The minimal length of your hair for making dreadlocks

Appropriate, minimal length of hair to make dreads is 3 - 4 inches (8 to 10 cm).

Out of the hair of this length you can make relatively short dreads which will be circa 3 inch (6 - 8 cm) long. Depending on your vision and needs you may wait for your dreads to grow slowly or you can extend them with natural or synthetic hair.
If from the very beginning you plan to extend them you can make dreads out of the hair of 3 inches (6 – 8 cm) long. I will go into details in the further part.
What is most important when you make dreads is that the shorter hair the less they curl. For instance out of 6 inches (15-cm) long hair you will make 4,5 inch (12-cm) long dreads, but out of 30 inch (50-cm) long hair you may expect 11 - 14 inches (25 – 30-cm) long dreads. At this length and with longer hair the hair condition is also important – the older hair the weaker and thinner it is so to braid a pretty dread in particular at the end they need to be made thicker.
Generally at a medium length of hair the dreads are circa 1/3 shorter than the hair. However type of hair and a technique of making dreads also affect their length.
That is why in my opinion if you want to have dreads it is better to make them short rather than wait for your hair to grow. Many people grow their hair to make dreads while actually it is better to make short dreads and wait for the dreads to grow.
Firstly, the hair will not get so short.
Secondly, you don’t need to wait for your hair to grow long to make dreads – and anyway after making dreads it will be shorter than the hair grown for long. If two people make dreads, one of short hair and one of long hair, after one year the dreads of the person with short hair will be longer.
Thirdly, dreads grow quicker than hair or at least you have the impression that they do as their growth is seen immediately and dreads do not scrub the way normal hair does.
Fourthly, after a dozen of months hair bulbs get used to a defined direction of growth and majority of hair starts to „dread” itself.