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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 0-100%.

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 Y-axis)

**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.

**8: Plotting the full line**

The graph below illustrates the calculated scale and offset values.

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