Advanced Math Operations

Convert between adjacency matrix, edge list, and adjacency list using MiniWebtool’s Adjacency Matrix Calculator. It auto-detects directed/undirected graphs and computes degree sequence, density, connected components, and matrix powers, with an interactive SVG graph visualization.

Reverse a logarithm by raising its base to the given exponent. MiniWebtool’s Antilog Calculator supports base 10, e, 2, or a custom base, with worked steps and comparisons.

MiniWebtool’s Beta Function Calculator evaluates B(x, y) for positive real inputs. Its worked calculation connects the beta function to gamma functions, with adjustable precision and a visualization of the function.

MiniWebtool’s Binomial Coefficient Calculator evaluates n choose k: the number of selections when order does not matter. Enter n and k to see the factorial calculation and its position in Pascal’s triangle.

Find the chance of a given success count with MiniWebtool’s Binomial Probability Distribution Calculator. Set trial count, a constant success probability, and k to inspect exact and cumulative probabilities for independent binomial trials.

MiniWebtool’s Bitwise Calculator shows integer operations one bit at a time. Choose an operation and bit width to inspect how AND, OR, XOR, or a shift changes the binary representation.

Simplify Boolean expressions with algebraic laws, Quine-McCluskey and Karnaugh maps using MiniWebtool’s Boolean Algebra Simplifier. Enter any AND, OR, NOT, XOR, NAND or NOR expression to get the minimal SOP/POS form, truth table, K-map, gate diagram and NAND-only equivalents.

MiniWebtool’s Central Limit Theorem Calculator uses a normal approximation for the sampling distribution of a mean. Population mean, standard deviation, sample size, and bounds determine the approximate probabilities and standard error.

Solve simultaneous modular conditions in MiniWebtool’s Chinese Remainder Theorem Calculator. Enter the congruences to see how their residue classes align, with a step-by-step derivation of the resulting solution.

MiniWebtool’s Combination Calculator counts ways to choose k items from n when order is irrelevant. Enter the two values to see C(n, k), its factorial calculation, and a Pascal’s triangle visualization.

MiniWebtool’s Complementary Error Function Calculator evaluates erfc(x), the complement of the error function. Choose decimal precision to inspect the numerical value, curve, worked explanation, and reference values for comparison.

Add, subtract, multiply, divide, convert forms, and calculate modulus, argument, conjugate, powers and roots with MiniWebtool’s Complex Number Calculator. Get detailed step-by-step solutions and an interactive complex plane visualization.

MiniWebtool’s Continued Fraction Calculator rewrites a decimal, fraction, or square root as nested integer terms. Set a term limit to explore convergents and how the rational approximations approach the input.

Count permutations with no item in its starting position using MiniWebtool’s Derangement (Subfactorial) Calculator. A set size n produces !n, with a derivation and visual explanation of the derangement condition.

Trace shortest paths in a nonnegative weighted graph with MiniWebtool’s Dijkstra's Shortest Path Calculator. Enter edges, choose a starting vertex, and set directed or undirected mode to follow the algorithm visually.

Measure uncertainty in a probability distribution with MiniWebtool’s Entropy Calculator. Enter outcome probabilities and a logarithm base to calculate Shannon entropy, follow each contribution, and visualize how probability concentration affects information.

Evaluate erf, erfc, or their inverse functions in MiniWebtool’s Error Function Calculator. Select a function and value to see the numerical result at your chosen precision, with a curve and explanation of its relationship to probability.

Count the positive integers up to n that are coprime to n in MiniWebtool’s Euler's Totient Function Calculator. Prime factorization and a coprime grid explain the resulting φ(n).

MiniWebtool’s Exponential Decay Calculator connects initial amount, final amount, decay rate, and elapsed time. Select the unknown to solve a constant-rate decay scenario and inspect its formula and declining curve.

Model a quantity changing by a constant proportional rate with MiniWebtool’s Exponential Growth Calculator. Solve for starting value, final value, rate, or time, with growth or decay interpretation and a curve of the scenario.

MiniWebtool’s Exponential Integral Calculator evaluates the special function Ei(x) at a selected input and precision. A worked explanation and interactive graph help inspect this function in mathematical or physical calculations.

Raise a base to a chosen power in MiniWebtool’s Exponents Calculator. Positive, negative, and fractional exponents are supported with adjustable precision and explanations showing how the exponent affects the operation.

MiniWebtool’s Extended Euclidean Algorithm Calculator finds gcd(a, b) and Bézout coefficients satisfying sa + tb = gcd(a, b). Two integers generate a division table, back-substitution, and a modular inverse when one exists.

MiniWebtool’s Factorial Calculator evaluates n!, the product of the positive integers through n, with 0! = 1. Enter a nonnegative integer to inspect the result and its scientific-notation representation.

Evaluate Γ(x) for supported real inputs with MiniWebtool’s Gamma Function Calculator. Step-by-step explanations, a graph, and factorial comparisons illustrate how the gamma function extends factorials beyond whole numbers; non-positive integers are poles rather than finite values.

Work out proportional lengths from the golden ratio, approximately 1.618, using MiniWebtool’s Golden Ratio Calculator. Start with the whole length or either segment to find the matching dimensions and examine a golden rectangle.

Assign colors to graph vertices so adjacent vertices differ. MiniWebtool’s Graph Coloring Calculator accepts an edge list or adjacency list, returns a coloring and chromatic-number result, and illustrates the DSATUR process alongside the graph.

Could these vertex degrees belong to a simple undirected graph? MiniWebtool’s Graph Degree Sequence Validator applies the Havel-Hakimi algorithm, displays its reductions, and supplies a sample graph and adjacency matrix when the sequence is graphical.

Explore finite cyclic, dihedral, and symmetric groups with MiniWebtool’s Group Theory Order Calculator. It calculates element orders, checks cyclic and abelian properties, and visualizes the Cayley table and subgroup relationships.

Solve an exponential-decay problem for half-life, starting quantity, remaining quantity, or elapsed time. MiniWebtool’s Half Life Calculator supplies formula steps and a decay curve, with isotope presets for exploring the constant-half-life model.

Can a route visit every vertex exactly once? MiniWebtool’s Hamiltonian Path Checker searches graphs of up to 20 vertices for a Hamiltonian path or cycle and shows a witness route when found. Difficult cases may exceed the search time budget.

Avoid double-counting overlaps when combining sets. MiniWebtool’s Inclusion-Exclusion Calculator accepts elements or intersection sizes for up to five sets and shows the signed expansion, union size, and regions in a Venn diagram.

Simplify a Boolean function visually using MiniWebtool’s Karnaugh Map (K-Map) Solver. Enter minterms, maxterms, or truth-table values to obtain grouped cells and a simplified sum-of-products or product-of-sums expression with worked steps.

Solve linear programming problems with the simplex method in MiniWebtool’s Linear Programming Solver. It supports maximize or minimize objectives, mixed constraints and up to eight decision variables; for two-variable problems, it plots the feasible region with the optimum marked.

MiniWebtool’s Markov Chain Steady State Calculator analyzes a transition matrix for a stationary distribution. A state diagram, solution steps, and power-iteration visualization help you examine long-run probabilities and convergence behavior.

Connect all vertices with the lowest combined edge weight using MiniWebtool’s Minimum Spanning Tree Calculator. Graphs of up to 50 nodes and 200 edges can be explored through Kruskal’s or Prim’s algorithm with visual steps.

Calculate a large power’s remainder without expanding the whole number. MiniWebtool’s Modular Exponentiation Calculator evaluates a^b mod n and shows the binary square-and-multiply steps behind the result.

MiniWebtool’s Modular Multiplicative Inverse Calculator looks for x such that ax ≡ 1 modulo m. The Extended Euclidean Algorithm explains the calculation and reveals when no inverse exists because a and m are not coprime.

Count the attempts needed to reach several successes with MiniWebtool’s Negative Binomial Distribution Calculator. A fixed per-trial success probability produces point and cumulative probabilities, counting either total trials or failures before the target success.

MiniWebtool’s Network Flow Calculator (Max Flow) finds source-to-sink flow in a directed capacitated network. Edmonds-Karp augmenting paths, residual capacities, and the final minimum cut show how the maximum is established.

MiniWebtool’s Percent Growth Rate Calculator compares simple growth, CAGR, and average-rate approaches. Beginning and ending values and time assumptions produce worked results and visualizations that distinguish one-period change from compounded growth.

Calculate permutations P(n,r) with MiniWebtool’s Permutation Calculator to find how many ways to arrange r items from n total items where order matters. Follow step-by-step solutions, visual explanations, a formula breakdown and practical examples.

Calculate permutations with repetition—ordered arrangements with replacement—using n^r in MiniWebtool’s Permutations with Repetition Calculator. Enter the number of items and positions for the result, worked steps, slot-machine visuals and examples from passwords, PINs and licence plates.

Show why a shared container is unavoidable with MiniWebtool’s Pigeonhole Principle Calculator. Item and container counts determine the minimum guaranteed occupancy, with a visualization and step-by-step argument explaining the bound.

Check whether a graph is planar—drawable without edge crossings—using Kuratowski’s theorem with MiniWebtool’s Planar Graph Checker. It detects K5 and K3,3 subdivisions, verifies Euler’s inequality and highlights the forbidden minor when the graph is non-planar.

MiniWebtool’s Poisson Distribution Calculator models event counts from a specified average rate. It calculates a selected count’s probability and cumulative probabilities, with PMF and CDF charts explaining the distribution.

Solve polynomial equations through degree four using MiniWebtool’s Polynomial Roots Calculator. Worked solutions and a graph help you inspect linear, quadratic, cubic, and quartic roots and their relationship to the polynomial.

Explore multiplicative cycles modulo an integer with MiniWebtool’s Primitive Root Calculator. It finds primitive roots when they exist, reports Euler’s totient, and uses power tables and cyclic-group diagrams to explain the generated residues.

Explore relationships between events in MiniWebtool’s Probability Calculator. Enter the probabilities required for the selected calculation to work through intersections, unions, conditional probability, or Bayes’ theorem with diagrams and formula steps.

Choose a probability model in MiniWebtool’s Probability Distribution Calculator to find probabilities, cumulative values, or quantiles. Supported continuous and discrete distributions include Normal, Binomial, Poisson, Exponential, Uniform, Chi-square, and Student’s t, with visual explanations.

Solve a missing term in a/b = c/d using MiniWebtool’s Proportion Calculator. Cross-multiplication steps and a visual diagram explain how the known quantities determine the remaining value.

Follow the quadratic formula from coefficients to roots in MiniWebtool’s Quadratic Formula Calculator. Discriminant analysis explains the root type, while vertex-form conversion and a parabola graph show the equation’s related geometry.

Compute in modular rings and finite fields with MiniWebtool’s Ring and Field Calculator. Explore operations, inverses, powers, and Cayley tables, and distinguish units from zero divisors in the selected algebraic structure.

MiniWebtool’s Rounding Calculator rounds to decimal places, significant figures, or a chosen increment. Compare six rounding methods with a number line and steps that explain why their answers can differ.

MiniWebtool’s Scientific Calculator handles arithmetic alongside trigonometric, logarithmic, exponential, and factorial functions. Choose degrees or radians, use memory and calculation history, and enter expressions with the keyboard.

Work with very large or small values in MiniWebtool’s Scientific Notation Calculator. Convert notation, perform arithmetic, or compare numbers, with significant-figure settings and steps explaining the normalized result.

MiniWebtool’s Set Theory Calculator performs operations on entered sets, including union, intersection, differences, Cartesian products, and power sets. Supply a universal set when calculating complements and use Venn diagrams to inspect relationships.

Round numbers to significant figures, count sig figs with digit-by-digit analysis, and perform arithmetic with proper significant figure rules in MiniWebtool’s Significant Figures Calculator.

MiniWebtool’s Stable Marriage Problem Solver applies Gale–Shapley to ranked preferences for two equal-sized groups. Choose the proposing side and inspect proposals and blocking-pair checks to understand the stable matching returned.

MiniWebtool’s Stirling Numbers Calculator evaluates unsigned first-kind cycle counts and second-kind set partitions. Enter n and k to follow the recurrence and explore the corresponding number triangle.

Explore sums of cubes with MiniWebtool’s Sum of Cubes Calculator. Use consecutive ranges or a supplied number list and review formula steps with a visual representation of the cube totals.

MiniWebtool’s Sum of Positive Integers Calculator adds a consecutive positive-integer range using Gauss-style summation. Pairing diagrams show how the endpoints combine to make the calculation shorter.

MiniWebtool’s Sum of Squares Calculator totals squared values from a sequence, range, or custom data. See formula steps and geometric views that explain how the sum is assembled.

Enter a directed graph into MiniWebtool’s Topological Sort Calculator to get a topological order with Kahn's algorithm or DFS, or the cycle path if the graph is not acyclic.

Find a round-trip route with MiniWebtool’s Traveling Salesman Solver (TSP). Coordinates or a distance matrix support exact Held–Karp solutions up to twelve cities or heuristic 2-opt searches up to forty.

Build a Boolean truth table with MiniWebtool’s Truth Table Generator. Enter an expression using up to eight variables, A through H, with logical operators such as AND, OR, XOR, negation, and conditionals.

Show three-set relationships with MiniWebtool’s Venn Diagram Generator (3 Sets). Enter elements or region counts, customize labels and colors, and export the diagram as PNG or SVG.