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Math Calculators > Bilinear Interpolation

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Bilinear Interpolation Formula

Although it is good practise when dealing with tables to choose a conservative lookup value if the exact value under consideration is not present, sometimes a more precise answer is required. The Lagrange's interpolation formula is one such method commonly adopted to get equivalent values from a table. The Bilinear interpolation formula shown works by using a ratio to find an intermediate number between four existing values in an existing table. As always care should be taken with the type of data used as not all tables display values which act with a linear progression.

StructX Calculator
Calculator Input Output
X1
X
X2
Y1
Y
Y2
Q11
Q21
Q12
Q22
Interpolation Calculator
Result, P:

Notation and Units

Bilinear Interpolation

Linear and Bilinear interpolation can be used to find values that are in between those shown in a lookup table. Because of the assumed straight line used to determine such values, care should be taken when determining if linear interpolation is a suitable and allowable method of approximation.

Notation

  • X1,X2,Y1,Y2 = First Coordinates
  • Q11,Q12,Q21,Q22 = Values to be interpolated between
  • X & Y = Defines point to perform the interpolation
  • P = The interpolated value and solution