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Guides to the maths behind the calculators, written to be followed with a pencil. Every worked example can be checked in one of the tools.

Using a calculator well

Why sin(30) can come out as −0.988, what a radian is, and a simple rule for which mode you need.

How many digits to keep, the rules for multiplying and adding, and why you should only round at the end.

Why 0.1 + 0.2 isn't exactly 0.3 in a computer, and the one kind of error that really matters.

What every key does, from sinh to n!, with examples and the order of operations.

Factorising, completing the square and the formula, plus a 10-second test for whether it factorises.

Four worked examples, the ambiguous case, and the trap that gives 84° instead of 96°.

The cofactor method with every step shown, a quick check, and solving three simultaneous equations.

A full worked table, sample vs population, and the shortcut formula's hidden danger.

Why doubling the power only adds 3 dB, how carbon dating works, and the rule of 72.

Gauge vs absolute pressure, squared units, kW vs kWh and more, each with the numbers worked through.

Algebra, trig, logs, areas and volumes, statistics and matrices on one page.

CODATA 2022 values for c, h, e, k_B, N_A, G and g, and what each one is for.

Why two calculators can give different answers to the same question.