Mathematics
Calculations, statistics, algebra and geometry.
- 2×2 and 3×3 matrices: determinant, inverse, systemDeterminant, inverse, transpose, products AB and BA, and linear system solving, with singularity detected at a relative threshold.
- Areas and volumes of common shapesArea and perimeter of ten plane figures, volume and surface of eight solids, with the formula shown and whatever is not determined flagged.
- Arithmetic and geometric sequencesGeneral term, sum of terms and infinite sum of an arithmetic or geometric sequence, with the starting index of your textbook (u₀ or u₁).
- Binomial and Poisson distributionsP(X = k), P(X ≤ k) and P(X ≥ k) for the binomial and Poisson distributions, computed in log space, tails summed from the right side.
- Chi-square test, goodness of fit and independenceχ² statistic, degrees of freedom, p-value and critical value, with cell-by-cell detail and Cochran’s rule checked.
- Combinations, permutations and factorialC(n, k), P(n, k) and n! as exact values (integer arithmetic, not floats) with the explanation of when order matters and when it does not.
- Confidence interval calculatorCI for a mean (Student or normal) and for a proportion using the wilson interval, more reliable than Wald, shown alongside for comparison.
- Correlation and linear regressionLeast-squares line, r and r², slope p-value, confidence and prediction intervals, residuals point by point.
- Cross multiplication (rule of three)Find the fourth proportional by cross multiplication, direct or inverse proportionality, with the worked calculation and the sentence that explains it.
- Descriptive statistics, mean, median, standard deviationCalculate mean, median, range, variance and standard deviation of a series of values, with the sample / population distinction.
- Equation of a lineFind y = mx + b from two points or a slope and a point: slope, y-intercept, root, vertical line included.
- GCD and LCMCompute the GCD and LCM of two or three integers, with the Euclidean algorithm unrolled line by line and the simplified fraction.
- Linear interpolation calculatorCalculate y from x or x from y between two points, with slope, y-intercept, line equation and extrapolation alert.
- Map and plan scaleConvert between map distance and real distance at a 1:n scale, or recover the scale of a document from two measurements.
- Normal distribution calculatorProbabilities, z-scores and critical values of the normal distribution (P(X ≤ x), P(a ≤ X ≤ b), quantiles) at machine precision, tails included.
- One-way ANOVA, comparing multiple meansCompare means across multiple groups with the complete ANOVA table: sum of squares, F-statistic, p-value, and cautious conclusion.
- Percentage and percentage change calculatorCalculate a percentage of a value, a ratio, an increase or decrease, the variation between two values, or find the original value.
- Quadratic equation solver with stepsSolve ax² + bx + c = 0 with every step shown: discriminant, real or complex roots, vertex form, sum and product, free.
- Slope: percent, degrees, ratioConvert a slope between percent, degrees and 1:n ratio, or compute it from rise and distance, with the real road length.
- Student's t-test, comparison of meansCompare a mean to a reference value or two independent samples (Welch's t-test): t, degrees of freedom, p-value, confidence interval and conclusion.
- Triangle solver (law of sines and cosines)Solve a triangle from SSS, SAS, ASA or SSA, with the ambiguous case handled honestly: zero, one or two triangles, all displayed.
- Vector calculator, dot product, cross product and angleNorms, sum, dot product, cross product, angle, projection and a collinearity verdict, in the plane as in space.