The radian unit

To measure how long the Roman Colosseum is around (circumference), the archaeologist can with a measuring wheel choose to walk all the way around. But she could also just measure the distance across (diameter) and use the formula:¹

$$\text{circumference}=\pi\;\text{diameter}$$

In fact, she could do it even quicker by just measuring the distance to the centre (radius), since two of those distances give the diameter:

$$ \text{circumference}=\pi \;\overbrace{2\;\text{radius}}^\text{diameter}$$

So, the circumference (the full round) is ‘$\pi$-times-the-diameter long’, or in other words: ‘$\pi$ diameters long’.² Or it is ‘$2\pi$ radiuses long’.³