How to Convert Units from one System To Another

For using this formula we need to first keep in mind that this formula is used only when the quantities are expressed in absolute units. i.e. in terms of Mass Length and Time.

Terms used in this formula
n₁ – Numerical Value in system 1
n₂ -Numerical Value in system 2
u₁ – Unit of Measurement in system 1
u₂ – Unit of Measurement in system 2
M₁ – Fundamental Unit of mass in system 1
M₂– Fundamental Unit of mass in system 2
L₁– Fundamental Unit of length in system 1
L₂– Fundamental Unit of length in system 2
T₁– Fundamental Unit of Time in system 1
T₂– Fundamental Unit of Time in system 2
a = Dimensions of Mass
b = Dimensions of Length
c = Dimensions of Time

Formula to convert is
n₂= n₁u₁/ u₂ = n₁[M₁/M₂]^a[L₁/L₂]^b[T₁/T₂]^c

Example showing how this formula works
How to convert 1 Newton to Dyne

We know the dimensional formula of Force F = [M¹ L¹ T^-2]

So a =1, b=1, c=-2
Now because Newton is in m.k.s system, we have
M₁ = 1kg
L₁ = 1m
T₁ = 1s

M₂ = 1g
L₂ = 1cm
T₂ = 1s

n₁= 1 Newton
n₂ = we have to find

Using the formula
n₂= n₁[M₁/M₂]^a[L₁/L₂]^b[T₁/T₂]^c

n₂=1 [1kg/1g]¹[1m/1cm]¹[1s/1s]^-2

n₂=1[1000g/1g]¹[100cm/1cm]¹x1
n₂=1000*100 = 100000 = 10⁵

Hence 1 Newton = 10⁵dyne