Introduction
This interpolation calculator finds a missing value on a straight line between two known points. You give it five out of six values (the X and Y for Point 1, Point 2, and Point 3) and it solves for the one you left blank. It works for both linear interpolation (when your point falls between the two known points) and extrapolation (when it falls outside them).
The calculator shows you the answer, a full step-by-step solution, the slope and equation of the line, and a graph of all three points. Just type your numbers into the table, leave one field empty, and press Calculate.
How to Use Our Interpolation Calculator
Enter five known values across three coordinate points and leave one field blank. The calculator will solve for the missing value, show the line equation, and display a step-by-step solution with a graph.
X₁ (Point 1, X value): Type the x-coordinate of your first known point. Leave blank if this is the value you want to find.
Y₁ (Point 1, Y value): Type the y-coordinate of your first known point. Leave blank if this is the value you want to find.
X₂ (Point 2, X value): Type the x-coordinate of your second known point. Leave blank if this is the value you want to find.
Y₂ (Point 2, Y value): Type the y-coordinate of your second known point. Leave blank if this is the value you want to find.
X₃ (Point 3, X value): Type the x-coordinate of your third point. Leave blank if this is the value you want to find.
Y₃ (Point 3, Y value): Type the y-coordinate of your third point. Leave blank if this is the value you want to find.
Calculate Button: Press this button after you fill in five fields. The calculator will find the missing value, show the slope and y-intercept, display the full line equation, and draw a graph of all three points.
Reset Button: Press this button to clear all fields and start over with new values.
What Is Linear Interpolation?
Linear interpolation is a way to find a missing value between two known points on a straight line. Think of it like this: if you know two points on a graph, you can draw a line through them. Any point along that line can be figured out using simple math. The word "interpolation" means finding a value between two known values. If the missing value falls outside the two known points, it is called extrapolation instead.
How Linear Interpolation Works
A straight line connects two points: Point 1 and Point 2. Each point has an X value and a Y value. When you know both points, the line between them is fixed. You can then pick any X value and find its matching Y value on that line, or pick a Y value and find its matching X. The math behind it uses the fact that the slope (steepness) of the line stays the same everywhere. The slope is calculated as the change in Y divided by the change in X.
The Interpolation Formula
The standard linear interpolation formula is:
Y₃ = Y₁ + (X₃ − X₁) × (Y₂ − Y₁) / (X₂ − X₁)
This formula takes the two known points, (X₁, Y₁) and (X₂, Y₂), and uses them to find the Y value at a third X position. You can also rearrange this formula to solve for any of the six values (X₁, Y₁, X₂, Y₂, X₃, or Y₃) as long as the other five are known. At its core, this formula relies on computing a rate of change between the two reference points and applying it to the third.
When Is Interpolation Used?
Linear interpolation is used in many fields. Engineers use it to estimate values from data tables. Scientists use it to fill in gaps between measurements. It is also common in computer graphics, finance, and everyday math. Any time you have two data points and need to estimate a value between them, linear interpolation is a fast and reliable method. For larger datasets where you want to fit a best-fit line through many points instead of just two, a linear regression is the better choice.
Interpolation vs. Extrapolation
When the third point falls between Point 1 and Point 2, the result is an interpolation. When it falls outside that range, the result is an extrapolation. Interpolation is generally more accurate because you are staying within your known data. Extrapolation assumes the same straight-line trend continues beyond your data, which may not always be true.