Linear Interpolation Explained: Estimate Values Between Data Points
ByMuhammad Ali•Founder of KruskalCode
14:37
5 min read
Ever needed to fill in a gap in your data? Linear interpolation is a simple yet powerful mathematical technique used to estimate an unknown value that falls between two known data points. It's like drawing a straight line between two points and finding where another point would sit on that line.
Explanation
Linear interpolation works by assuming a linear relationship between two consecutive data points. If you have two points (X1, Y1) and (X2, Y2), and you want to find the Y-value (Y) corresponding to a new X-value (X) that lies between X1 and X2, you can use the formula. This method is widely used in various fields, from engineering and computer graphics to finance and statistics, for estimating missing data or smoothing curves.
Formula
The core of linear interpolation is this formula: Y = Y1 + ( (X - X1) * (Y2 - Y1) / (X2 - X1) ) Where: - X1, Y1: Coordinates of the first known data point. - X2, Y2: Coordinates of the second known data point. - X: The x-coordinate for which you want to find the interpolated Y value. - Y: The estimated y-coordinate.
Example
Let's say you're tracking the growth of a plant. On day 5 (X1), it was 10 cm tall (Y1). On day 10 (X2), it was 15 cm tall (Y2). You want to estimate its height on day 7 (X). Using the formula: Y = 10 + ((7 - 5) * (15 - 10) / (10 - 5)) = 10 + (2 * 5 / 5) = 10 + 2 = 12 cm. So, on day 7, the plant was estimated to be 12 cm tall.
How to use the related calculator
Using our Linear Interpolation Calculator is straightforward. Simply enter the coordinates of your two known data points: 'First X Value (X1)', 'First Y Value (Y1)', 'Second X Value (X2)', and 'Second Y Value (Y2)'. Then, input the 'X Value to Interpolate (X)' for which you want to find the corresponding Y. The calculator will instantly provide the interpolated Y value.
Try the related calculator
Open toolFAQ
What is linear interpolation?
Linear interpolation is a method of estimating a value that lies between two known data points. It assumes a straight-line relationship between these points to find the intermediate value.
When should I use linear interpolation?
You should use linear interpolation when you have a set of data points and need to estimate a value for an x-coordinate that falls within the range of your known x-coordinates. It's useful for filling in missing data, smoothing curves, or making predictions where a linear trend is reasonable.
Can I use this calculator for extrapolation?
While the formula can technically calculate values outside the range of X1 and X2 (extrapolation), linear interpolation is generally less reliable for extrapolation. The further you go beyond your known data points, the less likely the linear assumption holds true, and your estimates may become inaccurate.
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About the author
Muhammad Ali. Muhammad Ali is a full-stack developer and founder of KruskalCode. He builds SaaS platforms and automation systems with React and Laravel, and helps teams ship fast, scalable tools.
Need a custom calculator, dashboard, or automation workflow? Reach out to KruskalCode.
