Textbook formulas worked in the open: statistics (sample size, confidence intervals, t-tests, z-scores), triangles, dilution and molarity, the ideal gas law, projectile motion.
The calculations of a statistics course, a geometry class and a first-year lab, done exactly and shown step by step: how many to sample for a margin of error, what a confidence interval or a t-test says about a set of numbers, every side and angle of a triangle from the ones you know, how to dilute a stock or weigh out a solution, what pressure, volume and temperature imply for a gas, where a projectile lands. Each page states its formula, the constants it uses with their source, and what it does not decide — and none of it is medical, dosing or safety advice.
A confidence interval for a mean (t or z, from pasted data or summary figures) or a proportion (Wald and Wilson), with critical value and standard error shown.
You get: Lower and upper bounds at your confidence level, the critical t or z used, the standard error, and a warning when the sample is too small for the method to be trusted.
Open Confidence Interval CalculatorHow many to survey for a margin of error and confidence level, for a proportion or a mean, with finite-population correction and an existing sample’s margin.
You get: A whole-number sample size for your margin and confidence, the same figure at 90, 95 and 99 %, and the formula with its z-value so the number can be checked by hand.
Open Sample Size CalculatorPaste one or two samples and run a one-sample, paired or two-sample t-test (Welch or pooled): t, degrees of freedom, p-value, confidence interval and Cohen’s d.
You get: The test statistic, exact degrees of freedom, a one- or two-sided p-value, a confidence interval for the mean or the difference, and an effect size, with the formula used stated.
Open t-Test CalculatorConvert between a value, its z-score and its percentile on a normal distribution with your mean and standard deviation, with tail probabilities and a ladder.
You get: The z-score and percentile of a value (or the value at a percentile), the probability above, below and in both tails, and where the 1st to 99th percentiles fall.
Open Z-Score & Percentile CalculatorGive any two of the legs, hypotenuse and acute angles of a right triangle and get the rest: sides, angles, area, perimeter, altitude, inradius and circumradius.
You get: Every side and angle of the triangle, its area and perimeter, and the altitude and circle radii — with the identity used (Pythagoras or the ratio) stated.
Open Right Triangle CalculatorGive any three parts of a triangle including a side and get all sides and angles, area, heights and circle radii — both triangles in the ambiguous SSA case.
You get: A fully solved triangle with its type, drawn to scale, and the law (sines or cosines) that produced each value — or both solutions when the data allow two.
Open Triangle Solver (SSS, SAS, ASA, AAS, SSA)Solve C₁V₁ = C₂V₂ for stock volume, final concentration or final volume with the diluent to add, or plan a serial dilution tube by tube with each concentration.
You get: The volume of stock to pipette and the diluent to make it up with — or a tube-by-tube serial dilution table — with the dilution factor and the equation shown.
Open Dilution Calculator (C₁V₁ = C₂V₂ & Serial)From the molar mass on the label, find the mass to weigh for a target molarity and volume — or the molarity, or the volume — with purity allowed for.
You get: The grams to weigh out (corrected for purity), the moles, the molarity in M and mM, and g/L, with n = m/M and c = n/V shown so the prep can be checked.
Open Molarity & Solution Prep CalculatorSolve PV = nRT for pressure, volume, moles or temperature in kPa, atm, bar, psi, L, m³, °C, °F or K with the CODATA R, plus molar volume, gas mass and density.
You get: The missing one of P, V, n and T in the unit you chose, the same pressure and volume in every other unit, and the gas’s mass and density if you give its molar mass.
Open Ideal Gas Law Calculator (PV = nRT)Range, maximum height, flight time and impact speed for a projectile launched at a speed and angle from any height, no air resistance, with a trajectory table.
You get: Where and when the projectile lands, how high it goes, how fast and at what angle it hits — plus its position at equal time steps — with the kinematic equations and g stated.
Open Projectile Motion Calculator