The Hertzsprung–Russell Diagram

What it plots — the luminosity of stars, usually relative to the Sun, against their surface temperature.

The axis that catches everyone out — temperature increases to the left. The horizontal axis runs from about 50 000 K on the left down to 2 500 K on the right, which is the reverse of every other graph you will draw. Luminosity increases upwards, on a logarithmic scale spanning many powers of ten.

The main sequence — a broad band running from hot, luminous stars at the top left to cool, dim stars at the bottom right. About 90% of stars lie here, including the Sun, and a star's position along the band is determined mainly by its mass: more massive stars are hotter and far more luminous.

Red giants and supergiants — upper right. They are cool, so each square metre of surface radiates relatively little, yet they are extremely luminous, which can only mean they are enormous. The diagram lets you deduce size from position without measuring it.

White dwarfs — lower left. Hot, so each square metre radiates intensely, yet very dim overall — so they must be tiny, roughly the size of the Earth.

Example: the deduction works through Stefan's law, L = 4πr²σT⁴. Given luminosity and temperature, the radius follows. That is why the H–R diagram is more than a catalogue: position on it encodes a star's size and its stage of life.

Reading a star's life story — a star spends most of its life at a fixed point on the main sequence. When hydrogen runs out it moves right and upwards into the giant region as it expands and cools, then, for a low-mass star, down to the lower left as it sheds its outer layers and leaves a white dwarf. The diagram is a snapshot of a population, and the paths across it are inferred from where stars cluster.

Main sequence lifetime and mass — more massive stars are far more luminous and burn through their hydrogen much faster, despite having more of it. A star ten times the Sun's mass lives only a thousandth as long.