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Linear Interpolation Calculator
Last updated: May 31, 2026
Written by Blake Boege
A linear interpolation calculator is a mathematical curve-fitting tool that estimates the value of a dependent variable y corresponding to an independent variable x lying between two coordinates (x1, y1) and (x2, y2). It assumes a constant rate of change (linear slope) between the boundary coordinates to calculate intermediate coordinates. It is widely used in scientific analysis, engineering, and tabular data lookup.
Estimate intermediate values between two coordinate points using the linear interpolation formula.
Quick Answer
Estimate intermediate y values for a given x between two coordinate points. Shows step-by-step linear calculations.
First Point (x1, y1)
e.g. 0
e.g. 0
Second Point (x2, y2)
e.g. 10
e.g. 50
Target Interpolation Point
The x coordinate for which you want to solve y. · e.g. 4
Interpolated y Value
20
Interpolation projects coordinates between the points, whereas extrapolation projects outside of the interval [x1, x2].
Examples
Point 1: (0, 0), Point 2: (10, 50), target x = 4
y = 0 + (4 − 0) × (50 − 0) ÷ (10 − 0) = 4 × 5 = 20
Point 1: (1, 10), Point 2: (5, 30), target x = 3
y = 10 + (3 − 1) × (30 − 10) ÷ (5 − 1) = 10 + 2 × 5 = 20
How it works
The calculator finds the slope of the line connecting Point 1 and Point 2, and then evaluates the linear equation at the target value of x.
Formula · y = y1 + (x − x1) × (y2 − y1) / (x2 − x1)
How to perform linear interpolation
Linear interpolation solves for an unknown value y between two known coordinates (x1, y1) and (x2, y2). The formula calculates the slope of the line and projects the height at the target x:
This can be rearranged to say that the slope between (x1, y1) and (x, y) is equal to the slope between (x1, y1) and (x2, y2):
Related math calculators
For other slope and rate calculations, check out:
- Interpolation Calculator — perform polynomial, cubic, or linear interpolations on datasets.
- Slope Calculator — find the rate of change or rise over run between coordinate pairs.
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Frequently asked questions
Linear interpolation is a method of curve fitting using linear polynomials to find new data points within the range of a discrete set of known data points.
The formula is: y = y1 + ((x − x1) × (y2 − y1)) ÷ (x2 − x1). It assumes the rate of change (slope) between the two points is constant.
Interpolation is finding values *inside* the range of your existing data points (x is between x1 and x2). Extrapolation is estimating values *outside* that range (x is smaller than x1 or larger than x2).
If x1 = x2, the denominator of the formula (x2 − x1) becomes 0, which results in a division by zero error. The two points must have different x-coordinates to define a line.
It is only an approximation. It assumes a straight-line relationship between the points. If the real relationship is non-linear (like exponential or quadratic), linear interpolation will introduce errors.
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