# Linear Interpolation Equation Calculator

Engineering - Interpolator Formula

To interpolate the y2 value:
x1, x3, y1 and y3 need to be entered/copied from the table.
x2 defines the point to perform the interpolation.
y2 is the interpolated value and solution.
 x1 y1 x2 y2 x3 y3

## Solving for y2 x1
unitless
x2
unitless
x3
unitless
y1
unitless
y3
unitless

## Solution:

y2
= NOT CALCULATED

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## What is linear interpolation?

Linear interpolation is a mathematical technique used to estimate an unknown value between two known data points on a straight line, assuming a constant rate of change between the points and that the function connecting them is linear.
Curve fitting, on the other hand, is a broader process of constructing a curve, or mathematical function, that best fits a series of data points. For example, linear interpolation can be considered a simple form of curve fitting where the curve is a straight line.

## Why it is essential?

Linear interpolation and curve fitting are essential because they provide efficient ways to estimate values within a data set when exact data is unavailable, analyze data trends, and create graphical representations of data. These techniques are critical for approximation, data analysis, and visualization.

## Linear interpolation equation

The linear interpolation equation is given by:
y = y1 + (x - x1) * ((y2 - y1) / (x2 - x1))
where (x1, y1) and (x2, y2) are the known data points, x is the unknown point's x-value, and y is the unknown point's y-value.

## How to solve:

To solve for y using linear interpolation, follow these steps:
• Identify the two known data points, (x1, y1) and (x2, y2), surrounding the x-value for which you want to estimate the y-value.
• Substitute the known values into the linear interpolation equation.
• Solve for y.

## Common mistakes:

• Extrapolating beyond the known data points can lead to inaccurate estimates.
• Using linear interpolation for non-linear data sets results in poor approximations.
• Not verifying the assumptions of a constant rate of change and linearity.
• Relying only on interpolation when more accurate methods or data are available.
• Misinterpreting the results, such as assuming the interpolated value equals the exact value.
• Sensitivity to outliers and extreme values in the data set.

## Areas of use:

• Computer graphics and image processing
• Finance (e.g., interest rate calculations)
• Engineering (e.g., temperature and pressure estimations)
• Geographical Information Systems (GIS) and mapping
• Medical imaging
• Video game development
• Weather forecasting
• Audio signal processing
• Data science and analytics

## Other types of interpolation:

• Polynomial interpolation
• Spline interpolation (e.g., cubic and B-spline)
• Hermite interpolation
• Rational interpolation
• Nearest-neighbor interpolation

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By Jimmy Raymond Contact: aj@ajdesigner.com