Algebra, Probability & Applied Mathematics

Mathematics & Statistics Calculators

Master algebra, descriptive statistics, discrete probability distributions, sequence algebra, and matrix linear systems with instant, step-by-step mathematical algorithms.

LCM & GCF Calculator

Popular

Find Least Common Multiple (LCM) and Greatest Common Factor (GCF) for 2+ numbers with prime factorization ladders.

Open Solver → Arithmetic

Racine Carrée (Square Root)

Hot

Calculate precise square roots, simplified surds (a√b), Babylonian iterations, and interactive function curves.

Open Solver → Algebra

Median & 5-Number Summary

Hot

Calculate median, quartiles (Q1, Q3), Interquartile Range (IQR), outliers, and render interactive box-and-whisker plots.

Open Solver → Statistics

Standard Deviation & Variance

Popular

Calculate sample (s) and population (σ) standard deviation, variance, standard error, and normal distribution curves.

Open Solver → Statistics

Binomial Distribution Solver

Hot

Compute exact P(X = k), cumulative P(X ≤ k), expected mean, variance, and probability mass histograms.

Open Solver → Probability

Correlation (Pearson r & R²)

Popular

Calculate Pearson correlation (r), Spearman rank, coefficient of determination (R²), and 2D scatter plots.

Open Solver → Statistics

Matrix Determinant (2x2 to 5x5)

Essential

Calculate square matrix determinants via Laplace cofactor expansion and Gaussian row reduction with step proofs.

Open Solver → Linear Algebra

Discriminant & Quadratic Roots

Popular

Determine Δ = b² - 4ac, real and complex roots, vertex coordinates, and interactive parabola function graphs.

Open Solver → Algebra

Nth Term & Sequence Solver

Hot

Solve arithmetic, geometric, and quadratic sequence general formulas (a_n), difference tables, and partial series sums.

Open Solver → Sequences

Interpolation Calculator

Essential

Calculate linear, bilinear, and polynomial curve interpolations between discrete data points with coordinate plotting.

Open Solver → Numerical Analysis

Percent Change & Difference

Popular

Calculate percentage increase, decrease, absolute difference, and relative percentage changes between any two values.

Open Solver → Arithmetic

Canvas Grade & Final Exam

Popular

Calculate weighted course grades from Canvas LMS and solve the exact final exam score needed for target letter grades.

Open Solver → Academic

Crosswind & Runway Vector

Essential

Compute exact crosswind, headwind, and tailwind velocity vectors based on runway magnetic heading and wind angle.

Open Solver → Trigonometry

Essential Foundations of Mathematics, Probability & Statistical Modeling

Mathematical and statistical computation forms the bedrock of modern engineering, scientific research, academic achievement, and data analysis. Whether you are solving quadratic polynomials with our Discriminant Calculator, modeling sequence progressions using the Nth Term Calculator, or computing percentage changes via the Percent Change Calculator, computational accuracy and step-by-step verification are essential.

Core Computational Formulas

1. Standard Deviation (Sample vs. Population):
s = sqrt( (1 / (n - 1)) * sum( (x_i - mean)^2 ) )
sigma = sqrt( (1 / N) * sum( (x_i - mu)^2 ) )

2. Pearson Correlation Coefficient (r):
r = sum( (x - x_bar)(y - y_bar) ) / ( sqrt(sum(x - x_bar)^2) * sqrt(sum(y - y_bar)^2) )

3. Binomial Distribution PMF:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

4. Quadratic Discriminant & Roots:
Delta = b^2 - 4ac (If Delta > 0: 2 real roots; Delta = 0: 1 real root; Delta < 0: 2 complex conjugate roots).

Quick Reference Guide to Descriptive Statistics

Statistical Metric Formula / Definition Sensitivity to Outliers Primary Use Case & Dedicated Tool
Mean (Arithmetic Average) x_bar = (sum x_i) / n High (skewed by extreme values) Normal / symmetric distributions
Median (Middle Value) 50th Percentile (Q2) Robust (unaffected by extreme values) Median & IQR Boxplot Calculator
Interquartile Range (IQR) IQR = Q3 - Q1 Robust 5-Number Summary & Outlier Filter
Standard Deviation (s) s = sqrt(Variance) High Standard Deviation & Variance Solver