Multiplication
Multiply two or more numbers instantly. Enter the count of numbers and their values — whole numbers, decimals or negatives — and get the product with a step-by-step example.
Mathematics Calculators: Algebra, Fractions and Matrices
Use these mathematics calculators to solve everyday arithmetic and more complex problems in algebra, fractions, percentages, matrices and vectors. The Fraction Calculator handles fraction operations, while the Percentage Calculator helps with common percentage questions. For equations, try the Quadratic Equation or Cubic Equation calculator.You can also explore the Matrix Multiplication calculator, find averages with the Weighted Mean calculator, or work through number theory with the Chinese Remainder Theorem calculator. Whether you are checking homework, preparing a lesson or using math at work, these tools help you calculate results and compare approaches.
Arithmetic 39
Addition
Add two or more numbers quickly and accurately. Enter how many values you want to sum, type them in, and the calculator instantly shows the total.
Square Root
Enter any number — integer, decimal or fraction — and this square root calculator gives the decimal value, checks whether it is a perfect square, and shows the simplified radical step by step using prime factorization.
Division
Divide two or more numbers instantly. Enter the dividend and divisor (or a whole chain of numbers) and the calculator performs the division step by step, left to right, and shows the exact quotient.
Subtraction
Subtract any quantity of numbers in sequence and get the exact difference instantly. Enter how many values you want to use, type the numbers, and the calculator subtracts each one from the running total.
Big Number
Performs exact arithmetic on very large numbers: add, subtract, multiply, divide, powers, factorials, square roots, GCD and LCM with up to 1,000 digits per number and no floating-point rounding. Choose an operation, enter two numbers, and get every digit.
Scientific Notation
Convert any decimal number into scientific notation (a × 10ⁿ) or expand scientific notation back into a plain decimal. Enter a value and get the coefficient, exponent and full explanation.
Team Work Time
Find how long a task takes when two people work on it together. Enter the time each person needs to finish the job alone, and the calculator returns the combined completion time.
Modular Exponentiation
Computes b^e mod m instantly, even when the power has hundreds of digits, using fast square-and-multiply exponentiation. Enter a base, a non-negative exponent and a positive modulus, and optionally see every repeated-squaring step.
Sum of Consecutive Cubes
Calculate the sum of the first n consecutive cubes instantly. Enter the number of terms and get the result using the closed-form formula (n(n+1)/2)^2, with a worked example and explanation.
Factors
Enter any whole number up to 10¹² and instantly get all of its factors, the number and sum of divisors, the prime factorization, factor pairs, and whether it is prime, perfect, abundant or deficient — or compare 2–5 numbers to find their common factors and GCF.
Euler’s Theorem
Apply Euler’s Theorem online: enter a base a and a modulus n (coprime), and the calculator computes Euler’s totient φ(n) and a^φ(n) mod n, which always equals 1 when the theorem’s conditions hold.
LCM
Find the least common multiple and greatest common divisor of 2 to 10 positive integers. Enter numbers separated by commas or spaces to see their prime factorizations and the steps behind the LCM.
Factorial
Calculate the exact factorial n! of any nonnegative integer up to 10000, with every digit shown, plus the digit count, trailing zeros and scientific notation.
Floor Division
This floor division calculator divides two numbers and rounds the result down to the nearest whole number. Enter a dividend and a non-zero divisor to get the floored quotient, useful in programming, pagination, and integer math.
Sum of Consecutive Squares
Calculate the sum of the squares of the first n natural numbers: 1² + 2² + ... + n². Enter the number of terms and get the instant result using the formula n(n+1)(2n+1)/6.
GCF
Find the greatest common factor of 2–10 integers, along with their least common multiple, prime factorizations, and Euclidean division steps. Enter numbers separated by commas or spaces.
Digital Root
Find the digital root of any non-negative integer by repeatedly summing its digits until one digit remains. Enter a number and get the result plus every intermediate step.
Magic Square
Generate an n×n magic square for any odd size (3, 5, 7, ...). Enter the size and get a grid where every row, column, and both diagonals sum to the same magic constant.
Stirling’s Factorial Approximation
Estimate the factorial of a large number instantly with Stirling's approximation: enter n and get n! ≈ √(2πn)(n/e)ⁿ in scientific notation. Ideal for statistics, probability, and combinatorics.
Arithmetic Progression
Enter the number of terms, the first term, and the common difference to generate the full arithmetic progression and the sum of its first n terms instantly.
Rounding
Round a number to the nearest thousand, hundred, whole number, decimal place or N significant figures. Seven rounding modes including banker's rounding — results are exact, with no floating-point errors.
Absolute Change
Calculate the absolute change between two values — enter an initial value and a final value to see how much the quantity changed, plus whether it increased or decreased. Works in any unit: numbers, currency, percentages, measurements.
Prime Factorization
Enter any integer from 2 to 1,000,000,000,000 and this calculator instantly finds its prime factorization in exponent form, lists all prime factors, identifies the largest one, and counts the number of divisors.
Average
Calculate the average (arithmetic mean) of two or more numbers. Enter how many values you have and type them in — the result appears instantly.
Summation
Evaluate any sum written in sigma notation: enter an expression f(n), the lower and upper bounds, and get the total, the number of terms and a closed-form check. You can also paste a plain list of numbers to add them up.
Prime Number Checker
Enter any whole number up to one trillion and instantly find out whether it is prime or composite. The calculator also shows the smallest prime factor and the complete prime factorization with an explanation.
Quadratic Mean
Calculate the quadratic mean (root mean square, RMS) of any set of numbers. Enter how many values you have and the values themselves — the calculator squares each one, averages the squares, and takes the square root.
Weighted Mean
Calculate the weighted mean of a dataset where each value has its own weight. Enter your values and weights to get the weighted average instantly — useful for grades, scores, and financial data.
Chinese Remainder Theorem
Solves a system of simultaneous congruences using the Chinese Remainder Theorem. Enter the remainders and pairwise coprime moduli to get the smallest non-negative solution.
Leibniz Harmonic Triangle
Generate the Leibniz Harmonic Triangle for up to 150 rows, with every entry shown as an exact fraction in lowest terms. Just enter the number of rows and read off the values, each computed as (1/k) × C(n,k).
Nth Root
Find the nth root of any real number: enter the number and the root degree (2 for square root, 3 for cube root, or any degree up to 100). The calculator returns the exact decimal value instantly.
Geometric Mean
Calculate the geometric mean of any set of positive numbers. Enter how many values you have, type them in, and get the n-th root of their product instantly — ideal for growth rates, ratios, and returns.
Scientific
Evaluate arithmetic, powers, roots, trigonometric functions, logarithms and factorials. Enter an expression, choose degrees or radians, and press =.
Floyd’s Triangle Sum
Generate Floyd's Triangle up to 500 rows and instantly get the sum of every row plus the total sum of all numbers, using the closed-form row sum formula n(n² + 1)/2.
Harmonic Mean
Enter two or more positive numbers and this calculator returns their harmonic mean — the reciprocal-of-the-average-of-reciprocals, ideal for averaging rates and speeds.
Multiplicative Inverse Modulo
Find the modular multiplicative inverse of a number: enter a value a and a modulus n, and the calculator solves a·x ≡ 1 (mod n) using the Extended Euclidean Algorithm, with a verification of the result.
Fermat’s Little Theorem
Verify Fermat's Little Theorem online: enter a base a and a prime p, and the calculator computes a^(p-1) mod p and checks whether the result equals 1. Useful for number theory, primality testing and cryptography.
Sig Figs
Count the significant figures of any number, round it to N sig figs, or add, subtract, multiply and divide two numbers with the correct sig fig rules applied automatically.
Geometry 37
Circle
Enter one known circle value — radius, diameter, circumference, or area — and instantly get all the other dimensions. Choose your preferred unit and the calculator does the rest.
Trigonometry
Calculate sin, cos and tan of any angle in degrees, radians or gradians — or enter a ratio and find the angle using arcsin, arccos or arctan.
3D Vector Magnitude
Find the length (magnitude) of any 3D vector instantly. Enter the x, y, and z components, and the calculator returns the Euclidean magnitude using the 3D Pythagorean theorem.
Area
Calculate the area of a square, rectangle, triangle, circle, ellipse, trapezoid, regular polygon, ring and more. Pick a shape, enter its dimensions, and get the result in square meters, square feet, acres and hectares.
Angle Bisector
Enter the coefficients of two lines in general form (ax + by + c = 0) and this calculator finds the equations of both angle bisectors — the lines that divide the acute and obtuse angles formed where the lines meet.
Linear Size
Enter an object's angular size in degrees and its distance from the observer, and this Linear Size Calculator returns the object's actual linear size D using D = 2·L·tan(α/2). Useful for astronomy, optics, photography, and surveying.
Angular Size
Enter an object's linear size and its distance from the observer to find its angular size in degrees — the angle the object subtends in your field of view, as used in astronomy, optics, and photography.
Length of the Angle Bisector
Enter the three side lengths of a triangle to find the length of the internal angle bisector — the segment that splits the angle between Side 1 and Side 2 into two equal parts.
Vertex of Quadratic Equation
Find the vertex of a quadratic equation y = ax² + bx + c instantly. Enter the coefficients a, b, and c, and the calculator returns the x and y coordinates of the parabola's turning point.
2D Vector Magnitude
Enter the X and Y components of a two-dimensional vector to instantly find its magnitude (length) using the Pythagorean theorem. The result shows how far the vector extends from the origin.
Distance Perspective Projection
Enter the linear size of an object and its angular size (in degrees) to find the distance at which the object must be placed so it appears under that angle. Uses the perspective projection formula L = D / (2·tan(α/2)).
Arc Length
Enter the radius and the central angle of a circle (in degrees, radians or gradians) and this calculator instantly returns the arc length using s = rθ, with the full calculation shown.
Volume
Volume calculator for 12 common 3D shapes: cube, box, cylinder, cone, sphere, hemisphere, pyramid, prism, capsule, frustum, ellipsoid and tube. Pick a shape, enter its dimensions, and get the volume in cubic units, liters and gallons.
2D Vector Angle
Enter the X and Y components of two vectors to find the angle between them in degrees. The calculator uses the dot product formula and is useful for physics, geometry, and computer graphics.
Cylinder Volume
Calculate the volume, height, or radius of a solid or hollow cylinder. Enter its dimensions or known volume, choose a length unit, and see surface areas and volume conversions.
Cone Volume and Surface Area
Calculate the volume, slant height, lateral area, base area and total surface area of a right circular cone. Enter the radius plus either the height or the slant height.
Surface Area
Calculate the total, lateral and base surface area of a cube, prism, cylinder, cone, sphere, hemisphere, pyramid, capsule or cone frustum. Pick a shape, enter its dimensions and get the area in the unit you choose.
Distance Between Two Points
Enter the coordinates of two points to get the straight-line distance between them, along with Δx, Δy and the midpoint of the segment. Supports meters, centimeters, feet and inches.
Eccentricity of an Ellipse
Enter the semi-major axis (a) and semi-minor axis (b) of an ellipse to find its eccentricity (E) — a number between 0 and 1 that shows how elongated the ellipse is. Widely used in geometry, astronomy, and orbital mechanics.
Midpoint
Find the midpoint of a line segment in 2D or 3D. Enter the coordinates of the two endpoints and get the midpoint plus the segment length instantly.
Right Triangle
Solve a right triangle from two known measurements, including at least one side. Enter side lengths, an acute angle, area, or perimeter to find the remaining measurements.
2D Vector Scalar Product
Enter the X and Y components of two vectors to compute their scalar (dot) product instantly. The result also tells you whether the angle between the vectors is acute, right, or obtuse.
3D Vector Projection
Enter the components of two 3D vectors and this calculator projects one onto the other, showing the scalar projection, vector projection, perpendicular component, dot product, magnitudes, and the angle between the vectors.
2D Vector Addition
Add two 2D vectors by entering their x and y components. The calculator returns the resulting vector's components instantly, ideal for physics, engineering, and math homework.
2D Vector Subtraction
Subtract one 2D vector from another by entering the X and Y components of both vectors. The calculator performs component-wise subtraction and instantly shows the resulting vector's coordinates.
Cylinder Surface Area
Calculate the curved (lateral) surface area, base area, and total surface area of a cylinder from its radius and height. Supports m, cm, mm, ft and in, with step-by-step working shown.
Polygon Interior Angles
Enter the number of sides to find the sum of interior angles of any polygon. For a regular polygon you also get each interior angle and each exterior angle, with steps shown.
Sector Area
Calculate the area of a circular sector from its radius and central angle. Enter the radius, choose units (deg, rad or grad), and get the sector area, arc length, perimeter and fraction of the full circle.
Sphere Volume and Surface Area
Calculate the volume, surface area, and great-circle circumference of a sphere from its radius or diameter. Enter one dimension, choose a unit, and get instant results with steps.
Distance from Point to Line
Enter the coordinates of a point and the coefficients of a line in the form Ax + By + C = 0 to find the shortest (perpendicular) distance between them, with full calculation steps.
Regular Polygon Area
Calculate the area of any regular polygon from its side length, apothem, or circumradius. Enter the number of sides and one known dimension to get the area, perimeter, and angles.
Triangle
Enter any three known values of a triangle — at least one side — and instantly get all three sides, all three angles, area, perimeter, heights, inradius, circumradius, plus a step-by-step solution and a scale drawing.
Pythagorean Theorem
Enter any two sides of a right triangle (legs a and b, or the hypotenuse c) and this calculator instantly finds the missing side, plus the area and perimeter.
3D Vector Scalar Product
Calculate the scalar (dot) product of two 3D vectors instantly. Enter the X, Y and Z components of both vectors and get the result, which tells you how much the vectors align.
Triangle Area
Calculate the area of a triangle from three side lengths (Heron's formula) or from a base and height. Enter your known values, pick a unit, and get the area with step-by-step calculations.
Triangle Inequality Checker
Check whether three side lengths can form a valid triangle. Enter the values for sides a, b, and c, and the calculator applies the Triangle Inequality Theorem to tell you if a triangle is possible.
3D Vector Cross Product
Enter the X, Y and Z components of two vectors to find their cross product instantly. The calculator shows the resulting vector, its magnitude and the full step-by-step calculation.
Algebra 32
Complex Number to Polar Form
Convert a complex number from rectangular form (a + bi) to polar form. Enter the real part a and the imaginary part b, and get the magnitude r and angle θ in degrees, displayed as r ∠ θ° or r(cosθ + i·sinθ).
Discriminant Quadratic Equation
Enter the coefficients a, b and c of a quadratic equation ax² + bx + c = 0 to instantly compute its discriminant Δ = b² − 4ac and find out how many real or complex roots the equation has.
Quartic Equation
Enter the coefficients a, b, c, d and e to solve any quartic equation ax⁴ + bx³ + cx² + dx + e = 0. The calculator finds all four roots, real or complex, using Ferrari's method.
Synthetic Division
Divide a polynomial by a linear divisor x − c or x + c using synthetic division. Enter the polynomial as text or as a list of coefficients and get the quotient, remainder, step-by-step table and root check.
Binomial Coefficient
Calculate the binomial coefficient C(n, k) — the number of ways to choose k items from n without regard to order. Enter n and k and get an instant result with the formula and a worked example.
FOIL
Expand the product of two binomials with the FOIL method (First, Outer, Inner, Last). Enter expressions like x + 2 and x + 3, and get the simplified quadratic result instantly.
Cubic Root
Find the cube root of any real number, including negatives. Enter a number like 8, −64 or 2.5 and get the real cube root, the exact value when possible, and all three (real and complex) cube roots.
Polynomial Long Division
Divide one polynomial by another step by step. Enter the coefficients of the dividend and the divisor (highest power first, including zeros) and get the quotient, the remainder and every division step.
Fibonacci Series
Generate the Fibonacci sequence up to any n-th term and instantly get the sum of all terms. Enter n, and the calculator lists F(0) through F(n) using the recurrence F(n) = F(n-1) + F(n-2).
Slope
Find the slope of the line through two points. Enter the x and y coordinates of both points to get the slope, line type, angle of inclination and the full line equation.
Fourth Root
Enter any non-negative number and instantly find its fourth root — the value that, raised to the fourth power, gives back the original number. Results are rounded to three decimal places.
Bernoulli Inequality
Check Bernoulli's inequality instantly: enter a value of x (x ≥ −1) and an exponent r, and the calculator compares (1 + x)^r with 1 + rx and shows which side is larger.
Modulus of Complex Number
Find the modulus (absolute value) of a complex number z = a + bi instantly. Enter the real and imaginary parts, and the calculator returns |z| = sqrt(a² + b²), the number's magnitude in the complex plane.
Complex Conjugate
Enter the real and imaginary parts of a complex number to instantly find its conjugate (a - bi) and absolute value |a + bi|. Works with negative values and shows the result step by step.
Equation of a Line
Enter the coordinates of two points and instantly get the equation of the line through them in slope-intercept form (y = mx + b) and standard form (Ax + By = C), with the slope and a step-by-step breakdown.
Quadratic Equation
Solve any quadratic equation ax² + bx + c = 0 instantly. Enter the coefficients a, b and c, and the calculator finds both real or complex roots using the quadratic formula and discriminant.
Complex Number
Perform multiplication, division, or square root on complex numbers in the form a + bi. Enter the real and imaginary parts of each number and get the result instantly with both components shown.
Proportion
This proportion calculator finds the missing value in a proportion of the form A/B = C/D. Enter any three known values (A, B, C) and it computes the fourth (D) using cross-multiplication.
Sum of Two Cubes
Instantly compute a³ + b³ for any two numbers. Enter the values of a and b, and the calculator shows each cube and their sum, with the factoring identity a³ + b³ = (a + b)(a² − ab + b²).
Difference of Cubes
Quickly calculate the difference of two cubes A³ − B³. Enter any two numbers and get A³, B³, and their difference, with the identity (A − B)(A² + AB + B²) explained.
Cubic Equation
Enter the coefficients a, b, c and d to solve any cubic equation of the form ax³ + bx² + cx + d = 0. The calculator finds all real roots using Cardano's method and indicates when the remaining roots are complex.
Linear Inequality
This linear inequality calculator shows what happens when you add, subtract, multiply, or divide both sides of an inequality. Enter the operation and three values X, Y, and Z to see the original inequality, the transformation, and the step-by-step result.
Direct Variation
Find the constant of variation k and the direct variation equation y = kx from one pair of x and y values. Enter the values you know and get k, the equation, and the ratio explained.
Complex Root
Find all n roots of any complex number a + bi. Enter the real part, imaginary part, and root degree, and the calculator returns every nth root in rectangular (a + bi) form using De Moivre's theorem.
Logarithm
Calculate the logarithm of any positive number to any base — 2, 10, e (natural log), or a custom base. Enter the number, pick a base, and get the result plus a verification and common, natural, and binary logs for comparison.
Cubic Equation
Solves any cubic equation ax³ + bx² + cx + d = 0 using Cardano's method. Enter the four coefficients and the calculator returns the real roots, flags complex ones, and detects repeated roots.
Geometric Progression
Find the n-th term of a geometric progression instantly. Enter the first term, the common ratio, and the term number, and the calculator returns the value of aₙ using aₙ = a₁ · rⁿ⁻¹.
Elimination Method
Solve a system of two linear equations with the elimination method. Enter the six coefficients a1, b1, c1, a2, b2, c2 and get the values of x and y, or a message when there is no unique solution.
Linear Diophantine Equation
Solves the linear Diophantine equation ax + by = c in integers. Enter the coefficients a, b and c to check whether solutions exist, get one particular solution and the full family x = x₀ + (b/g)t, y = y₀ − (a/g)t.
Descartes’ Rule of Signs
Estimate the number of positive, negative and non-real roots of a polynomial using Descartes' Rule of Signs. Enter the coefficients in descending order of powers to see all possible root counts.
Exponent
Calculate a base raised to an exponent, or find a missing base or exponent. Choose what to solve for, then enter the two known values.
Ratio
Solve a proportion A : B = C : D for any missing term, simplify a ratio with 2–4 parts to its lowest whole-number form, or scale a ratio to a given factor, part value, or total. Enter your values and the result appears instantly.
Fractions 24
Compare Fractions Converter
Compare two fractions instantly and see which is greater, smaller, or whether they are equal. Enter the numerators and denominators as simple fractions or mixed numbers to get the result.
Dividing Fractions
Divide two or more fractions or mixed numbers step by step. Enter numerators and denominators and get a simplified fraction plus its decimal value instantly.
Fraction to Percentage Table
Enter any set of fractions and instantly get a sorted table showing each fraction's decimal value and percentage. Useful as a printable reference chart for students, teachers, and everyday math.
Adding Fractions
Add two or more fractions or mixed numbers with this free calculator. Enter numerators and denominators, and it finds the common denominator, adds the fractions, and simplifies the result.
Convert Ratio to Fraction
Convert any ratio A : B into a simplified fraction and a decimal. Enter the two parts of the ratio and get the reduced fraction instantly, with a step-by-step example.
Mixed Number to Improper Fraction
Convert any mixed number (a whole number with a fraction) into an improper fraction instantly. Enter the whole number, numerator, and denominator — the calculator handles negative values too.
Multiplying Fractions
Multiply two or more simple fractions or mixed numbers and get the answer as a simplified fraction, a mixed number, and a decimal. Enter the numerators and denominators, and the result is calculated instantly.
Simplify Fraction
Enter a numerator and denominator (plus an optional whole number) to reduce any fraction to lowest terms instantly. The tool divides both parts by their greatest common divisor and also shows the decimal value.
Subtracting Fractions
Subtract two or more fractions, simple or mixed, with any denominators. Enter the numerators and denominators and get the simplified result plus its decimal form.
Fraction Calculator
Add, subtract, multiply or divide two simple fractions or mixed numbers. Enter the numerators and denominators, choose an operation, and get the exact result as a reduced fraction, mixed number, and decimal.
Decimal Conversion Table
Convert any list of decimal numbers into simplified fractions, mixed numbers, and percentages in one table. Enter up to any count of decimals and get an instant conversion chart you can use for study or reference.
Convert Percent to Mixed Number
Convert any percentage into a simplified fraction and a mixed number. Enter a value such as 250%, 87.5%, or 33% and get the result instantly, with the whole number and proper fraction shown separately.
Fraction to Ratio
Convert any proper, improper, or mixed fraction into a ratio in simplest form. Enter an optional whole number, the numerator, and the denominator to get the result as A:B plus its decimal value.
Fraction Comparison Chart Generator
Compare up to several fractions at a glance: enter any number of numerators and denominators, and the tool converts each fraction to a decimal and ranks them from smallest to largest in a chart.
Fraction to Decimal
Convert any proper, improper, or mixed fraction to a decimal number instantly. Enter an optional whole number, the numerator, and the denominator to get the decimal result rounded to 6 places.
Percentage into Fraction
Convert any percentage into a simplified fraction in one step. Enter a value such as 75 or 12.5, and the calculator returns the reduced fraction and its decimal equivalent.
Percentage of a Fraction Converter
This tool converts any fraction into its percentage form. It’s perfect for students, teachers, and professionals who need to understand proportions or express values in percent. Just input a fraction, and the calculator returns the exact percentage equivalent.
Improper Fraction to Mixed Number
Convert an improper fraction to a mixed number instantly. Enter the numerator and denominator, and the calculator returns the mixed form plus the decimal equivalent.
Decimal to Fraction
Enter any terminating decimal and this converter instantly returns the simplified fraction, plus its whole and decimal parts. Works with negative numbers and mixed values such as 2.625.
Mixed Numbers
This mixed number calculator adds, subtracts, multiplies and divides mixed numbers such as 1 1/2 and 2 1/3. Enter the whole part, numerator and denominator of each number, and the result appears as a mixed number, an improper fraction and a decimal — with a full step-by-step solution.
Least Common Denominator
Enter two or more denominators and instantly get their least common denominator (LCD) — the smallest number all of them divide into, ideal for adding, subtracting, or comparing fractions.
Mixed Number to Percent
Convert a mixed number into a percent instantly. Enter the whole number, numerator, and denominator, and the calculator returns the decimal value and the equivalent percentage, rounded to two decimal places.
Mixed Numbers Table
Enter any list of mixed numbers and instantly get a conversion table showing each one as an improper fraction, a decimal, and a percentage. Perfect for homework checks, lesson prep, and quick reference.
Mixed Numbers to Percent Table
Convert any list of mixed numbers into a percent conversion table. Enter each whole number, numerator and denominator, and get the improper fraction, decimal and percentage for every value at once.
Matrix 14
Eigenvalues and Eigenvectors 3×3
Enter the nine entries of a 3×3 matrix to find its eigenvalues and eigenvectors, plus the determinant, trace and characteristic polynomial. Includes a worked example you can reproduce with the default values.
Inverse Matrix 3×3
Enter the nine entries of a 3×3 matrix to find its inverse, determinant, and adjugate. The calculator uses the adjugate (cofactor) method and tells you when the matrix is singular.
Matrix Squared
This calculator computes the square of a 2×2 or 3×3 matrix, i.e. the product A × A. Enter the matrix elements and get the resulting squared matrix instantly.
Matrix Multiplication
Multiply two matrices of compatible sizes (up to 3 × 3) instantly. Choose the dimensions of matrix A and B, enter their elements, and get the full product matrix A × B.
Determinant Multiplication
Enter two square matrices (2×2 or 3×3) and instantly get det(A), det(B), and their product. Based on the multiplicative property of determinants: det(AB) = det(A)·det(B).
Rank of 3×3 Matrix
Enter the nine entries of a 3×3 matrix to find its rank instantly. The calculator uses Gaussian elimination and works for any matrix, including singular ones where the determinant is zero.
Eigenvalues and Eigenvectors 2×2
Enter the four elements of a 2×2 matrix to get its eigenvalues and eigenvectors, plus the determinant, trace, and characteristic polynomial with a full worked solution.
Matrix Trace
Enter the entries of a 2 × 2 or 3 × 3 square matrix and instantly get its trace — the sum of the main diagonal elements a₁₁ + a₂₂ (+ a₃₃).
Addition of Two Matrices
Add two matrices of the same size (2×2 or 3×3) by entering their elements. The calculator sums corresponding entries and displays the resulting matrix instantly.
Determinant
Compute the exact determinant of any square matrix from 2×2 to 6×6. Enter your entries as integers, decimals or fractions and get the exact result, a decimal value, singularity check and step-by-step solution.
Sum of Determinants
Enter the entries of two square matrices (2 × 2 or 3 × 3) and this calculator finds each determinant and their sum |A| + |B| instantly, with step-by-step formulas explained.
Matrix Transpose
Enter the entries of a 2 × 2 or 3 × 3 matrix and this calculator instantly swaps its rows and columns to produce the transposed matrix Aᵀ, shown as a table.
Subtraction of Two Matrices
Subtract a 2×2 or 3×3 matrix B from matrix A element by element. Enter the values of both matrices and get the resulting matrix C = A − B instantly, with the formula and a worked example.
Matrix Scalar Multiplication
Multiply a 2 × 2 or 3 × 3 matrix by a scalar (constant). Enter the scalar k and the entries of matrix A to get the resulting matrix kA instantly.
Percentages 9
Percentage Increase
Find the percentage increase between two values. Enter the initial value and the final value, and the calculator shows how much the number grew in percent.
Percentage Decrease
Calculate the percentage decrease from an initial value to a final value. Enter both numbers and instantly find how much a price, quantity, or measurement dropped in percent.
Relative Percentage Difference
Enter two numbers to find their relative percentage difference (RPD): the absolute difference divided by the average of the values, expressed as a percent. Useful for comparing duplicate measurements, lab samples, and two equally valid values.
Percentage Calculator
Solve the three most common percentage problems in one tool: find X% of Y, work out what percent X is of Y, and find the number that X is Y% of. Just pick a calculation type and enter your values.
Average Percentage
Enter two or more percentages and instantly get their average. Choose a simple mean or a weighted average that accounts for sample sizes, making the result accurate even when groups differ in size.
Percentage Difference
Calculate the percentage difference between two values by comparing their absolute difference to their average. Enter Value A and Value B to get a symmetric, direction-neutral measure of how far apart they are.
Percentage Error
Calculate the percentage error between an observed (measured) value and the true (accepted) value. Enter both numbers to instantly quantify the accuracy of your experiment or measurement.
Reverse Percentage
Find the original value before a percentage increase or decrease was applied. Enter the final value, the percentage change, and whether it was an increase or a decrease — the calculator reverses the change to reveal the starting number.
Percentage Change
Calculate the percentage change between an initial and a final value. Enter the original and new numbers to see the increase or decrease as a percentage.
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