Linear Interpolation Worksheet with Example

This worksheet help you to understand how to calculate Linear Interpolation. The unknown value which lies between the two known rates/ points can be calculated by linear interpolation.

The below formula is used to
(y-y₀)/(x-x₀)=(y₁-y₀)/(x₁-x₀)
Lets consider (x₁,y₁), (x₃, y₃) are two points to find the value of the point x₂ or y₂

Linear Interpolation Formulas to find unknown:
To find y₂,
y₂=(x₂-x₁)*(y₃-y₁)/(x₃-x₁)+y₁
To find x₂,
x₂=(y₂-y₁)*(x₃-x₁)/(y₃-y₁)+x₁

To findout the value of X₂ we must know the value of y₂; to find y₂ we must know the value of x₂

Linear Interpolation Example:
x1 =1 x2 =2 x3 = 3
y1 = 4 y2 = ? y3 = 6
The formula to find y2 is,
y2=(x2-x1)*(y3-y1)/(x3-x1)+y1
y2=(2 - 1)*(6 - 4)/(3 - 1) + 4
y2 = 2/2 + 4
y2 = 5

Hence the unknown point Value is 5

When you try such calculations on your own, this linear interpolation calculator can be used to verify your results.