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Free Online Calculators: Algebra, Geometry, Matrix & More

Covering algebra, geometry, trigonometry, matrix, functions, number theory, base conversion, electronics physics, statistics, and personal finance. Fast, mobile-friendly, and completely free.

Algebra Tools 48 tools

Proportion Calculator
Solve a/b=c/x proportions using cross multiplication with clear algebra steps.
Absolute Value Inequality Solver
Solve |ax+b| inequalities with interval notation, boundary cases, and clear derivation.
Algebraic Expression Simplifier
Simplify algebra expressions by combining like terms with clean step-by-step workflow.
E Exponent Calculator
Evaluate e raised to any exponent (eˣ) with calculation logic and exponential basics.
Polynomial Addition and Subtraction Calculator
Add or subtract polynomials by aligning like powers and simplifying coefficients.
Completing the Square Calculator
Convert quadratic expressions from standard form to vertex form with full derivation.
Synthetic Division Calculator
Use synthetic division to divide a polynomial by x-c with quotient and remainder steps.
Exponent Rules Calculator
Apply product, quotient, and power rules to same-base exponent expressions.

Geometry Tools 89 tools

Apothem Calculator
Compute the apothem, circumradius, area, and perimeter of any regular polygon
Heptagon Area Calculator
Calculate regular heptagon area, perimeter, and apothem from side length
Pythagorean Theorem Calculator
Use a²+b²=c² to find the hypotenuse of a right triangle
Radius Calculator
Find circle radius from diameter using r=d/2 with simple steps
Ellipse Circumference Calculator
Approximate ellipse circumference using Ramanujan formula
Triangular Prism Surface Area Calculator
Calculate triangular prism total surface area and volume from base sides and length
Polygon Diagonal Calculator
Count total diagonals and diagonals per vertex for any n-sided polygon
Cylinder Volume Calculator
Calculate cylinder volume and surface area from radius and height using πr²h

Trigonometry Tools 69 tools

Cotangent Calculator
Calculate cot(x) as cosine divided by sine in degrees or radians
Arccos Calculator
Calculate inverse cosine in degrees and radians for values from -1 to 1
Unit Circle Calculator
Find unit circle coordinates from an angle using cos θ and sin θ
Cotangent Graph Calculator
Find vertical stretch, period, phase shift, and midline for a cotangent graph
Cosine Graph Calculator
Find amplitude, period, phase shift, and midline for a cosine graph
Complementary Angle Calculator
Find the angle that adds with a given angle to make 90 degrees
Cosine Calculator
Calculate cos(x) for angles in degrees or radians with unit circle explanation
Secant Graph Calculator
Find vertical stretch, period, phase shift, and midline for a secant graph

Matrix Tools 42 tools

Idempotent Matrix Checker
Verify if A² = A (idempotent matrix) with detailed step-by-step verification
Moore-Penrose Pseudoinverse Calculator
Compute A⁺ (pseudoinverse) using SVD method with detailed step-by-step computation
LU Decomposition Calculator
Compute A = LU where L is lower triangular and U is upper triangular
Schur Decomposition Calculator
Compute A = QUQ⁻¹ with unitary Q and upper triangular U
Orthonormal Basis Generator
Generate orthonormal basis with Gram-Schmidt and normalization for 2D and 3D vectors
Matrix Trace Calculator
Compute trace (sum of diagonal elements) for 2x2 and 3x3 matrices
Matrix Null Space Calculator
Find basis for null space (kernel) of Ax=0 via RREF
Matrix Power Calculator
Compute A^n by repeated matrix multiplication for 2x2 and 3x3 matrices

Function Tools 51 tools

Logarithmic Function Solver
Solve log_a(x)=b and evaluate logarithmic functions
Concave Function Checker
Check if f(x) <= 0 for concavity of common functions
Periodic Function Validator
Check periodicity and find the fundamental period of functions
Function Monotonicity Calculator
Analyze increasing/decreasing behavior and find monotonic intervals
Asymptote Finder
Find vertical and horizontal asymptotes of rational functions
Monotonicity Checker
Determine increasing and decreasing intervals for common function types
Exponential Function Solver
Solve a^x=b and evaluate exponential functions using logarithms
Piecewise Function Solver
Evaluate piecewise-defined functions at any x with branch selection

Number Theory Tools 39 tools

Radical of an Integer Calculator
Calculate rad(n), the product of distinct prime factors of an integer
Prime Number Checker
Test whether a positive integer is prime or composite with step-by-step divisibility checks
Lucky Number Sieve Calculator
Generate and test lucky numbers using the Josephus elimination sieve process
Carmichael Number Checker
Test if a number is a Carmichael (absolute pseudoprime) using Korselt criterion
Prime Counting Function Calculator
Calculate pi(n), the number of primes less than or equal to n, using a sieve method
Square-Free Number Checker
Check whether an integer is square-free using prime factorization
Mersenne Prime Checker
Test if a Mersenne number (2^n-1) is prime using Lucas-Lehmer test
Perfect & Amicable Number Checker
Determine if a number is perfect, amicable, or ordinary

Base Converter 56 tools

Binary Bitwise Calculator
Perform AND, OR, XOR, NOT, left shift, right shift bitwise operations
Base100 Centesimal Converter
Bidirectional conversion between base100 (centesimal) and decimal numbers
Text to Base58 Converter
Convert plain text to base58 encoded strings with step-by-step process
Repeating Radix Fraction Converter
Convert fractions and detect repeating digit sequences with detailed steps
Text to Base32 Converter
Convert plain text to base32 encoded strings with detailed steps
BCD to Decimal Converter
Convert Binary-Coded Decimal (BCD) to decimal
Decimal to Base3 Converter
Convert decimal numbers to ternary (base3) with detailed step-by-step derivation
Base6 Senary Converter
Bidirectional conversion between base6 (senary) and decimal numbers

Electronics & Physics 53 tools

Linear Regulator Power Dissipation Calculator
Compute P=(Vin-Vout)×I and junction temperature with thermal analysis
Power Factor Calculator
Compute PF = cos φ = P/S from real, reactive, and apparent power
Parallel Resistor Calculator
Calculate equivalent resistance for 2 to 5 resistors in parallel
Coulomb Law Calculator
Calculate electric force between two point charges from charge and distance
RLC Quality Factor Q Calculator
Compute Q factor, damping ζ, and bandwidth for resonant circuits
RLC Bandwidth Calculator
Compute Δf = f₀/Q and lower/upper cutoff frequencies f₁ and f₂
RC Time Constant Calculator
Compute τ=RC and charge/discharge percentages with time derivation
Zener Diode Regulator Calculator
Design shunt regulator: compute Rs, Zener current, and power dissipation

Statistics Tools 55 tools

Percentile Calculator
Calculate percentiles using linear interpolation and nearest rank methods
Median Grouped Data Calculator
Calculate median for grouped data using interpolation
Sampling Error Calculator
Calculate sampling error, standard error, and margin of error
Correlation Coefficient Calculator
Calculate Pearson correlation coefficient r between two variables
Normal Distribution Calculator
Compute normal distribution PDF and CDF values
Combination Calculator
Calculate combinations C(n,k) with step-by-step derivation for probability and statistics
Normal Distribution Calculator
Calculate probabilities, z-scores, and percentiles for normal distribution with step-by-step derivation
P Value Calculator
Calculate p-value for z-tests and t-tests to determine statistical significance

Life & Finance 71 tools

Net Profit Margin Calculator
Calculate business net profit margin.
Lump Sum Investment Calculator
Calculate lump sum investment growth.
Price Per Unit Calculator
Compare unit prices between products of different sizes
Workday Business Day Calculator
Calculate business days, add/subtract workdays, and find deadlines
Fixed Deposit Calculator
Calculate maturity amount and interest for fixed deposits
Grocery Budget Calculator
Plan monthly food budget based on household size and income
Currency Exchange Rate Converter
Convert between major world currencies.
Pregnancy Due Date Calculator
Estimate your pregnancy due date and milestones.
Algebra Tools Geometry Tools Trigonometry Tools Matrix Tools Function Tools Number Theory Tools Base Converter Electronics & Physics Statistics Tools Life & Finance

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