Guides

Percent of a number, one number as a percent of another, and percentage increase or decrease — the four calculations that cover almost every real situation, with worked examples.

How body mass index is calculated, what the standard categories mean, why it misreads some people, and which other measures fill the gaps.

Where your monthly payment comes from, why early payments are mostly interest, and how extra payments change the picture — the amortization formula explained in plain terms.

Three encodings that look similar and solve different problems. What each one does, what it is not, and how to tell which you are looking at.

The full JSON grammar fits on a postcard. Here it is, plus the handful of mistakes — trailing commas, single quotes, stray comments — that cause almost every parse error.

V = I x R and P = V x I, the six formulas they produce, and how to use them to size a resistor, check a wire, or work out what a component dissipates.

Where to put the tape, how the waist-to-hip ratio and the US Navy body-fat formula work, what the numbers mean, and where they stop being reliable.

Work out how much heat a resistor dissipates with P = I squared R or V squared over R, why the I squared term matters, and how much headroom to leave.

What map() actually does (integer linear scaling), the truncation and overflow traps, when to use floating point instead, and how to reverse or constrain it.

The three-digit EIA code, letter-as-decimal shorthand, plain pF values, and the tolerance letter — how to turn a tiny printed marking into a real capacitance.

The check-digit formula behind every credit card and IMEI number: how to compute it by hand, what it catches, and why passing it says nothing about a real account.

What a UART frame looks like on the wire, why 8N1 gives only 80% throughput, and how an integer clock divisor produces baud rate error that corrupts data past 2-3%.