24  Calculating Scale and Offset
This article shows how to convert the data from a Mini/Micro input module into a more meaningful format, for example converting a voltage from a throttle or brake pedal into something more useful like a throttle pedal percentage 0100%.
It should be noted that this calculation only works for linear data where the plot of the data produces a straight line.
For those who don't like maths  please use our 'Scale and Offset Calculator'.
1: Obtain zero and full scale voltage values For example, say the throttle position sensor gives 0.5 volts on closed throttle, and 5 volts at full throttle. To convert this into a percentage, the equation of the straight line needs to be calculated. The equation describing a straight line is as follows: Y = mX + c Where; Y = The Y values (% pedal press) X = The X values (sensor voltage) m = scale (gradient of the line) c = offset (intercept with the Yaxis) 

2: Calculate the gradient of the line
The gradient of a line is the change in Y divided by the change in X which gives:
m (gradient) = dY/dX (change in Y) / (change in X)
dY = 100 – 0 = 100 change in Y = 100%  0% = 100
dX = 5 – 0.5 = 4.5 change in X = 5 volts – 0.5 volts = 4.5
Therefore the gradient of the line is:
dY/dX = 100 / 4.5
= 22.22 The Scale is 22.22
3: Calculate the offset
To find the offset value, substitute the known values at zero throttle, back into the equation:
Y = percent = 0, X = Voltage = 0.5 V
Y = mX + c Therefore
0 = (22.22 * 0.5) + c Zero throttle% = gradient x 0.5 volts + Offset
0 = 11.11 + c
C = 11.11 The Offset is 11.11
4: The full equation for the line
Substituting these values back into the equation again gives us the full equation of the line which passes through our two points.
Y = 22.22X – 11.11
5: Checking the equation
We can double check our equation is correct by calculating a percentage value for a known voltage output.
We know that:
Voltage (x)  Percent Pedal Press (y) 

0.5  0 
5  100 
Using the equation we have just derived produces the following results:
Y = 22.22X – 11.11
Y = (22.22 * 0.5) – 11.11 = 0% This is correct, as 0.5 volts is equal to a 0% pedal press.
Y = (22.22 * 5.0) – 11.11 = 99.99% This is also correct as we know that 5 volts = 100% pedal press.
6: Plotting the full line
The graph below illustrates the calculated scale and offset values.