Twelve metres and 8% are terminating decimals, so the derived rise is exact under those assumptions. The corresponding angle uses arctangent.
Multiply run by decimal slope
8% = 8/100 = 0.08 exactly. Rise = 12 m × 0.08 = 0.96 m.
Convert the exact rise if needed
0.96 m is exactly 96 cm or 960 mm using defined metric factors.
The matching angle is approximate
θ = arctan(0.08) ≈ 4.573921°. The geometric conversion says nothing about whether 8% is permissible for a particular use.
Reverse the calculation as a check
Divide the 0.96 metre rise by the 12 metre horizontal run. The result is 0.08 exactly, and multiplying by 100 returns 8%. This confirms the linear arithmetic while leaving the angle explicitly approximate.