# How to Convert Units from one System To Another

Posted in Dimensional Formulae | Email This Post |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**

n_{1} – Numerical Value in system 1

n_{2} -Numerical Value in system 2

u_{1} – Unit of Measurement in system 1

u_{2} – Unit of Measurement in system 2

M_{1} – Fundamental Unit of mass in system 1

M_{2}– Fundamental Unit of mass in system 2

L_{1}– Fundamental Unit of length in system 1

L_{2}– Fundamental Unit of length in system 2

T_{1}– Fundamental Unit of Time in system 1

T_{2}– Fundamental Unit of Time in system 2

a = Dimensions of Mass

b = Dimensions of Length

c = Dimensions of Time

**Formula to convert is**

n_{2}= n_{1}u_{1}/ u_{2}** = **n_{1}[M_{1}/M_{2}]^{a}[L_{1}/L_{2}]^{b}[T_{1}/T_{2}]^{c}

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

We know the dimensional formula of Force F = [M^{1} L^{1} T^{-2}]

So a =1, b=1, c=-2

Now because Newton is in m.k.s system, we have

M_{1} = 1kg

L_{1} = 1m

T_{1} = 1s

M_{2} = 1g

L_{2} = 1cm

T_{2} = 1s

n_{1}= 1 Newton

n_{2} = we have to find

Using the formula

n_{2}= n_{1}[M_{1}/M_{2}]^{a}[L_{1}/L_{2}]^{b}[T_{1}/T_{2}]^{c}

n_{2}=1 [1kg/1g]^{1}[1m/1cm]^{1}[1s/1s]^{-2}

n_{2}=1[1000g/1g]^{1}[100cm/1cm]^{1}x1

n_{2}=1000*100 = 100000 = 10^{5}

Hence **1 Newton = 10 ^{5}dyne**

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