Why was radians and gradians invented?

Gradians were most likely invented because right angles are 100 gradians which is easy to calculate and angles can be easily split in 2.

Circle Proportions:

1 = 400ᵍ

1/2 = 200ᵍ

1/4 = 100ᵍ

1/8 = 50ᵍ

1/16 = 25ᵍ….