Every conversion is the same two questions: which way am I going, and by what factor. Get those two and the rest is just a multiply or a divide.
The Factors Worth Knowing
There are only three steps on the area ladder, and each is the square of its length factor:
mm² ↔ cm²: ×100 or ÷100 (because 1 cm = 10 mm, and 10² = 100)
cm² ↔ m²: ×10 000 or ÷10 000 (because 1 m = 100 cm, and 100² = 10 000)
m² ↔ ha: ×10 000 or ÷10 000 (a hectare is a 100 m × 100 m square)
Which Way: Multiply or Divide?
Going to a smaller unit, you'll need more of them, so you multiply. Going to a bigger unit, you'll need fewer, so you divide. A square metre is a big tile; chop it into little square centimetres and you get loads — 10 000 — so m² → cm² multiplies.
A Worked One
Convert 3 m² into cm². We're heading to a smaller unit, so multiply. The factor for m² → cm² is 10 000. So 3 × 10 000 = 30 000 cm². Going the other way, 50 000 cm² into m²? Divide: 50 000 ÷ 10 000 = 5 m².
Choosing the Unit in the First Place
Before you convert anything, pick a unit that makes the number friendly. A desk top in cm² (a few thousand), a stamp in mm², a classroom in m², a paddock in hectares. If your number has a silly pile of zeros or a tiny string of decimals, you've probably picked the wrong unit — that's the quiz at the bottom of the toy.