Math
Solve percentages, fractions, quadratic equations, ratios, statistics, and matrices with step-by-step breakdowns.
Calculators (36)
Compound Interest Calculator
Model geometric wealth growth, periodic contributions, inflation adjustments, and annual compounding schedules.
Percentage Calculator
Solve percentage increases, decreases, differences, fractions to percents, and reverse percentage calculations.
Fraction Calculator
Add, subtract, multiply, divide, and simplify fractions with step-by-step common denominators and mixed numbers.
Quadratic Equation Solver
Solve second-degree polynomial equations ax² + bx + c = 0 with real and complex roots, vertex, and discriminant analysis.
Scientific Calculator
Evaluate complex arithmetic, trigonometry, logarithms, exponentials, and powers with live formula rendering.
Statistics Calculator
Calculate mean, median, mode, sample variance, standard deviation, quartiles, and IQR for data series.
Probability Calculator
Calculate single and multiple independent event odds, combinations (nCr), permutations (nPr), and risk probabilities.
GPA Calculator
Calculate weighted and unweighted semester and cumulative GPA across standard 4.0 and honors scales.
Ratio Calculator
Simplify, scale, and solve proportions A:B = C:D with part-to-part and part-to-whole conversion breakdowns.
Matrix Calculator
Perform matrix determinant, inverse, multiplication, transpose, and row reduction up to 4x4 dimensions.
Triangle Calculator
Solve sides, angles, area, and perimeter of right and oblique triangles using SOHCAHTOA and the Law of Cosines.
Law of Sines Calculator
Solve oblique triangles with the Sine Rule across AAS, ASA, and the SSA ambiguous case.
Greatest Common Factor Calculator
Find the Greatest Common Factor (GCF / GCD) and Least Common Multiple (LCM) with step-by-step Euclidean division and prime trees.
Exponent Calculator
Calculate powers, negative exponents, fractional roots, and complex numbers with step-by-step exponent laws.
Coefficient of Variation Calculator
Calculate the Coefficient of Variation (CV / RSD) to compare relative dispersion and risk across different scales.
A/B Test Significance Calculator
Evaluate whether conversion differences between control and variant are statistically significant using two-proportion z-tests.
Binomial Distribution Calculator
Compute exact PMF and cumulative CDF binomial probabilities, distribution moments, and discrete histogram projections.
CAGR Calculator
Calculate Compound Annual Growth Rate (CAGR), absolute capital gains, and investment doubling horizons.
Future Value Calculator
Calculate compound future value of initial lump sums and periodic additions across any interest rate.
Population Growth Calculator
Model Malthusian exponential expansion and Verhulst logistic growth with environmental carrying capacity limits.
Area of a Circle Calculator
Calculate circular area, diameter, circumference, radius, and sector slice geometry.
Binary Calculator & Base Converter
Perform binary, octal, decimal, and hexadecimal arithmetic with two's complement signed logic.
Distance Formula Calculator
Calculate 2D and 3D Euclidean distances, radicals, midpoint, and Manhattan metric.
Prime Factorization Calculator
Decompose composite numbers into prime factors, divisors, totient, and aliquot sums.
Law of Cosines Calculator
Solve SAS and SSS oblique triangles, angles, perimeter, and area via Heron's formula.
Least Common Multiple (LCM) Calculator
Calculate the least common multiple and greatest common divisor across multiple integers.
Logarithm Calculator
Evaluate natural (ln), common (log10), binary (log2), and arbitrary custom base logarithms.
Percent Error Calculator
Determine experimental discrepancy, relative error, and percent difference against standard values.
Slope Calculator
Calculate linear slope, angle of inclination, percent grade, and perpendicular line equations.
Box Plot Generator
Generate Tukey box-and-whisker five-number summaries and detect statistical outliers.
Chi-Square Test Calculator
Evaluate contingency table independence, goodness-of-fit, p-values, and Cramér's V effect size.
Confidence Interval Calculator
Calculate confidence intervals for continuous means and proportions with margin of error.
Pearson Correlation Coefficient Calculator
Evaluate bivariate linear association (r), R-squared, t-test significance, and OLS trendline.
Interquartile Range (IQR) Calculator
Determine non-parametric statistical dispersion, quartiles Q1/Q3, and Tukey outlier boundaries.
Sample Size Calculator
Determine required survey sample size, margin of error, and finite population corrections.
Z-Score Calculator
Convert raw scores to standard z-scores, normal percentiles, and psychometric scales.
Guides (32)
Percentage Calculations in Practice: Relative Change, Deltas & Reversals
Master the 5 percentage formulas, mental math hacks, sales tax back-outs, percentage changes, and asymmetric loss recovery.
Fraction Arithmetic: Common Denominators, Mixed Numbers & Simplification
Euclidean algorithm GCD reduction, least common denominator (LCD) methods, mixed number conversions, and fraction division.
Trigonometric & Transcendental Functions: Radian vs. Degree Computing
Master circular trigonometry in degrees and radians, natural and common logarithms, exponential powers, and permutations vs combinations.
Descriptive Statistics: Mean, Median, Variance & Standard Deviation
Arithmetic mean, median, modes, sample vs population standard deviation with Bessel correction, 5-number summaries, and Tukey outlier detection.
Combinatorics and Odds: Permutations, Combinations & Probability Trees
Kolmogorov probability axioms, union and intersection laws for independent events, binomial distributions, and permutations vs combinations.
Calculating High School & College GPA: Credit Hours, Honors & Weighting
Master standard 4.0 quality points, weighted Honors (+0.5) and AP/IB (+1.0) scaling, cumulative transcript blending, and Latin honors classifications.
Ratio & Proportion Math: Scaling Dimensions, Aspect Ratios & Part-to-Part
Euclidean ratio reduction, proportion cross-multiplication equations (A:B = C:D), display aspect ratio resizing, and square-cube scaling laws.
Solving Quadratic Equations: The Quadratic Formula, Discriminant & Vertex
Master the quadratic formula, real and complex discriminant analysis (Δ), parabola vertex (h, k), axis of symmetry, and conic focus/directrix geometry.
Matrix Operations & Linear Algebra: Determinants, Inverses & Transformations
Multiplication dot products, Laplace cofactor determinant expansions, adjugate inversion formulas, matrix transpositions, and Frobenius norms.
Solving Any Triangle: The Laws of Sines, Cosines & Heron's Area
Master SSS, SAS, and ASA triangle solving with the Law of Sines/Cosines, Pythagorean theorem, Heron area formula, and incircle/circumcircle radii.
Analytic Trigonometry of Oblique Triangles: Law of Sines, Ambiguous SSA Cases & Circumradii
Solving AAS, ASA, and ambiguous SSA configurations, circumcircle proofs, and spherical astronomy extensions.
Number Theoretic Foundations of Common Divisors: Euclidean Algorithm & Coprimality
Euclidean division algorithm, prime factorization, Bézout identity, and RSA public-key applications.
Exponential Arithmetic: Power Laws, Fractional Radicals, Negative Indices & Complex Powers
Comprehensive treatment of integer exponents, negative powers, indeterminate forms (0^0), and complex roots.
Relative Statistical Dispersion: The Coefficient of Variation, Risk Ratios & Sample Bias
Normalizing standard deviation across disparate scales, Sokal-Rohlf bias correction, and Sharpe ratio comparisons.
Frequentist Hypothesis Testing in Digital Experimentation: Two-Proportion Z-Scores
Z-test formulations, p-value calculations, statistical power, Type I/II errors, and sample size sizing.
Bernoulli Trials & Discrete Probability: Binomial Distributions, Factorials & Poisson Limits
Derivation of PMF, cumulative distribution functions, log-gamma stable calculations, and normal approximations.
Euclidean Circular Geometry: Archimedean Approximations, Sectors & Segments
Historical quadrature, thin-ring calculus derivations, circular sectors, and engineering tolerance standards.
Digital Logic & Binary Mathematics: Positional Radices, Two's Complement & Bitwise Algebra
Foundations of digital representation, signed two's complement arithmetic, bit shifting, and IEEE 754 floating-point standards.
Cartesian Metrics: Euclidean Distance, Minkowski Norms & Spatial Coordinates
Geometric derivation from Pythagoras, multidimensional vector norms, Manhattan urban grid metrics, and Great-Circle spherical paths.
The Fundamental Theorem of Arithmetic: Prime Factorization, Pollard's Rho & Cryptography
Canonical prime decompositions, divisor functions, aliquot abundance, and computational complexity underlying RSA encryption.
The Law of Cosines: Vector Derivations, Oblique Trigonometry & SSS Triangulation
Dot product proofs, generalizing Pythagoras to obtuse angles, Heron's area formula, and unambiguous triangle solving.
The Least Common Multiple: Number Theory, Multi-Integer Algorithms & Fraction Arithmetic
The duality of LCM and GCD, min/max lattice theory, least common denominators, and mechanical gear resonance.
The Foundations of Logarithms: Napierian Inverses, Change-of-Base & Information Entropy
Napierian history, natural logarithms in continuous calculus, decibels, Richter magnitude, and Shannon information entropy.
Metrology & Error Analysis: Percent Error, Instrumental Uncertainty & Propagation
Systematic calibration vs random noise, error propagation in quadrature, and significant figure tolerances in laboratory assays.
Linear Rate of Change: Cartesian Slopes, Orthogonality & Derivative Foundations
Connecting algebraic rise-over-run to calculus limits, negative reciprocal orthogonality, and civil engineering grade standards.
Exploratory Data Analysis: Tukey Boxplots, Five-Number Summaries & Outlier Fences
Tukey non-parametric order statistics, quartile interpolation conventions, the 1.5 IQR fence rationale, and distribution skewness.
Categorical Data Analysis: Pearson's Chi-Square, Contingency Tables & Residual Modeling
Sum of squared normal variates, contingency independence vs goodness of fit, Cochran's criteria, and Cramér's V effect size.
Inferential Parameter Estimation: Confidence Intervals, Margin of Error & Student's t
Frequentist coverage definitions, Central Limit Theorem square-root scaling, Gosset's t-distribution, and Wilson score intervals.
Bivariate Linear Association: Pearson's r, Anscombe's Quartet & Spurious Correlation
Covariance normalization, Anscombe's quartet visualization imperative, causation fallacies, and OLS regression slopes.
Robust Statistics: The Interquartile Range, Non-Parametric Dispersion & Outlier Fences
Parametric vs non-parametric dispersion, 25% breakdown points, economic net worth modeling, and quartile deviation coefficients.
Survey Metrology: Sample Size Determination, Finite Population Corrections & Power
The economics of sample sizing, the 50% conservative variance ceiling, diminishing returns in polling, and finite population corrections.
The Standard Normal Distribution: Z-Scores, Gaussian Integration & Percentile Scaling
Standardization mechanics, the empirical 68-95-99.7 rule, psychometric T/IQ score translations, and Altman Z-score financial distress.
All Math Calculators
Compound Interest Calculator
Model geometric wealth growth, periodic contributions, inflation adjustments, and annual compounding schedules.
Percentage Calculator
Solve percentage increases, decreases, differences, fractions to percents, and reverse percentage calculations.
Fraction Calculator
Add, subtract, multiply, divide, and simplify fractions with step-by-step common denominators and mixed numbers.
Quadratic Equation Solver
Solve second-degree polynomial equations ax² + bx + c = 0 with real and complex roots, vertex, and discriminant analysis.
Scientific Calculator
Evaluate complex arithmetic, trigonometry, logarithms, exponentials, and powers with live formula rendering.
Statistics Calculator
Calculate mean, median, mode, sample variance, standard deviation, quartiles, and IQR for data series.
Probability Calculator
Calculate single and multiple independent event odds, combinations (nCr), permutations (nPr), and risk probabilities.
GPA Calculator
Calculate weighted and unweighted semester and cumulative GPA across standard 4.0 and honors scales.
Ratio Calculator
Simplify, scale, and solve proportions A:B = C:D with part-to-part and part-to-whole conversion breakdowns.
Matrix Calculator
Perform matrix determinant, inverse, multiplication, transpose, and row reduction up to 4x4 dimensions.
Triangle Calculator
Solve sides, angles, area, and perimeter of right and oblique triangles using SOHCAHTOA and the Law of Cosines.
Law of Sines Calculator
Solve oblique triangles with the Sine Rule across AAS, ASA, and the SSA ambiguous case.
Greatest Common Factor Calculator
Find the Greatest Common Factor (GCF / GCD) and Least Common Multiple (LCM) with step-by-step Euclidean division and prime trees.
Exponent Calculator
Calculate powers, negative exponents, fractional roots, and complex numbers with step-by-step exponent laws.
Coefficient of Variation Calculator
Calculate the Coefficient of Variation (CV / RSD) to compare relative dispersion and risk across different scales.
A/B Test Significance Calculator
Evaluate whether conversion differences between control and variant are statistically significant using two-proportion z-tests.
Binomial Distribution Calculator
Compute exact PMF and cumulative CDF binomial probabilities, distribution moments, and discrete histogram projections.
CAGR Calculator
Calculate Compound Annual Growth Rate (CAGR), absolute capital gains, and investment doubling horizons.
Future Value Calculator
Calculate compound future value of initial lump sums and periodic additions across any interest rate.
Population Growth Calculator
Model Malthusian exponential expansion and Verhulst logistic growth with environmental carrying capacity limits.
Area of a Circle Calculator
Calculate circular area, diameter, circumference, radius, and sector slice geometry.
Binary Calculator & Base Converter
Perform binary, octal, decimal, and hexadecimal arithmetic with two's complement signed logic.
Distance Formula Calculator
Calculate 2D and 3D Euclidean distances, radicals, midpoint, and Manhattan metric.
Prime Factorization Calculator
Decompose composite numbers into prime factors, divisors, totient, and aliquot sums.
Law of Cosines Calculator
Solve SAS and SSS oblique triangles, angles, perimeter, and area via Heron's formula.
Least Common Multiple (LCM) Calculator
Calculate the least common multiple and greatest common divisor across multiple integers.
Logarithm Calculator
Evaluate natural (ln), common (log10), binary (log2), and arbitrary custom base logarithms.
Percent Error Calculator
Determine experimental discrepancy, relative error, and percent difference against standard values.
Slope Calculator
Calculate linear slope, angle of inclination, percent grade, and perpendicular line equations.
Box Plot Generator
Generate Tukey box-and-whisker five-number summaries and detect statistical outliers.
Chi-Square Test Calculator
Evaluate contingency table independence, goodness-of-fit, p-values, and Cramér's V effect size.
Confidence Interval Calculator
Calculate confidence intervals for continuous means and proportions with margin of error.
Pearson Correlation Coefficient Calculator
Evaluate bivariate linear association (r), R-squared, t-test significance, and OLS trendline.
Interquartile Range (IQR) Calculator
Determine non-parametric statistical dispersion, quartiles Q1/Q3, and Tukey outlier boundaries.
Sample Size Calculator
Determine required survey sample size, margin of error, and finite population corrections.
Z-Score Calculator
Convert raw scores to standard z-scores, normal percentiles, and psychometric scales.
Authoritative Guides for Math
Percentage Calculations in Practice: Relative Change, Deltas & Reversals
Master the 5 percentage formulas, mental math hacks, sales tax back-outs, percentage changes, and asymmetric loss recovery.
Fraction Arithmetic: Common Denominators, Mixed Numbers & Simplification
Euclidean algorithm GCD reduction, least common denominator (LCD) methods, mixed number conversions, and fraction division.
Trigonometric & Transcendental Functions: Radian vs. Degree Computing
Master circular trigonometry in degrees and radians, natural and common logarithms, exponential powers, and permutations vs combinations.
Descriptive Statistics: Mean, Median, Variance & Standard Deviation
Arithmetic mean, median, modes, sample vs population standard deviation with Bessel correction, 5-number summaries, and Tukey outlier detection.
Combinatorics and Odds: Permutations, Combinations & Probability Trees
Kolmogorov probability axioms, union and intersection laws for independent events, binomial distributions, and permutations vs combinations.
Calculating High School & College GPA: Credit Hours, Honors & Weighting
Master standard 4.0 quality points, weighted Honors (+0.5) and AP/IB (+1.0) scaling, cumulative transcript blending, and Latin honors classifications.
Ratio & Proportion Math: Scaling Dimensions, Aspect Ratios & Part-to-Part
Euclidean ratio reduction, proportion cross-multiplication equations (A:B = C:D), display aspect ratio resizing, and square-cube scaling laws.
Solving Quadratic Equations: The Quadratic Formula, Discriminant & Vertex
Master the quadratic formula, real and complex discriminant analysis (Δ), parabola vertex (h, k), axis of symmetry, and conic focus/directrix geometry.
Matrix Operations & Linear Algebra: Determinants, Inverses & Transformations
Multiplication dot products, Laplace cofactor determinant expansions, adjugate inversion formulas, matrix transpositions, and Frobenius norms.
Solving Any Triangle: The Laws of Sines, Cosines & Heron's Area
Master SSS, SAS, and ASA triangle solving with the Law of Sines/Cosines, Pythagorean theorem, Heron area formula, and incircle/circumcircle radii.
Analytic Trigonometry of Oblique Triangles: Law of Sines, Ambiguous SSA Cases & Circumradii
Solving AAS, ASA, and ambiguous SSA configurations, circumcircle proofs, and spherical astronomy extensions.
Number Theoretic Foundations of Common Divisors: Euclidean Algorithm & Coprimality
Euclidean division algorithm, prime factorization, Bézout identity, and RSA public-key applications.
Exponential Arithmetic: Power Laws, Fractional Radicals, Negative Indices & Complex Powers
Comprehensive treatment of integer exponents, negative powers, indeterminate forms (0^0), and complex roots.
Relative Statistical Dispersion: The Coefficient of Variation, Risk Ratios & Sample Bias
Normalizing standard deviation across disparate scales, Sokal-Rohlf bias correction, and Sharpe ratio comparisons.
Frequentist Hypothesis Testing in Digital Experimentation: Two-Proportion Z-Scores
Z-test formulations, p-value calculations, statistical power, Type I/II errors, and sample size sizing.
Bernoulli Trials & Discrete Probability: Binomial Distributions, Factorials & Poisson Limits
Derivation of PMF, cumulative distribution functions, log-gamma stable calculations, and normal approximations.
Euclidean Circular Geometry: Archimedean Approximations, Sectors & Segments
Historical quadrature, thin-ring calculus derivations, circular sectors, and engineering tolerance standards.
Digital Logic & Binary Mathematics: Positional Radices, Two's Complement & Bitwise Algebra
Foundations of digital representation, signed two's complement arithmetic, bit shifting, and IEEE 754 floating-point standards.
Cartesian Metrics: Euclidean Distance, Minkowski Norms & Spatial Coordinates
Geometric derivation from Pythagoras, multidimensional vector norms, Manhattan urban grid metrics, and Great-Circle spherical paths.
The Fundamental Theorem of Arithmetic: Prime Factorization, Pollard's Rho & Cryptography
Canonical prime decompositions, divisor functions, aliquot abundance, and computational complexity underlying RSA encryption.
The Law of Cosines: Vector Derivations, Oblique Trigonometry & SSS Triangulation
Dot product proofs, generalizing Pythagoras to obtuse angles, Heron's area formula, and unambiguous triangle solving.
The Least Common Multiple: Number Theory, Multi-Integer Algorithms & Fraction Arithmetic
The duality of LCM and GCD, min/max lattice theory, least common denominators, and mechanical gear resonance.
The Foundations of Logarithms: Napierian Inverses, Change-of-Base & Information Entropy
Napierian history, natural logarithms in continuous calculus, decibels, Richter magnitude, and Shannon information entropy.
Metrology & Error Analysis: Percent Error, Instrumental Uncertainty & Propagation
Systematic calibration vs random noise, error propagation in quadrature, and significant figure tolerances in laboratory assays.
Linear Rate of Change: Cartesian Slopes, Orthogonality & Derivative Foundations
Connecting algebraic rise-over-run to calculus limits, negative reciprocal orthogonality, and civil engineering grade standards.
Exploratory Data Analysis: Tukey Boxplots, Five-Number Summaries & Outlier Fences
Tukey non-parametric order statistics, quartile interpolation conventions, the 1.5 IQR fence rationale, and distribution skewness.
Categorical Data Analysis: Pearson's Chi-Square, Contingency Tables & Residual Modeling
Sum of squared normal variates, contingency independence vs goodness of fit, Cochran's criteria, and Cramér's V effect size.
Inferential Parameter Estimation: Confidence Intervals, Margin of Error & Student's t
Frequentist coverage definitions, Central Limit Theorem square-root scaling, Gosset's t-distribution, and Wilson score intervals.
Bivariate Linear Association: Pearson's r, Anscombe's Quartet & Spurious Correlation
Covariance normalization, Anscombe's quartet visualization imperative, causation fallacies, and OLS regression slopes.
Robust Statistics: The Interquartile Range, Non-Parametric Dispersion & Outlier Fences
Parametric vs non-parametric dispersion, 25% breakdown points, economic net worth modeling, and quartile deviation coefficients.
Survey Metrology: Sample Size Determination, Finite Population Corrections & Power
The economics of sample sizing, the 50% conservative variance ceiling, diminishing returns in polling, and finite population corrections.
The Standard Normal Distribution: Z-Scores, Gaussian Integration & Percentile Scaling
Standardization mechanics, the empirical 68-95-99.7 rule, psychometric T/IQ score translations, and Altman Z-score financial distress.
Editorial Articles for Math
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