Linear Interpolation Calculator

- April 15, 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

First point x₁:

First point y₁:

Second point x₂:

Second point y₂:

Interpolation point x:

Display Options

Decimal Places:

Show calculation steps

Show graph visualization

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.

What Is the Linear Interpolation Calculator?

The Linear Interpolation Calculator helps you estimate values that fall between two known data points on a straight line. It’s based on the assumption that the change between the two points is linear, making it ideal for quick approximations when you know the start and end values of a trend.

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

Slope-Intercept Form (Alternative):
y = mx + b, where m = (y₂ - y₁) / (x₂ - x₁)

Why Use This Calculator?

This tool is useful when you want to:

Estimate a missing value between two measured points
Visualize the relationship between the data on a graph
Understand the line equation that connects two known coordinates
Get a step-by-step explanation of the calculations

You might find this especially handy in fields like engineering, data analysis, or even when working with scientific calculators or math solver tools. It's a quick and easy way to derive values without needing complex computations.

How to Use the Calculator

Using the calculator is simple and straightforward:

Enter the coordinates of the first point (x₁, y₁)
Enter the coordinates of the second point (x₂, y₂)
Input the x-value you want to interpolate at
Choose how many decimal places you want to see
Select if you'd like to view the graph or step-by-step solution
Click "Calculate" to see the interpolated result

The output includes:

The interpolated y-value
The slope of the line connecting the two points
The linear equation of the line
An optional graph showing the points and the interpolation
A detailed breakdown of each calculation step

When Can This Be Helpful?

This calculator is great for:

Estimating unknown data between measurements
Learning how interpolation works with visual and detailed steps
Students working with line equation solvers or slope intercept form calculators
Professionals needing quick estimates between two known values
Educators demonstrating the basics of linear equations

Frequently Asked Questions (FAQ)

Can I use this for values outside the range of x₁ and x₂?

You can, but it becomes extrapolation, which may lead to less accurate results. For values outside the known points, consider tools like a quadratic formula calculator or higher-order interpolation methods.

What happens if x₁ equals x₂?

The calculator will alert you. This creates a division by zero, which is mathematically undefined. You'll need two distinct x-values to perform interpolation.

How is this different from a percent error calculator?

While a percent error calculator helps you compare actual vs. expected values using the percent error formula, the Linear Interpolation Calculator helps you estimate a missing value between two points. They both support math learning, but serve different purposes.

Is this similar to using a matrix calculator or scientific calculator?

This calculator is more focused. It specifically handles straight-line estimates between two known points. Matrix calculators and scientific calculators deal with a wider range of operations, such as matrix transformations or complex equations.

Does it show how the answer is calculated?

Yes. If you enable "Show calculation steps," the tool walks you through the entire process — including how the slope and line equation are formed — making it an excellent math learning companion.

Conclusion

Whether you're estimating sensor data, forecasting simple trends, or learning about straight-line math, this Linear Interpolation Calculator offers a quick, accurate, and visually clear way to get the job done. It’s a useful addition alongside tools like the percent calculator, exponent solver, or rounding calculator when precision matters.