry CalculatorTrigonometryEvaluate sin, cos, tan, cot, sec, and csc of any angle, find an angle from a trig ratio with the inverse functions, or solve a right triangle from any two parts.
Law of Sines CalculatorTrigonometrySolve any triangle with the law of sines: enter two angles and a side (AAS or ASA) or two sides and an opposite angle (SSA) and get every side, angle, the area, perimeter, and both circle radii - with full ambiguous-case detection.
Arctan CalculatorTrigonometryFind the inverse tangent (arctan) of any real number. Read the angle in degrees, radians, gradians, or turns, with the sine, cosine, complementary angle, a four-quadrant atan2 mode, common values, and a graph.
Arcsin CalculatorTrigonometryFind the inverse sine (arcsin) of any value from -1 to 1. Read the angle in degrees, radians, gradians, or turns, with the cosine, the complementary angle, common values, and a graph.
Arccos CalculatorTrigonometryFind the inverse cosine (arccos) of any value from -1 to 1. Read the angle in degrees, radians, gradians, or turns, with the sine, the complementary angle, common values, and a graph.
Angle of Depression CalculatorTrigonometryFind the angle of depression from a vertical drop and horizontal distance, or solve the whole right triangle from any two parts, with slope, roof pitch, and line of sight.
Angle Between Two Vectors CalculatorTrigonometryFind the angle between two vectors in 2D or 3D from their components or from two points, with the dot product, lengths, cosine, sine, and a parallel or perpendicular verdict.