# Linear Interpolation

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Linear interpolation is incredibly useful to engineers, as it allows us to calculate points on a curve. This calculation is typically conducted when an engineer is using a table which informs them of the yield stress with respect to temperature - as yield stress drops as temperature rises. Lets take a look at SA-105 from ASME Section II Part D which gives the data below:

 Temperature (deg C) Yield Stress (MPa) -30 to 200 138 <250 136 <300 129 <325 125 <350 122 <375 117 <400 101 <425 83.9 <450 67 <475 51.1 <500 33.6 <525 21.3 <550 12.9

Below this data is visualised, now say for example I want to find the yield stress at 360 degrees C - which is represented by the vertical line. X1 (350), Y1 (122), X3 (375) and Y3 (117) are points which we already know from the table above and are clearly defined. X2 is the temperature we are operating at (360), so we would like to know Y2. Using the Equation below - we can calculate yield stress as 120MPa Linear Interpolation Calculator:

 X1 Y1 X2 Y2 X3 Y3