# Derivation of standard 4-20 mA equation and 4-20 mA formula

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## Derivation of standard 4-20 mA equation and 4-20 mA formula

4-20 mA scale is linear with 0-100 scale. So can use linear function on this 4-20 mA. As shown in figure

As you can use slope intercept form on this linear function
Y=mx+b    ………………(1)
You can consider
Y= transmitter current signal output
B= y-intercept point (zero point live in instrument range )
X= percentage of process variable
We can predict any value of current signal just by finding the slope (m)  and y-intercept point  as shown in figure

M= rise/run
=20-4/100-0= 16/100
Putting this value in slope intercept equation
Y=(16/100)x+b
Now we have to find slope-intercept point (b) . For this we will select any coordinates x,y
In this calculation we are using x=0 and y=4
Now the equation is
4= (16/100)*0+b
b=4
Now the final formula for converting percentage in to mA is
Y=(16/100)X+ 4
For any given percentage we can find the current equivalent mA.
For example one control valve is 65 % open what will be equivalent current signal?
Y=(16/100)X+ 4
Y = (16/100) 65+4
=14.4 mA
Output current will be 14.4 if the control valve is 65 % open.
We use this linear equation for value of Y when x is given and vice versa. We can calculate the value of current signal mA of any process transmitter i.e pressure, temperature, flow and control valve.