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