solve ρ=m/V for density, mass, or volume, find density of cylinders and spheres, use water displacement, and look up water density in kg/m³, lb/ft³, g/cm³, and lb/gal at any temperature
Calculate population variance (σ²) and sample variance (s²) from any data set. Shows mean calculation, squared deviations, and standard deviation. Handles raw data and frequency tables.
Find critical values for z-tests, t-tests, chi-square tests, and F-tests at any significance level. Shows rejection regions and p-value interpretation for one-tailed and two-tailed tests.
Convert polar coordinates (r, θ) to rectangular (x, y) and back. Works in degrees and radians. Converts polar equations to rectangular form.
Find all real zeros of any function using bisection method, Newton-Raphson, and rational root theorem. Shows complete step-by-step root-finding process with graph of the function.
Decompose rational expressions into partial fractions. Handles distinct linear, repeated linear, and irreducible quadratic factors. Shows every algebraic step for integration prep.
Find inflection points using the second derivative test with full sign-change verification, concavity intervals, and complete step-by-step working. Not just root-finding — genuine concavity change confirmed.
Solve first-order ordinary differential equations with initial conditions. Handles separable, linear, and exact ODEs. Shows complete integration and constant-finding steps.
Free inverse Laplace transform calculator. Find ℒ⁻¹{F(s)} = f(t) via direct table lookup or partial fraction decomposition — with complete step-by-step working for polynomials, exponentials, trig, and damped oscillations
Solve p, q, p², 2pq, q² from any known value recessive phenotype frequency, allele frequency, or observed counts Includes genotype frequency calculator, allele frequency calculator, and phenotype frequency calculator