Mathematik
Prozente, Brüche, Geometrie und Statistik.
Calculators (36)
Zinseszinsrechner
Simulieren Sie Vermögenswachstum mit Zinseszins, regelmäßigen Einzahlungen und Inflationsbereinigung.
Prozentrechner
Lösen Sie prozentuale Steigerungen, Rabatte, Verhältnisse und prozentuale Veränderungen.
Bruchrechner
Addieren, subtrahieren, multiplizieren und dividieren Sie echte, unechte und gemischte Brüche.
Mitternachtsformel-Rechner
Lösen Sie quadratische Gleichungen ax² + bx + c = 0 mit Diskriminante und reellen/komplexen Nullstellen.
Wissenschaftlicher Rechner
Auswertung trigonometrischer, logarithmischer, exponentieller und kombinatorischer Ausdrücke.
Statistik-Rechner
Berechnen Sie Mittelwert, Median, Modus, Varianz, Standardabweichung und Quartile für Datensätze.
Wahrscheinlichkeitsrechner
Berechnen Sie Permutationen, Kombinationen, Binomialverteilung und bedingte Wahrscheinlichkeiten.
Notendurchschnittsrechner (GPA)
Berechnen Sie den gewichteten und ungewichteten Notendurchschnitt nach ECTS- oder 4.0-Skala.
Verhältnisrechner
Lösen Sie Proportionen A:B = C:D, skalieren Sie Seitenverhältnisse und vereinfachen Sie Raten.
Matrix-Rechner
Berechnen Sie Matrixmultiplikation, Determinanten, Inverse und Transpositionen für 2x2 und 3x3 Matrizen.
Dreiecksrechner
Lösen Sie Dreiecke über Sinussatz, Kosinussatz und Satz des Pythagoras mit Flächenberechnung.
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-Rechner
Ermitteln Sie die durchschnittliche jährliche Wachstumsrate (CAGR) und Kapitalverdopplungszeiten.
Zukunftswert-Rechner (Future Value)
Berechnen Sie das zukünftige Endkapital aus Einmalanlage und regelmäßigen Sparraten.
Populationswachstums-Rechner
Modellieren Sie malthusianisches exponentielles Wachstum und logistisches Verhulst-Wachstum mit Umweltkapazitätsgrenzen.
Kreisflächen-Rechner
Berechnen Sie Kreisfläche, Durchmesser, Umfang, Radius und Kreissektoren.
Binärrechner & Basis-Konverter
Führen Sie binäre, oktale, dezimale und hexadezimale Arithmetik mit Zweierkomplement aus.
Abstandsformel-Rechner
Berechnen Sie euklidische Abstände in 2D und 3D, Wurzelformen, Mittelpunkte und Manhattan-Metrik.
Primfaktorzerlegung-Rechner
Zerlegen Sie zusammengesetzte Zahlen in Primfaktoren, Teiler, Totient und echte Teilersummen.
Kosinussatz-Rechner
Lösen Sie beliebige Dreiecke nach SWS und SSS, inklusive Winkeln, Umfang und Herons Flächenformel.
Kleinstes gemeinsames Vielfaches (kgV) Rechner
Berechnen Sie das kleinste gemeinsame Vielfache und den größten gemeinsamen Teiler.
Logarithmus-Rechner
Berechnen Sie natürliche (ln), dekadische (log10), binäre (log2) und benutzerdefinierte Logarithmen.
Prozentualer Fehler Rechner
Ermitteln Sie experimentelle Abweichungen, relative Fehler und prozentuale Differenzen.
Steigungsrechner
Berechnen Sie Steigung, Neigungswinkel, prozentuale Steigung und orthogonale Geradengleichungen.
Boxplot-Generator
Erstellen Sie Tukey-Boxplots mit Fünf-Punkte-Zusammenfassung und Ausreißererkennung.
Chi-Quadrat-Test Rechner
Berechnen Sie Unabhängigkeit in Kontingenztafeln, Anpassungsgüte, p-Werte und Cramér-V.
Konfidenzintervall-Rechner
Berechnen Sie Konfidenzintervalle für Mittelwerte und Anteile samt Fehlerspanne.
Pearson-Korrelationskoeffizient Rechner
Berechnen Sie lineare Korrelation (r), Bestimmtheitsmaß R², Signifikanz und OLS-Regressionsgerade.
Interquartilsabstand (IQR) Rechner
Ermitteln Sie nichtparametrische Streuung, Quartile Q1/Q3 und Tukey-Ausreißergrenzen.
Stichprobengröße-Rechner
Berechnen Sie benötigte Stichprobengrößen, Fehlerspannen und Endlichkeitskorrekturen.
Z-Score Rechner
Rechnen Sie Rohwerte in Z-Scores, Normalverteilungs-Perzentile und T-Scores um.
Anleitungen (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.
Alle Mathematik-Rechner
Zinseszinsrechner
Simulieren Sie Vermögenswachstum mit Zinseszins, regelmäßigen Einzahlungen und Inflationsbereinigung.
Prozentrechner
Lösen Sie prozentuale Steigerungen, Rabatte, Verhältnisse und prozentuale Veränderungen.
Bruchrechner
Addieren, subtrahieren, multiplizieren und dividieren Sie echte, unechte und gemischte Brüche.
Mitternachtsformel-Rechner
Lösen Sie quadratische Gleichungen ax² + bx + c = 0 mit Diskriminante und reellen/komplexen Nullstellen.
Wissenschaftlicher Rechner
Auswertung trigonometrischer, logarithmischer, exponentieller und kombinatorischer Ausdrücke.
Statistik-Rechner
Berechnen Sie Mittelwert, Median, Modus, Varianz, Standardabweichung und Quartile für Datensätze.
Wahrscheinlichkeitsrechner
Berechnen Sie Permutationen, Kombinationen, Binomialverteilung und bedingte Wahrscheinlichkeiten.
Notendurchschnittsrechner (GPA)
Berechnen Sie den gewichteten und ungewichteten Notendurchschnitt nach ECTS- oder 4.0-Skala.
Verhältnisrechner
Lösen Sie Proportionen A:B = C:D, skalieren Sie Seitenverhältnisse und vereinfachen Sie Raten.
Matrix-Rechner
Berechnen Sie Matrixmultiplikation, Determinanten, Inverse und Transpositionen für 2x2 und 3x3 Matrizen.
Dreiecksrechner
Lösen Sie Dreiecke über Sinussatz, Kosinussatz und Satz des Pythagoras mit Flächenberechnung.
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-Rechner
Ermitteln Sie die durchschnittliche jährliche Wachstumsrate (CAGR) und Kapitalverdopplungszeiten.
Zukunftswert-Rechner (Future Value)
Berechnen Sie das zukünftige Endkapital aus Einmalanlage und regelmäßigen Sparraten.
Populationswachstums-Rechner
Modellieren Sie malthusianisches exponentielles Wachstum und logistisches Verhulst-Wachstum mit Umweltkapazitätsgrenzen.
Kreisflächen-Rechner
Berechnen Sie Kreisfläche, Durchmesser, Umfang, Radius und Kreissektoren.
Binärrechner & Basis-Konverter
Führen Sie binäre, oktale, dezimale und hexadezimale Arithmetik mit Zweierkomplement aus.
Abstandsformel-Rechner
Berechnen Sie euklidische Abstände in 2D und 3D, Wurzelformen, Mittelpunkte und Manhattan-Metrik.
Primfaktorzerlegung-Rechner
Zerlegen Sie zusammengesetzte Zahlen in Primfaktoren, Teiler, Totient und echte Teilersummen.
Kosinussatz-Rechner
Lösen Sie beliebige Dreiecke nach SWS und SSS, inklusive Winkeln, Umfang und Herons Flächenformel.
Kleinstes gemeinsames Vielfaches (kgV) Rechner
Berechnen Sie das kleinste gemeinsame Vielfache und den größten gemeinsamen Teiler.
Logarithmus-Rechner
Berechnen Sie natürliche (ln), dekadische (log10), binäre (log2) und benutzerdefinierte Logarithmen.
Prozentualer Fehler Rechner
Ermitteln Sie experimentelle Abweichungen, relative Fehler und prozentuale Differenzen.
Steigungsrechner
Berechnen Sie Steigung, Neigungswinkel, prozentuale Steigung und orthogonale Geradengleichungen.
Boxplot-Generator
Erstellen Sie Tukey-Boxplots mit Fünf-Punkte-Zusammenfassung und Ausreißererkennung.
Chi-Quadrat-Test Rechner
Berechnen Sie Unabhängigkeit in Kontingenztafeln, Anpassungsgüte, p-Werte und Cramér-V.
Konfidenzintervall-Rechner
Berechnen Sie Konfidenzintervalle für Mittelwerte und Anteile samt Fehlerspanne.
Pearson-Korrelationskoeffizient Rechner
Berechnen Sie lineare Korrelation (r), Bestimmtheitsmaß R², Signifikanz und OLS-Regressionsgerade.
Interquartilsabstand (IQR) Rechner
Ermitteln Sie nichtparametrische Streuung, Quartile Q1/Q3 und Tukey-Ausreißergrenzen.
Stichprobengröße-Rechner
Berechnen Sie benötigte Stichprobengrößen, Fehlerspannen und Endlichkeitskorrekturen.
Z-Score Rechner
Rechnen Sie Rohwerte in Z-Scores, Normalverteilungs-Perzentile und T-Scores um.
Authoritative Guides for Mathematik
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 Mathematik
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