CITIZEN TOOLS
Real physics and mathematics for the analytically minded citizen.
Compute relativistic time dilation at near-light velocities.
Calculate relativistic Doppler shift for observed frequencies.
Solve the four kinematic equations of motion.
Convert frequency and wavelength, calculate wave speed and period, and learn wave physics.
Estimate cosmological distances using Hubble's law.
Solve systems of linear equations step by step.
Graph a linear equation y = mx + b and inspect its points.
Compute mean, median, mode, variance, standard deviation, and view a bell curve.
Quartiles, IQR, five-number summary, skewness, kurtosis, z-scores, outliers, and box plots.
Normal, binomial, and Poisson distributions with CDFs, PMFs, and shaded curves.
Confidence intervals and one-sample hypothesis tests with p-values and worked steps.
Compute population density and youth, old, and total dependency ratios.
Evaluate variable relationships within datasets.
Calculate odds ratios and confidence intervals.
Compute escape velocity for any planetary body.
Calculate buoyant force on submerged objects.
Calculate Young's modulus, stress, strain, force, area or extension with step-by-step solutions, graphs, and a virtual tensile-test lab.
Compute momentum and impulse for collisions.
Model radioactive decay over time.
Calculate photon diffraction patterns and wavelengths.
