Science cluster
Algebra & Calculus Calculators
Solve equations, matrices, polynomials, integrals, derivatives, and transforms, along with number-theory and combinatorics problems.
Top calculators
A short starting set for the most common algebra & calculus calculators workflows.
3×3 Matrix Eigenvalue and Eigenvector Calculator
Enter a real 3×3 matrix to compute its characteristic polynomial, eigenvalues, and a real eigenvector for each real root.
Characteristic Polynomial Calculator for 2×2, 3×3, and 4×4 Matrices
Compute the characteristic polynomial of a small real matrix and see how its coefficients connect to trace, determinant, and eigenvalues.
Lambert W Calculator for Real Branches W0 and W-1
Use this Lambert W calculator to solve w e^w = x on the real branches W0 and W-1 with Newton iteration, derivative output, domain guidance, and worked examples.
Quartic Equation Solver | Find Real and Complex Roots of Fourth-Degree Polynomials
Solve quartic equations of the form ax⁴ + bx³ + cx² + dx + e = 0. Enter coefficients to compute all four real or complex roots with a clear numerical explanation and an optional quartic-themed mini-game.
Bisection Method Calculator for Bracketed Root Finding
Approximate a real root with the bisection method by entering a sign-changing interval, a tolerance, and a maximum iteration count.
Factorial Calculator (n!) — Exact BigInt Results & Digit Count
Compute n! exactly for any non‑negative integer. Includes digit count, worked examples, common values table, and practical limits for very large factorials.
Gauss-Seidel Calculator for 2×2 and 3×3 Linear Systems
Use this Gauss-Seidel calculator to iteratively approximate 2×2 or 3×3 linear-system solutions from a zero initial guess, with residual and last-sweep change.
Gaussian Elimination Calculator for 2×2 and 3×3 Systems
Solve 2×2 or 3×3 linear systems with Gaussian elimination, partial pivoting, and back substitution. Enter coefficients a11 through a33 and constants b1 through b3 to find x, y, and z.
All calculators in this cluster
Browse 35 calculators matched to this topic, or return to the Science category.
2×2 and 3×3 Matrix Cofactor & Adjugate Calculator | Determinant
Find the determinant, signed cofactor matrix, and adjugate of a 2×2 or 3×3 matrix; review minors, transpose placement, and an interactive adjugate practice game.
3×3 LU Decomposition Calculator | Doolittle L and U Factors
Factor a 3×3 matrix into Doolittle lower and upper triangular matrices, with no pivoting, for linear algebra practice.
3×3 Matrix Eigenvalue and Eigenvector Calculator
Enter a real 3×3 matrix to compute its characteristic polynomial, eigenvalues, and a real eigenvector for each real root.
Airy Isostatic Root Depth Calculator for Mountain Crust
Calculate a mountain's compensating crustal root and total crustal thickness from elevation, reference crust, and crust–mantle densities using Airy isostasy.
Arc Length Calculator | Simpson’s Rule Curve Length
Calculate the arc length of y = f(x) over an interval with Simpson’s rule and symbolic differentiation.
Bernoulli Principle Streamline Simulator
Explore Bernoulli's equation with an interactive pipe animation. Adjust pressures, velocities, and elevations; watch energy bars change and download time-series data.
Bisection Method Calculator for Bracketed Root Finding
Approximate a real root with the bisection method by entering a sign-changing interval, a tolerance, and a maximum iteration count.
Characteristic Polynomial Calculator for 2×2, 3×3, and 4×4 Matrices
Compute the characteristic polynomial of a small real matrix and see how its coefficients connect to trace, determinant, and eigenvalues.
Child Height Predictor Calculator | Mid-Parental Adult Height Estimate
Estimate a child’s adult height from the parents’ heights with the mid-parental method. Enter mother and father heights in centimeters or inches, choose the child’s sex, and see a midpoint estimate with a practical range.
Collatz Path Analyzer: Exact Stopping Time and 3n+1 Trajectory
Trace any Collatz (3n+1) trajectory with exact big-integer arithmetic: total stopping time, Terras stopping time, peak excursion, log-scale chart and CSV export.
Completing the Square Calculator | Quadratic Vertex Form and Vertex
Convert ax² + bx + c to a(x − h)² + k with this completing-the-square calculator. Find the vertex coordinates and a four-decimal vertex-form result from your coefficients.
Conjugate Gradient Calculator for Symmetric Positive-Definite Systems
Solve 2×2 and 3×3 symmetric positive-definite linear systems iteratively with this conjugate gradient calculator.
Continued Fraction Convergent Explorer | Rational Approximation Table
Compute continued-fraction convergents for a decimal, fraction, or named constant, inspect rational-approximation errors, and download the convergent table as CSV.
Derangement Counter - Count No-Fixed-Point Permutations
Count derangements for a labeled set, compare !n with n!, and see how no-fixed-point permutations approach 1/e.
Dijkstra Shortest Path Calculator for Weighted Graphs
Use this Dijkstra shortest path calculator to enter a small weighted graph, set start and end nodes, and trace the minimum-cost route with nonnegative edge weights.
Factorial Calculator (n!) — Exact BigInt Results & Digit Count
Compute n! exactly for any non‑negative integer. Includes digit count, worked examples, common values table, and practical limits for very large factorials.
Fraction Simplifier Calculator | Reduce and Combine Fractions Online
Simplify fractions and calculate addition, subtraction, multiplication, or division in your browser. Enter numerators and denominators, then see each result reduced automatically.
Frobenius Norm Calculator for Matrix Magnitude and Difference
Find the Frobenius norm of a matrix or the norm of A-B for two same-size matrices. Enter rows with spaces or commas and see the result instantly.
Gauss-Seidel Calculator for 2×2 and 3×3 Linear Systems
Use this Gauss-Seidel calculator to iteratively approximate 2×2 or 3×3 linear-system solutions from a zero initial guess, with residual and last-sweep change.
Gaussian Elimination Calculator for 2×2 and 3×3 Systems
Solve 2×2 or 3×3 linear systems with Gaussian elimination, partial pivoting, and back substitution. Enter coefficients a11 through a33 and constants b1 through b3 to find x, y, and z.
Hartley Transform Calculator for Real Sequences - Real-Valued DHT Spectrum Tool
Compute the discrete Hartley transform of a real sequence, inspect cas-based coefficients, and compare the real-valued spectrum with the DFT.
Heat Equation Solver | 1D Rod Diffusion with Finite Differences
Solve the one-dimensional heat equation for a rod with fixed end temperatures, then inspect the explicit finite-difference profile, grid spacing, and stability ratio.
Jordan Form Calculator for 2×2 Matrices
Calculate the Jordan canonical form of a 2×2 matrix, identify repeated or distinct eigenvalues, and see whether the matrix is diagonalizable or a single Jordan block.
Kaprekar Routine Analyzer (4–7 Digit Inputs) | Kaprekar Sequence Calculator
Use this Kaprekar routine analyzer to explore digit-rearrangement sequences, inspect iteration tables, understand the classic 6174 fixed point, and experiment with longer starting values.
Kidney Failure Risk Equation (KFRE) Calculator
Estimate a two-year kidney failure risk percentage for chronic kidney disease using age, eGFR, ACR, and sex in the Kidney Failure Risk Equation.
Lambert W Calculator for Real Branches W0 and W-1
Use this Lambert W calculator to solve w e^w = x on the real branches W0 and W-1 with Newton iteration, derivative output, domain guidance, and worked examples.
Linear Diophantine Equation Solver for ax + by = c
Find integer solution families for linear Diophantine equations ax + by = c, test gcd divisibility, and view a particular solution.
Numerical Function Limit Calculator | Left- and Right-Hand Estimate
Estimate a function limit at a chosen point by comparing left-hand and right-hand values with shrinking step sizes. See the estimated limit, the final step size, and how the calculation behaves near holes, jumps, and asymptotes.
PageRank Calculator for Five-Page Link Graphs
Compute PageRank scores for a five-node directed graph. Enter the adjacency matrix and damping factor to see how link structure and teleportation shape the ranking.
Partition Function Calculator for Integer Partitions p(n)
Find p(n), the number of unordered partitions of a non-negative integer, and use this calculator to explore examples, formulas, assumptions, and growth in partition counts.
Quartic Equation Solver | Find Real and Complex Roots of Fourth-Degree Polynomials
Solve quartic equations of the form ax⁴ + bx³ + cx² + dx + e = 0. Enter coefficients to compute all four real or complex roots with a clear numerical explanation and an optional quartic-themed mini-game.
Repeating Decimal to Fraction Converter – Express Infinite Repeats as Rational Numbers
Convert repeating decimals into exact fractions with this simple browser tool for students and teachers.
Self-Similar Fractal Dimension Calculator
Estimate the self-similar fractal dimension from the number of copies N and scaling ratio r, with examples, interpretation, and limitations for ideal fractals.
Thin Lens Equation Calculator with Ray Diagram
Solve 1/f = 1/do + 1/di for image distance, magnification and dioptres. Live ray diagram, unit switching and an object-distance sensitivity sweep.
Walsh-Hadamard Transform Calculator for Normalized Coefficients
Transform a power-of-two sequence into normalized Walsh-Hadamard coefficients, inspect the add-subtract butterfly process, and copy the result for quick comparison.