Linear Interpolation Calculator

- May 11, 2025
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Calculate a value at any point along a line between two known points. Linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.

Formula: y = y₁ + (x - x₁) × (y₂ - y₁) / (x₂ - x₁)

Input Values

Display Options

About Linear Interpolation

Linear interpolation is one of the simplest methods of interpolation, involving the construction of new data points within the range of a discrete set of known data points. It assumes a linear relationship between adjacent points and calculates intermediate values along a straight line between them.

Applications of Linear Interpolation
  • Computer Graphics: Generating intermediate frames in animations
  • Mathematics: Approximating functions at points not directly computed
  • Engineering: Estimating values between measured data points
  • Data Analysis: Filling in missing values in datasets
  • Financial Analysis: Estimating values between known market data points
Limitations of Linear Interpolation

While linear interpolation is computationally simple and easy to implement, it has some limitations:

  • Assumes a linear relationship, which may not represent the actual relationship between data points
  • May provide poor approximations for highly curved functions
  • Not suitable for extrapolation (predicting values outside the range of known data points)

For more accurate interpolation of curved functions, consider higher-order methods such as cubic spline interpolation or polynomial interpolation.

Understanding the Linear Interpolation Calculator

The Linear Interpolation Calculator is a handy tool that helps you find a value along a line between two known points. This method is useful when you want to estimate values that fall within a range of known data points. With this calculator, you can quickly compute interpolated values without needing advanced maths skills.

How Linear Interpolation Works

Linear interpolation uses a simple formula to calculate new data points. The formula is: y = y₁ + (x - x₁) × (y₂ - y₁) / (x₂ - x₁). In this formula:

  • x₁, y₁: The first known point.
  • x₂, y₂: The second known point.
  • x: The point where you want to interpolate.
  • y: The interpolated value at x.

Input Values for Accurate Results

To use the Linear Interpolation Calculator, you need to input values for the two known points and the interpolation point. You'll enter the coordinates for both points, as well as the x-value you want to estimate. This ensures that the calculator can provide accurate results based on your data.

Display Options to Tailor Your Output

This calculator offers various display options to make your results clearer. You can choose how many decimal places to show, from none to six. Additionally, there are options to display calculation steps and a graph visualisation. These features help you understand the interpolation process better.

Why Use Linear Interpolation?

Linear interpolation is popular for several reasons. It’s straightforward and doesn’t require complex calculations. It’s also widely used in various fields like:

  • Engineering: Estimating values based on measured data.
  • Data Analysis: Filling in missing values in datasets.
  • Computer Graphics: Creating smooth animations by generating intermediate frames.

Limitations of Linear Interpolation

While linear interpolation is useful, it has its limitations. It assumes a straight-line relationship between points, which may not always be true. For highly curved functions, linear interpolation might not provide accurate estimates and is not suitable for predicting values outside the known data range.

Practical Applications of This Calculator

The Linear Interpolation Calculator finds applications in many real-world scenarios. It helps in:

  • Mathematics: Approximating functions at points not directly calculated.
  • Financial Analysis: Estimating values between known market data points.
  • Science: Predicting results in experiments based on limited data.

Conclusion: Your Go-To Tool for Estimations

This calculator is an invaluable resource for anyone needing quick estimations between two known data points. Whether you’re a student, engineer, or data analyst, the Linear Interpolation Calculator simplifies the process and provides accurate results in an easy-to-understand format.