Formula Library

Formulas you can actually use

A formula sheet is only half useful. Knowing that the bending stress in a beam is My/I does not help you when the question gives you a load in kilonewtons and a span in millimetres and you need the answer in megapascals.

Every formula in the library is stored with its variables named and described, so the symbols are explained rather than assumed — and where a formula has a numeric answer, a calculator is attached to it.

Plug in the numbers, get the answer

Open a formula and you get a field for each variable. Enter the values your question gives you and the result is computed on the spot, with the working shown so you can follow where the number came from rather than trusting a black box.

The calculator insists you fill in every variable before it answers. It will not quietly substitute a zero for a value you have not entered, which is the fastest way to get a confidently wrong answer out of a calculator and never notice.

Most formulas have no calculator, and that is deliberate

The calculator is attached to just over 2,200 of them — roughly a third. It handles arithmetic only: add, subtract, multiply, divide, powers and brackets. A formula gets a calculator when its answer can be reached that way.

Two kinds of formula are left without one. Some are statements rather than sums — that the pressure change across a reversible isobaric process is zero, that a conservative field is the gradient of a potential. There is no number to compute. The rest need a function: a logarithm, a sine, a square root of a sum.

That second restriction exists to prevent a specific failure. Handed an expression it does not fully understand, a calculator can produce a plausible number from the wrong arithmetic, and you would have no reason to doubt it. Rather than show you a calculator that might be quietly wrong, those formulas ship with the formula, the variable definitions and the worked explanation, and no calculator section at all. Every formula in the library has that worked example — the question, the values given, the substitution and the answer — whether or not a calculator sits under it.

Where the maths allowed it, a formula was rearranged so it could be evaluated: roots are written as fractional powers and constants are written out in full rather than as named functions, which brings them back inside what the evaluator can do honestly.

Built for the way questions are actually set

Formula values take the units they are normally given in, so the library is organised by the subject you are studying rather than as one enormous alphabetical list. You reach a formula by the topic it belongs to, the way you would reach for it in an exam.